More re zombie claims.

Also: Egnor , a neurosurgeon, told Skrobot: “My wife jokes with me that meeting me is always the worst part of a person’s life.”

Wednesday, January 19, 2022

Serving The Intelligent Design Community

More re zombie claims.

Also: Egnor , a neurosurgeon, told Skrobot: “My wife jokes with me that meeting me is always the worst part of a person’s life.”

As to,

I have to disagree with Dr. Egnor with his claim that “consciousness is something outside the purview of physical science.”. While the mental attribute of qualia itself may forever be outside the ‘outside the purview of physical science’ ,,, (i.e. Mary’s room)

,,, While the mental attribute of qualia itself may forever be outside the ‘outside the purview of physical science’ ,,, (i.e. Mary’s room), there are other defining attributes of consciousness that do lend themselves to scientific examination.

In short, Qualia is not the only attribute of mind that distinguishes it from the material brain. As Dr. Egnor himself pointed out, besides qualia, the immaterial mind can also be distinguished from the material brain by the mental attributes of, “Intentionality,,, Persistence of Self-Identity,,, Restricted Access,,, Incorrigibility,,, Free Will,,,”

You can read more in-depth definitions of each of the six properties of immaterial mind in Dr. Egnor’s article.

Likewise, J. Warner Wallace has a very similar list, (but not an exact match to Dr. Egnor’s list), of six properties of immaterial mind that are irreconcilable with reductive materialism.

And while, as Dr. Egnor pointed out, qualia is forever beyond ‘the purview of physical science’, other mental attributes do lend themselves to examination by physical science. Specifically, ‘Persistence of Self-Identity through time’ (which may also be termed ‘the experience of ‘the Now”), and ‘free will’, although both being irreconcilable with reductive materialism, nonetheless, both of those defining attributes of immaterial mind that Dr. Egnor listed, unlike qualia, do make their presence known to us in recent experimental evidence from quantum mechanics.

As to defining the specific mental attribute of the ‘Persistence of Self-Identity through time’ (and/or ‘the experience of ‘the Now”) in particular, it is first important to note that we each have a unique perspective of being outside of time. In fact we each seemingly watch from some mysterious outside perspective of time as time seemingly passes us by. Simply put, we seem to be standing on an island of ‘now’ as the river of time continually flows past us.

In the following video, Dr. Suarez states that the irresolvable dilemma for reductive materialists as such, “it is impossible for us to be ‘persons’ experiencing ‘now’ if we are nothing but particles flowing in space time. Moreover, for us to refer to ourselves as ‘persons’, we cannot refer to space-time as the ultimate substratum upon which everything exists, but must refer to a Person who is not bound by space time. (In other words) We must refer to God!”

In further defining the mental attribute of ‘the experience of the now’, in the following article Stanley Jaki states that “There can be no active mind without its sensing its existence in the moment called now.,,, ,,,There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future. The mind remains identical with itself while it lives through its momentary nows.”

And ‘the experience of ‘the now” also happens to be exactly where Albert Einstein got into trouble with leading philosophers of his day and also happens to be exactly where Einstein, eventually, got into trouble with quantum mechanics itself.

Around 1935, Einstein was asked by Rudolf Carnap (who was a philosopher):

Einstein’s denied that it was possible, and stated:

Prior to that encounter with Carnap, Einstein also had another disagreement with another famous philosopher, Henri Bergson, over what the proper definition of time should be (Bergson was also very well versed in the specific mental attribute of the ‘experience of the now’). In fact, that disagreement with Henri Bergson over what the proper definition of time should be was actually one of the primary reasons that Einstein failed to ever receive a Nobel prize for his work on relativity:

The specific statement that Einstein made to Carnap on the train, “The experience of ‘the now’ cannot be turned into an object of physical measurement, it can never be a part of physics.” was a very interesting statement for Einstein to make to the philosopher since “The experience of ‘the now’ has, from many recent experiments in quantum mechanics, established itself as very much being a defining part of our physical measurements in quantum mechanics.

For instance, the following delayed choice experiment with atoms demonstrated that, “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,”

Likewise, the following violation of Leggett’s inequality stressed the quantum-mechanical assertion that reality does not exist when we’re not observing it.

The Mind First and/or Theistic implications of quantum experiments such as the preceding are fairly obvious. As Professor Scott Aaronson of MIT once quipped, “Look, we all have fun ridiculing the creationists,,, But if we accept the usual picture of quantum mechanics, then in a certain sense the situation is far worse: the world (as you experience it) might as well not have existed 10^-43 seconds ago!”

Thus, contrary to what Einstein himself thought was possible for experimental physics, physicists have now shown, in overwhelming fashion, that ‘the experience of the now’ is very much a part of experimental physics. In fact, due to advances in quantum mechanics, it would now be much more appropriate to rephrase Einstein’s answer to the philosopher Rudolph Carnap in this way:

The ‘experience of the now’ also makes itself known in experimental science through what is termed the quantum zeno effect.

An old entry in wikipedia described the Quantum Zeno effect as such “an unstable particle, if observed continuously, will never decay.”

Likewise, the present day entry on wikipedia about the Quantum Zeno effect also provocatively states that “a system can’t change while you are watching it”

Atheistic materialists have tried to get around the Quantum Zeno effect by postulating that interactions with the environment are sufficient to explain the Quantum Zeno effect.

Yet, the following interaction-free measurement of the Quantum Zeno effect demonstrated that the presence of the Quantum Zeno effect can be detected without interacting with a single atom.

In short, the quantum zeno effect, regardless of how atheistic materialists may feel about it, is experimentally shown to be a real effect that is not reducible to any materialistic explanation. And thus the original wikipedia statement of, “an unstable particle, if observed continuously, will never decay”, stands, as far as the science itself is concerned, as being a true statement to make.

Moreover, on top of the quantum zeno effect, the mental attribute of ‘the experience of the now’ is also now verified by recent experiments in quantum mechanics that have now shown that “entropy is always dependent on the observer.”

As the following article states, the deletion of data, under certain conditions, can create a cooling effect instead of generating heat. The cooling effect appears when the strange quantum phenomenon of entanglement is invoked.,,, In the new paper, the researchers,,, show that when the bits to be deleted are quantum-mechanically entangled with the state of an observer, then the observer could even withdraw heat from the system while deleting the bits. Entanglement links the observer’s state to that of the computer in such a way that they know more about the memory than is possible in classical physics.,,,

In measuring entropy, one should bear in mind that an object does not have a certain amount of entropy per se, instead an object’s entropy is always dependent on the observer. Applied to the example of deleting data, this means that if two individuals delete data in a memory and one has more knowledge of this data, she perceives the memory to have lower entropy and can then delete the memory using less energy.,,,

And as the following 2017 article states: James Clerk Maxwell (said), “The idea of dissipation of energy depends on the extent of our knowledge.”,,,

quantum information theory,,, describes the spread of information through quantum systems.,,,

Fifteen years ago, “we thought of entropy as a property of a thermodynamic system,” he said. “Now in (quantum) information theory, we wouldn’t say entropy is a property of a system, but a property of an observer who describes a system.”,,,

The reason why I am very impressed with the preceding experiments demonstrating that the mental attribute of ‘the experience of the now’ is very much a part of entropy, is that the second law of thermodynamics, entropy, is very foundational to any definition of time that we may have.

As the following article states, “Entropy explains time; it explains every possible action in the universe;,,”,, “Even gravity,,,, can be expressed as a consequence of the law of entropy.,,,”

On top of the fact that “(Entropy) explains time; it explains every possible action in the universe”, Entropy is also, by a wide margin, the most finely tuned of the initial conditions of the Big Bang. Finely tuned to an almost incomprehensible degree of precision, 1 part in 10 to the 10 to the 123rd power. As Roger Penrose himself stated that, “This now tells us how precise the Creator’s aim must have been: namely to an accuracy of one part in 10^10^123.”

In the following video, Dr, Bruce Gordon touches upon just how enormous that number truly is. Dr. Gordon states, “you would need a hundred million, trillion, trillion, trillion, universes our size, with a zero on every proton and neutron in all of those universes just to write out this number. That is how fine tuned the initial entropy of our universe is.”

In fact, entropy is also the primary reason why our own material, temporal, bodies grow old and eventually die in this universe,,,

And yet, to repeat the last sentence from the quantum information paper, “we wouldn’t say entropy is a property of a system, but a property of an observer who describes a system.”

That statement is just fascinating! Why in blue blazes should the finely tuned entropic actions of the universe, entropic actions which also happen to explain time itself, even care if I am consciously observing them, and/or describing them, unless ‘the experience of ‘the now’ really is more foundational to reality than the finely tuned 1 in 10^10^123 entropy of the universe is? To state the obvious, this finding of entropy being “a property of an observer who describes a system.” is very friendly to a Mind First, and/or to a Theistic view of reality.

For instance Romans chapter 8: verses 20 and 21 itself states, “For the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope that the creation itself will be liberated from its bondage to decay and brought into the glorious freedom of the children of God.”

Besides the Quantum Zeno effect, Quantum information theory and the experimental realization of Maxwell’s demon thought experiment all confirming that the mental attribute of ‘the experience of the now’ is very much a part of present day quantum physics, Quantum Mechanics also now shows that Stanley Jaki’s contention that “There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future” is confirmed by recent experimental breakthroughs in quantum mechanics.

As to the ability of the mind to extend from its experience of the now to past moments in time, in recent experiments in quantum mechanics, it is now found that “quantum mechanics can even mimic an influence of future actions on past events”

And as the following 2017 article states, “a decision made in the present can influence something in the past.”

And to drive this point further home, in the following 2018 article Professor Crull provocatively states “entanglement can occur across two quantum systems that never coexisted,,, it implies that the measurements carried out by your eye upon starlight falling through your telescope this winter somehow dictated the polarity of photons more than 9 billion years old.”

It is also very interesting to point out that these experiments demonstrating ‘quantum entanglement in time’ are very friendly to Dr. Michael Egnor’s (Theistic) contention (via Aristotle) that “Perception at a distance is no more inconceivable than action at a distance.”

And it is also interesting to note that this finding or ‘quantum entanglement in time’ also refutes Dr Vincent Torley’s strenuous objection against Dr Egnor. Dr. Torley strenuously objected that perception cannot possibly occur ‘at a distance’ since a Supernova that we might be observing “ceased to exist nearly 200 millennia ago, long before the dawn of human history.”

Yet, despite Dr. Torley’s strenuous (materialistic) objection against Dr. Egnor’s claim that “Perception at a distance is no more inconceivable than action at a distance.” and to repeat Professor Crull’s provocative statement, the findings of quantum entanglement in time “implies that the measurements carried out by your eye upon starlight falling through your telescope this winter somehow dictated the polarity of photons more than 9 billion years old.”

In short, quantum mechanics itself could care less about Dr. Torley’s materialistic presuppositions.

In further confirmation of Stanley Jaki’s contention that, “There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future.”, in further confirmation of that contention, not only does “quantum mechanics show us that “a decision made in the present can influence something in the past.”, but quantum mechanics also shows us that our present conscious choices ultimately determine what type of future will be presented to us in our measurements of quantum systems.

As leading experimentalist Anton Zeilinger states in the following video, “what we perceive as reality now depends on our earlier decision what to measure. Which is a very, very, deep message about the nature of reality and our part in the whole universe. We are not just passive observers.”

As well, with contextuality we find that, “In the quantum world, the property that you discover through measurement is not the property that the system actually had prior to the measurement process. What you observe necessarily depends on how you carried out the observation”

Thus, Stanley Jaki’s contention that “There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future.”, is now experimentally established to be true by the fact that “a decision made in the present can influence something in the past.” and is also established by the fact that, “We are not just passive observers,,, what we perceive as reality now depends on our earlier decision what to measure”.

Thus, (contrary to what Einstein himself thought was possible for experimental physics), advances in quantum mechanics have now shown, in overwhelming fashion, that ‘the experience of the now’ is very much a part of experimental physics.

Likewise, as mentioned previously, the mental attribute of free will also makes its presence known by recent advances in quantum mechanics.

As Steven Weinberg, an atheist himself, states in the following article, In the instrumentalist approach (in quantum mechanics) humans are brought into the laws of nature at the most fundamental level.,,, the instrumentalist approach turns its back on a vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else.,,, In quantum mechanics these probabilities do not exist until people choose what to measure,,, Unlike the case of classical physics, a choice must be made,,,

In fact Weinberg, again an atheist, rejected the instrumentalist approach precisely because “humans are brought into the laws of nature at the most fundamental level” and because it undermined the Darwinian worldview from within. Yet, regardless of how he and other atheists may prefer the world to behave, quantum mechanics itself could care less how atheists prefer the world to behave.

For instance, this recent 2019 experimental confirmation of the “Wigner’s Friend” thought experiment established that “measurement results,, must be understood relative to the observer who performed the measurement”.

Moreover, although there have been several major loopholes in quantum mechanics over the past several decades that atheists have tried to appeal to in order to try to avoid the ‘spooky’ Theistic implications of quantum mechanics, over the past several years each of those major loopholes have each been closed one by one. The last major loophole that was left to be closed was the “setting independence” and/or the ‘free-will’ loophole:

And now Anton Zeilinger and company have recently, as of 2018, pushed the ‘free will loophole’ back to 7.8 billion years ago, thereby firmly establishing the ‘common sense’ fact that the free will choices of the experimenter in the quantum experiments are truly free and are not determined by any possible causal influences from the past for at least the last 7.8 billion years, and that the experimenters themselves are therefore shown to be truly free to choose whatever measurement settings in the experiments that he or she may so desire to choose so as to ‘logically’ probe whatever aspect of reality that he or she may be interested in probing.

Thus regardless of how Steven Weinberg and other atheists may prefer the universe to behave, with the closing of the last remaining free will loophole in quantum mechanics, “humans are indeed brought into the laws of nature at the most fundamental level”, and thus these recent findings from quantum mechanics directly undermine, as Weinberg himself stated, the “vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else.”

Moreover allowing free will and/or Agent causality into the laws of physics at their most fundamental level has some fairly profound implications for us personally.

First and foremost, allowing the Agent causality of God ‘back’ into physics, as the Christian founders of modern science originally envisioned,,,, (Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders),,, and as quantum mechanics itself now empirically demands (with the closing of the free will loophole by Anton Zeilinger and company), rightly allowing the Agent causality of God ‘back’ into physics provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead provides an empirically backed reconciliation, via the Shroud of Turin, between quantum mechanics and general relativity into the much sought after ‘Theory of Everything”. Here are a few posts where I lay out and defend some of the evidence for that claim:

To give us a small glimpse of the power that was involved in Christ’s resurrection from the dead, the following recent article found that, ”it would take 34 Thousand Billion Watts of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.”

Verse:

Thus in conclusion, and as Dr. Egnor pointed out, although the mental attribute of qualia is forever beyond ‘the purview of physical science”, we are not left completely in the dark as to seeing how the immaterial mind might relate to the physical world. Specifically, the mental attributes of the ‘experience of the now’ and of free will do lend themselves very much to scientific investigation and confirm, in over the top fashion, that, as Richard Conn Henry put the current situation in quantum mechanics, “The Universe is immaterial — mental and spiritual. Live, and enjoy.”

We really need an open thread around here so I can post fun things like this.

Apeirogons are generalized polygons whose sides are countably infinite.

https://en.m.wikipedia.org/wiki/Apeirogon

RP:

How do you know?

He spent a week in a hotel counting the sides.

It would have been a weekend but more guests kept on turning up, so RP had to change rooms repeatedly.

@Bob it seemed like I was changing rooms

forever.Next time you go there, you should check the rooms carefully. They might look rectangular, but they’re actually arranged around a circle.

Ok wait, if infinite rooms are filled with infinite guests, how do more guests show up? If they can just pop into existence then so can then the rooms to accommodate them can also pop into existence. You get the rooms from the same place Hilbert got the newly arriving guests, from his arse. No need for anyone to move.

ET: Ok wait, if infinite rooms are filled with infinite guests, how do more guests show up?There are infinitely many of them so the queue extends forever.

If they can just pop into existence then so can then the rooms to accommodate them can also pop into existence.They already exist, just like the positive integers. An infinitely long line of rooms and guests.

You get the rooms from the same place Hilbert got the newly arriving guests, from his arse. No need for anyone to move.Which room in the infinite hotel would you like then? Pick a positive integer, any positive integer. We will have that room and can make it available.

JVL:

Infinitely many? That isn’t a thing. But that is still a non-sequitur.

That isn’t what Hilbert said.

Hilbert said there was a hotel with infinite rooms, that were filled by infinite guests. Then another guest shows up, making it infinity + 1, which is incorrect.

The issue is there isn’t any queue. The guests would turn and enter the room they are next to

Andrew’s Infinite Public Service Announcement:

Conceptually, mixing infinite in with finite gives you absurdity.

Carry on.

Andrew

ET: Hilbert said there was a hotel with infinite rooms, that were filled by infinite guests. Then another guest shows up, making it infinity + 1, which is incorrect.What’s incorrect about it? It’s just a thought ‘experiment’. Infinity + 1 = infinity. Simple.

The issue is there isn’t any queue. The guests would turn and enter the room they are next toYup, that’s correct. I was just messin’ with you earlier.

Asauber: Conceptually, mixing infinite in with finite gives you absurdity.If you can’t do the math, stay out of the kitchen . . . or something.

“If you can’t do the math, stay out of the kitchen ”

says the man with no ‘mathematical kitchen’ to cook in,

JVL:

There isn’t any such thing as infinity + 1

“If you can’t do the math, stay out of the kitchen”

JVL,

This has nothing to do with math.

Andrew

Bornagain77: says the man with no ‘mathematical kitchen’ to cook in,Because I cannot conceive of mathematics working any differently than it does I do not believe mathematics depends on any kind of design. I may be wrong but I think math HAS to be the way it is.

ET: There isn’t any such thing as infinity + 1Of course there is! If you have an infinite number of things and you add one more you still have an infinite amount of things. Simple.

Asauber: This has nothing to do with math.I was just being silly.

JVL,

Let me put it to you philosophically, which happens before you start math.

Finity = context. Infinity = context removed.

They don’t work together, other than in someone’s imagination.

Andrew

Asauber: Let me put it to you philosophically, which happens before you start math.Finity = context. Infinity = context removed.

They don’t work together, other than in someone’s imagination.Well, I don’t have the heart to tell several centuries of mathematicians who have been using infinity that they are wrong. You’re going to have to do it.

Did you ever take Calculus by the way? And take a limit as x goes to infinity? Just wondering.

“mathematicians who have been using infinity”

JVL,

Of course they are using it. But it’s all in their heads. 😉

Andrew

JVL,

And I didn’t say mathematicians are “wrong”. You are just trying to put words in my mouth.

Andrew

Asauber: Of course they are using it. But it’s all in their heads. ????But then so are a lot of higher level mathematical operations and manipulations.

And I didn’t say mathematicians are “wrong”. You are just trying to put words in my mouth.Well, I don’t know what you meant then when you said they don’t work together.

When you take a limit to infinity you start with something finite and let it grow without bound so you are using the concepts of finite and infinite together. The mathematics is pretty simple and straightforward and has been used for quite a while now. I don’t think it’s just in the mathematicians head since, I believe, any being of any kind in any reality would come upon the same procedure and use it the same way. How could it be otherwise?

“When you take a limit to infinity you start with something finite and let it grow without bound so you are using the concepts of finite and infinite together.”

JVL,

“so are a lot of higher level mathematical operations and manipulations”

Of course. Abstractly.

“you start with something finite”

And you end with something finite, right?

Andrew

JVL:

What “one more”? You already have everything.

Asauber: And you end with something finite, right?It depends. For example: in Calculus when you’re trying to figure out if an infinite series converges or diverges you might get a finite result (it converges) or you might get an infinite answer (it diverges).

Have you taken Calculus? There’s tons of examples.

On of my favourites is: take the function 1/x for x > 1 and rotate it about the x-axis. You get a horn-shaped thing (sometimes nicknamed the horn of Gabriel). It turns out, if you do the math right, that that object has a finite volume but an infinite surface area. So, again, the finite and infinite are manifest in the same object.

Fractals are another good example: they have infinite perimeter but finite area.

“So, again, the finite and infinite are manifest in the same object.”

JVL,

Sure. In your imagination.

Andrew

ET: What “one more”? You already have everything.Not necessarily. Take the set of all even integers. That’s an infinite set. Add in the integer ‘3’ which is not an even integer. You still have an infinite number of integers. Add in all the odd integers and you still have an infinite set. Add in all the values like 0.5, 1.5, 2.5, 3.5 . . . you still have an infinite set.

Hilbert’s metaphor isn’t something I find very useful to be honest. Just doing the math works and makes more sense.

Math is like a language, the pleasure you get out of it depends on how well you speak it.

Thank you for proving that the set of even integers is smaller than the set of all integers.

Asauber: Sure. In your imagination..NOT in my imagination. Anyone who knows the mathematical procedures would get the same result. The procedures work for finite objects you could actually measure and touch. Use the same procedures on something that’s infinite and you can get infinite and finite results depending on what procedure you followed.

Math HAS to work that way. Or it wouldn’t work at all. It’s not made up or imagined. It’s pure logic.

“It’s pure logic.”

JVL,

You are stuck on something. I’m not sure what it is. Pure logic resides in your mind. I don’t think you can find it anywhere else.

Andrew

ET: Thank you for proving that the set of even integers is smaller than the set of all integers.Is an incorrect conclusion. As shown by the work of Cantor and others.

You can match up the integers with the even integers one-to-one so that no even integer is unpaired with and integer and no integer is unpaired with an even integer. You tell me an integer and I’ll tell you what even integer its matched with. You tell me an even integer and I’ll tell you an integer it’s matched up with. Nothing is left out.

That can only happen if both sets have the same number of elements. If they had different number of elements there would be something unmatched. But there isn’t.

So, the set of all even integers is the same ‘size’ as the set of all integers. QED

That same kind of matching procedure works for finite sets as well: if you can match two sets up one-to-one they must be the same size. In fact, that’s how we count how many objects there are: we are matching up the positive integers with the elements of a set.

Asuaber: You are stuck on something. I’m not sure what it is. Pure logic resides in your mind. I don’t think you can find it anywhere else.Math has to work the way it does. It can’t be any different. Therefore it must exist outside of my mind or imagination.

If you start with the same basic counting techniques humans arrived at millenniums ago and extend it you will get the same mathematical truths we know now. Maybe not in the same order, maybe expressed differently but the same truths. That’s not down to me or you; that’s something invariant.

Try and find some other kind of mathematics. See if it’s just in your mind.

“That’s not down to me or you;”

JVL,

But it is. No mind, no math.

Andrew

JVL:

LOL, Too funny, a Darwinian materialist appeals to logical necessity to try to claim that mathematics does not depend ‘on any kind of design’.

To point out the glaringly obvious elephant in the living room, both mathematics and logic have no place to stand within the Darwinist’s materialistic worldview.

As the old joke goes about God telling the scientist to go ‘get your own dirt’,,

Likewise JVL, go get your own mathematics,

I see that the concepts of addition an subtraction and addition still elude JVL. Strange that set subtraction refutes Cantor’s alleged proof.

Cantor’s diagonal just proves that the sets are countable.

Asauber: But it is. No mind, no math.I disagree. I think it takes a mind to experience or perceive math but the math is there regardless.

You are an experiencialist. I’m not.

BornAgain77: LOL, Too funny, a Darwinian materialist appeals to logical necessity to try to claim that mathematics does not depend ‘on any kind of design’.If you can propose another kind of mathematics then I’ll be very, very interested. If you can’t then . . . .

ET: I see that the concepts of addition an subtraction and addition still elude JVL. Strange that set subtraction refutes Cantor’s alleged proof.Uh huh. If you’d like to propose a different system for handling infinities and then face the heat and answer questions about your system then by all means do so.

Cantor’s diagonal just proves that the sets are countable.SOME sets are countably infinite.

If you’ve got a better system lay it out and let us query it.

“I think it takes a mind to experience or perceive math but the math is there regardless.”

JVL.

Where is it?

Andrew

Asauber: Where is it?It exists outside of space and time. It just is.

You cannot get away from one plus two equals three. You might use different words or terms but the basic mathematics stays true. Always.

“It exists outside of space and time.

It just is.”Godel begs to differ.

Moreover, exactly how do you, a Darwinist who believes we are purely material beings, account for the fact that we can grasp mathematical concepts that have no material basis? Again, you, as a Darwinian materialist, simply have no place to stand. Whereas, we, as Christian Theists who rightly believe that we have immaterial minds, readily do have foundation to stand upon.

As Wallace himself stated,

“It exists outside of space and time.”

JVL,

How Twilight Zone of you. lol

Andrew

BornAgain77: Godel begs to differ.So?

Moreover, exactly how do you, a Darwinist who believes we are purely material beings, account for the fact that we can grasp mathematical concepts that have no material basis? Again, you, as a Darwinian materialist, simply have no place to stand. Whereas, we, as Christian Theists who rightly believe that we have immaterial minds, readily do have foundation to stand upon.The more intelligent and successful creatures are more aware of the basic rules that underlie the universes’s existence. It’s simple. The more advanced the intelligence the better able they are at grasping the basic rules and using and extending them. No god or soul needed. Just a better understanding of how things work.

You look at the universe and look for justifications for your belief in God. Everything you find beautiful or complicated is an indication of your deity. I don’t see it that way. I see the universe being built on some basic structures and rules and as we advance and pay attention we grasp those things better and better.

You don’t need a soul, you just need to pay attention and remember.

“the basic rules”

JVL,

People are trying to give you an opportunity to present coherent ideas and you keep failing.

How did the basic rules come about?

Andrew

Asauber: People are trying to give you an opportunity to present coherent ideas and you keep failing.What? Because I’m not saying what you want to hear?

How did the basic rules come about?The basic rules of what? Mathematics? Physics? Chemistry?

Chemistry is a subset of physics. The rules of chemistry are based on the underlying physics.

Physics is a reflection of the basic underlying structures of the universe. It’s complicated but let’s say you start with electrons, protons and neutrons. The interactions between those particles give rise to a lot of other rules and laws. We are learning to delve deeper than those three particles. We are learning to dig further down. There’s no indication it’s planned or dictated. It’s all just the way it is. Perhaps the very fabric of the universe can only react in certain ways?

Mathematics I don’t think can be another way. That doesn’t mean that it was dictated or defined. I don’t know why anyone would look at it and just say: see, that indicated some kind of design. I hear that more from people who haven’t studied mathematics. I mean really studied it. That means a Bachelor’s degree or more.

“The basic rules of what? Mathematics? Physics? Chemistry?”

JVL,

You tell me. You are the one who brought it up.

Andrew

Yes, JVL ascribes to the “this all just happened to happen” scenario. Untestable and takes more faith to believe than Christianity.

BA77: “Godel begs to differ.”

JVL: “So?”

Nothing to see here eh JVL?

Contrary to JVL’s nonchalant attitude towards evidence that directly falsifies his claim, and as the following article states, “Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous.”

Physicists (and mathematicians) today, especially with the proof of Godel’s incompleteness theorems sitting right before them, simply have no basis for their belief that mathematics, all by its lonesome, can somehow function as a God substitute,

Stephen Hawking himself, an atheist, honestly admitted that “Gödel’s incompleteness theorem (1931), proves that there are limits to what can be ascertained by mathematics. Kurt Gödel halted the achievement of a unifying all-encompassing theory of everything in his theorem that: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove”

As well, Steven Weinberg, also an atheist, also honestly admitted that, ” “I don’t think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws of nature what they are rather than some other laws?’. And I don’t see any way out of that.”

In fact, there are an infinite number of mathematical theorems that could have described the universe but don’t, As Gregory Chaitin pointed out, “what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms. ”

Mathematics, contrary to what the vast majority of theoretical physicists believe today, simply never will have the capacity within itself to function as a God substitute.

As Dr. Bruce Gordon explains, “The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,,

Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.”

Moreover, an essential belief in the rise of modern science, a belief that distinctly separated it from Platonic philosophy that preceded it, (a philosophy that held math to exist separate from God), was the Christian’s belief that mathematics, especially any mathematics that might describe this universe, was, and is, the product of the Mind of God.

And as Paul Davies observed, “All the early scientists, like Newton, were religious in one way or another. They saw their science as a means of uncovering traces of God’s handiwork in the universe. What we now call the laws of physics they regarded as God’s abstract creation: thoughts, so to speak, in the mind of God. So in doing science, they supposed, one might be able to glimpse the mind of God – an exhilarating and audacious claim.”

In fact, in 1619, Johannes Kepler, shortly after discovering the laws of planetary motion, stated,

Likewise in 1687, Sir Isaac Newton, after discovering the law of universal gravitation, (which has been referred to as the first major unification in physics), stated that, “This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.,,,This Being governs all things, not as the soul of the world, but as Lord over all;”

As well, as Ian H. Hutchinson noted in the following article on Faraday and Maxwell, “Lawfulness was not, in their thinking, inert, abstract, logical necessity, or complete reducibility to Cartesian mechanism; rather, it was an expectation they attributed to the existence of a divine lawgiver.,,, For them, the coherence of nature resulted from its origin in the mind of its Creator.”

As well in quantum mechanics and relativity, we find that both Eugene Wigner and Einstein are on record as to regarding it as a ‘miracle’ that mathematics is applicable to the universe. In fact, Einstein went so far as to disparage ‘professional atheists’ when he called it a miracle:

Moreover, when we rightly allow the Agent causality of God ‘back’ into physics, as the Christian founders of modern science originally envisioned,,,, (Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders),,, and as quantum mechanics itself now empirically demands (with the closing of the free will loophole by Anton Zeilinger and company), when we rightly allow the Agent causality of God ‘back’ into physics then that provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead provides an empirically backed reconciliation, (via the Shroud of Turin), between quantum mechanics and general relativity into the much sought after ‘Theory of Everything”. Here are a few posts where I lay out and defend some of the evidence for that claim:

To give us a small glimpse of the power that was involved in Christ’s resurrection from the dead, the following recent article found that, ”it would take 34 Thousand Billion Watts (34 trillion Watts) of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.”

Verse:

ET: Yes, JVL ascribes to the “this all just happened to happen” scenario. Untestable and takes more faith to believe than Christianity.The math works. It can be proved. It’s the most testable discipline ever.

BornAgain77:I did not say nor do I believe that mathematics is a replacement or substitute for God. You choose to look at is as evidence for God. I think that’s misplaced and incorrect. I think mathematics has nothing to do with God. But you think all of existence is due to God so there is nothing I can say that will get you to change your mind. Your belief is unfalsifiable so I’m not going to try and argue with you about it.

If you want to talk about mathematics that’s fine. If you are going to use mathematics as support for God (and I gather you haven’t studied math much yourself) then we’ve got nothing to say to each other really.

JVL: “I did not say nor do I believe that mathematics is a replacement or substitute for God.”

All evidence to the contrary be damned eh JVL?

And, irony of ironies, JVL accuses me of holding an unfalsifiable position in the face of he himself refusing to accept Godel’s falsification of his position.

JVL:

What are you talking about? There isn’t any math for all of this just happening to happen. The only reason math exists is because the universe was designed using it. It permeates our existence.

ET: What are you talking about? There isn’t any math for all of this just happening to happen. The only reason math exists is because the universe was designed using it. It permeates our existence.I disagree. I can not see any way math could work differently.BornAgain77: And, irony of ironies, JVL accuses me of holding an unfalsifiable position in the face of he himself refusing to accept Godel’s falsification of his position.I agree with Godel’s mathematics but interpreting it as theology . . . nah. That’s why I said “so?”, it’s your use of Godel’s mathematics to make a religious statement. That doesn’t wash.

JVL:

If math exists, which you believe, then where did it originate? I am sure you know that new formulas are not referred to as having been created, but of discovering what already exists. Without intelligence designing the entire universe, there can be no math to discover. Something created the formulas, just as something created the laws of physics.

So at the end of the day, JVL is just another unresponsive troll. Again. Good Times, though.

Andrew

JVL- You aren’t even responding to my comments. It’s as if you cannot comprehend what I am posting, Mathematics cannot work any differently because it permeates our universe. It permeates our universe because mathematics was used in its Intelligent Design.

Materialism doesn’t work. It cannot account for mathematics. That’s because it cannot account for this universe. There isn’t any math that supports materialism.

ET: You aren’t even responding to my comments. It’s as if you cannot comprehend what I am posting, Mathematics cannot work any differently because it permeates our universe. It permeates our universe because mathematics was used in its Intelligent Design.How was it used then? Do you think the math existed before the design was conceived?

Materialism doesn’t work. It cannot account for mathematics. That’s because it cannot account for this universe. There isn’t any math that supports materialism.Math has nothing to do with theology or materialism. It’s separate from any world view and supports none.

Asuaber: So at the end of the day, JVL is just another unresponsive troll. Again. Good Times, though.Sorry for not agreeing with you.

JVL:

Most likely the same way we use it to design things today. Or very similar.

Yes.

That’s your opinion. However, materialism is incoherent and is a non-starter.

BobRyan: If math exists, which you believe, then where did it originate?I think it’s always been there. I don’t see how 2 + 2 can equal anything but 4, ever.

I am sure you know that new formulas are not referred to as having been created, but of discovering what already existsDepends on the mathematician.

Without intelligence designing the entire universe, there can be no math to discover.Why? If math can be no other way then what does intelligent design have to do with it? Design implies choices were made. I don’t think there are choices with mathematics. It is what it is.

Something created the formulas, just as something created the laws of physics.I disagree. The fact that the infinite series 1 + 1/2 + 1/4 + 1/8 + 1/16 + . . . . converges has nothing to do with a designer. You couldn’t decide to make that come out to be something else.

Can you conceive of a different kind of mathematics? If you can’ then doesn’t that mean it has to be the way it is? If that’s true then there’s no choice about it. That means, if intelligent design is true, that the math existed before the design was implemented.

ET: Most likely the same way we use it to design things today. Or very similar.Give an example of something you think was designed and how math was used in the design process.

Yes.So we agree!

That’s your opinion. However, materialism is incoherent and is a non-starter.I say math has nothing to do with materialism, especially if materialism is incoherent since math is very coherent.

If math existed before choices were made in the design process then math has nothing to do with design. It might have been used during the design process but it exists apart from design. So math was not designed.

Bridges require mathematics. Tall buildings require mathematics. Rocket launches and recovery depend on mathematics.

That doesn’t follow.

That doesn’t follow, either.

How do you figure?

Math was designed so that the universe could then follow.

Mathematics was part of the Intelligent Design.

Does it? Just because choices were made does not mean mathematics was not intelligently designed. Perhaps there was a different math that didn’t work in the physical realm

ET: Bridges require mathematics. Tall buildings require mathematics. Rocket launches and recovery depend on mathematics.Those were not part of the design intelligent design is talking about. Give an example of something BIOLOGICAL you think was designed and how math was used.

That doesn’t follow.You agreed that math existed before biological design was implemented. So it’s independent from that design process. It existed before then. So it was not affected by the design process. So it exists apart from the biological design you believe happened.

Math was designed so that the universe could then follow.So, how could math have been designed differently? How could math have been designed without using math?

Mathematics was part of the Intelligent Design.So, step 1? Again, if math was designed then it could have been done differently. How could it have been done differently?

Does it? Just because choices were made does not mean mathematics was not intelligently designed. Perhaps there was a different math that didn’t work in the physical realmLike what? Give an example.

LoL! @ JVL- You lose and now you try to change the subject. The entire universe required mathematics, Jerad. The laws that govern the universe are purely mathematical.

It had to. Mathematics was used to design the universe.

Not necessarily.

ET: You lose and now you try to change the subject. The entire universe required mathematics, Jerad. The laws that govern the universe are purely mathematical.That doesn’t mean math was designed does it? I say math was NOT designed because it has to be the way it is.

It had to. Mathematics was used to design the universe.Like how? Give an example.

Not necessarily.Give an example.

JVL:

Just because it has to be the way it is does not mean it wasn’t intelligently designed.

Mathematics was used to design the universe in a similar fashion to the way we use it for engineering.

Of what? You want an example that math couldn’t be different? Are you daft?

ET: Just because it has to be the way it is does not mean it wasn’t intelligently designed.Design implies choices were made, yes? If something has to be a certain way then there are no choices, yes?

Of what? You want an example that math couldn’t be different? Are you daft?Okay, so you think math has to be the way it is? How are there any choices in that? How can it be designed then?

Design implies choices. If there are no choices there is no design.

If math has to be the way it is then it wasn’t designed. If you think it was designed then you should be able to come up with choices or alternative to the way math works as we understand it. You should be able to come up with a different kind of math.

Can you do that?

If there are no alternatives then was it designed? I say no.

JVL:

Not necessarily.

Even if there aren’t any alternatives mathematics had to come into existence somehow. And seeing that it was required to design the universe it is obvious we did not invent it.

Oh noes! Car designers did not have any choice but to make the wheels round! Houses all have roofs and walls! No choice!!! And bridges they can’t be just anywhere.

ET: Not necessarily.You think you can have design without choices being made? That’s the same as necessity isn’t it? How does the explanatory filter view that?

Even if there aren’t any alternatives mathematics had to come into existence somehow. And seeing that it was required to design the universe it is obvious we did not invent it.Yes so . . . was mathematics designed? I say no.

Oh noes! Car designers did not have any choice but to make the wheels round! Houses all have roofs and walls! No choice!!! And bridges they can’t be just anywhere.Wheels don’t have to be round. Houses can be in caves. Bridges are partially dependent on land rights and available spaces aside from the geographic considerations.

https://www.youtube.com/watch?v=vk7s4PfvCZg

https://en.wikipedia.org/wiki/Non-circular_gear

And, guess what: you still haven’t been able to provide an example of a different kind of mathematics. So, I say, mathematics was not designed or decided upon. It just is. It’s pre-design, if design in nature exists.

How do you think mathematics came to be, then, JVL? Your turn- your “math just is” is a cop out.

A cave as a house still has a roof and walls. Bridges are only where they are needed.

I don’t have to give an example of a different kind of math. That has nothing to do with what I said. What I said is more of a thought experiment. That is why you are so confused.

The bike on youtube is close to useless. And I never said anything about gears

ET: How do you think mathematics came to be, then, JVL? Your turn- your “math just is” is a cop out.How did your designer come to be?

I think mathematics is just part of the fabric of reality. No being had to design it or create it.

I don’t have to give an example of a different kind of math. That has nothing to do with what I said. What I said is more of a thought experiment. That is why you are so confused.You don’t HAVE to do anything. But if you can’t come up with a different kind of mathematics then you have less of platform to say it was designed. Designed means having choices. Means things could have been different. Could math have been different? If you haven’t got an example then maybe you’re wrong.

The bike on youtube is close to useless. And I never said anything about gearsWheels don’t have to be round. Sorted.

“I think mathematics is just part of the fabric of reality.”

JVL,

That’s very poetic but it doesn’t explain why or how there is math.

Andrew

Asauber: That’s very poetic but it doesn’t explain why or how there is math.Do you have an explanation of how math came to be? And, if it was designed, how it could have been different? Design means there are choices. What choices did the designer make regarding mathematics?

JVL:

Question-begging.

That’s the way the universe was designed.

Just because you can say something stupid that doesn’t make it so.

That doesn’t follow.

Yes, they do. If you put a non-round wheel on a car, either the wheel or something on the car, will break. The road will be torn up, too.

JVL:

To design or not to design is a choice. To have the laws that govern nature to be the way they are, was also a choice- to have intelligent observers or not, was a choice that affected that prior choice.

Choices abound, choices all around. But do keep flailing about.

JVL holds that the ‘beyond space and time’ math that describes this universe ‘just is’ and that it is not contingent upon the Mind of God for its existence and also holds that God did not choose the particular mathematical form that this universe takes.

JVL’s position, as far as the philosophy of science is concerned, is a major step backwards. JVL’s position is very similar, if not exactly like, the position that was held by the ancient Greeks.

The ancient Greeks held to a necessartarian view of mathematics. A view in which mathematics, to use JVL’s term ‘just is’. And that necessartarian, i.e. ‘just is’, view of mathematics, played a major role in preventing the rise of modern science. As Peter Williams notes in the following article, “Both Greek and biblical thought asserted that the world is orderly and intelligible. But the Greeks held that this order is necessary and that one can therefore deduce its structure from first principles. Only biblical thought held that God created both form and matter, meaning that the world did not have to be as it is and that the details of its order can be discovered only by observation. ”

And as Henry F. Schaefer III noted in the following video, “The emergence of modern science was associated with a disdain for the rationalism of Greek philosophers who pronounced on how the world should behave, with insufficient attention to how the world in fact did behave.”

In fact, it was only with the quote-unquote ‘outlawing’ of the ancient Greek philosophers’s deterministic and necessitarian views of creation that modern science was finally able to achieve a viable birth.

As the following article states, “If science suffered only stillbirths in ancient cultures, how did it come to its unique viable birth? The beginning of science as a fully fledged enterprise took place in relation to two important definitions of the Magisterium of the Church. The first was the definition at the Fourth Lateran Council in the year 1215, that the universe was created out of nothing at the beginning of time. The second magisterial statement was at the local level, enunciated by Bishop Stephen Tempier of Paris who, on March 7, 1277, condemned 219 Aristotelian propositions, so outlawing the deterministic and necessitarian views of creation.

These statements of the teaching authority of the Church expressed an atmosphere in which faith in God had penetrated the medieval culture and given rise to philosophical consequences. The cosmos was seen as contingent in its existence and thus dependent on a divine choice which called it into being; the universe is also contingent in its nature and so God was free to create this particular form of world among an infinity of other possibilities. Thus the cosmos cannot be a necessary form of existence; and so it has to be approached by a posteriori investigation. The universe is also rational and so a coherent discourse can be made about it. Indeed the contingency and rationality of the cosmos are like two pillars supporting the Christian vision of the cosmos.”

As to the last sentence of the preceding quote, “Indeed the contingency and rationality of the cosmos are like two pillars supporting the Christian vision of the cosmos”, it is important to note just how radical of a departure this ‘contingency vs. necessatarian’ transformation in the philosophy of mathematics was.

As Edward Fesser notes in the following article, for Christian scholastic philosophers of the medieval period “Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts,” whereas for ancient Greek philosophers, “mathematical objects such as numbers and geometrical figures exist not only independently of the material world, but also independently of any mind, including the divine mind.”

In the minds of the Christian founders of modern science, mathematics, especially any mathematics that might describe the universe, was certainly not held to be necessary, as the ancient Greeks held and JVL currently holds, but any mathematics that might describe was instead held to be contingent upon God’s thoughts.

Perhaps the best example that I can give for the fact that the Christian founders of modern science held mathematics, especially any mathematics that might describe the universe, to be God’s thoughts is the following quote by Kepler, (which he made shortly after discovering the laws of planetary motion),,

Several quotes along similar lines we presented in post #53

https://uncommondescent.com/neuroscience/michael-egnor-talks-with-podcaster-lucas-skrobot-about-how-we-can-know-we-are-not-zombies/#comment-706255

Thus JVL is actually defending a necessitarian view of mathematics that the ancient Greeks also held. A fruitless view of mathematics that played a major role in preventing the rise of modern science since a necessitarian view of gives rise to the “Greek philosophers who pronounced on how the world should behave, with insufficient attention to how the world in fact did behave”.

In short, a necessitarian view of mathematics and/or creation, undermines empirical science itself since those who hold to a necessitarian view of mathematics, apparently, didn’t, and still don’t, believe that it was possible for the universe to take any other mathematical form than the one it currently has..

On this point they are sadly, and profoundly mistaken.

Godel’s incompleteness theorem is more that enough, in and of itself, to prove this point. But to add even more weight to the claim that the mathematics that describe this universe could have been different. The free will loop-hole in quantum mechanics has now been closed by Anton Zeilinger and company.

On top of that, “Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information.”

And as James Franklin noted, “the intellect (is) immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.,,,”

Thus the Christian Theist has multiple lines of strong evidence, (many more lines than what I have presented here in this short post), that he can appeal to to support his claim that the mathematics that describe this universe is contingent upon the Mind of God for its existence, and indeed that God chose this particular mathematical form that this universe has taken. Whereas JVL has, basically, only his ignorance of the history of science, and his ignorance of the evidence itself, to appeal to,

It is truly sad that he repeatedly chooses ignorance over God:

JVL,

I am late to the party, but observe:

>>Do you have an explanation of how math came to be?>>

1: Yes, as you know I have examined a core of Mathematics, showing that once a distinct possible world is, a certain logically ordered structure linked to quantity obtains. Indeed, we then see that such core aspects necessarily extend to any possible world, i.e. all of them, securing universality and global relevance. Which in turn answers Wigner on the astonishing power of Mathematics.

2: So, this is not a matter of clever rhetorical games dependent on whatever ideas, suggestions or gaps may obtain with particular interlocutors, but something established as a base for further thought.

3: There is, however, a second order question: how are possible worlds just that, possible?

4: To answer that, notice, that were there ever utter, genuine nothingness — utter non-being — then as such has no causal capability, such would forever obtain. Further, transfinite regress cannot be traversed in finite stage steps, i.e. an actual infinity of successive contingent worlds with finite duration [years, say] is also ruled out, as is retro-causation by which a not yet future state reaches back to generate the chain that leads to itself. That, too would be pulling a world out of a non-existent hat.

5: That is, there is adequate, finitely remote root cause for the actual world we inhabit and others that may or do actually exist. Such, is a reality root, necessary being. Once a world is, something always was, a something of different order from ourselves. Something, capable of creating worlds.

6: So, there are consequences to there being possible worlds.

>> And, if it was designed, how it could have been different?>>

7: Possibility of a distinct world W implies near neighbour worlds such as W’ that lack some particular attribute or aspect A unique to W and singling it out. This of course then leads to world partition W = {A|~A} thence 0,1,2 etc, and on to structured core sets and frameworks of Mathematics.

8: Distinct identity directly implies just that, distinction, i.e. actualisability of what else could also be, here W’. So, we have general possibility of alternatives pivoting on locally unique defining thus structural attributes such as A,

9: In addition, a given world will be structured and does not preclude that other worlds may be structured in equally distinct but distinguishable ways. So, we see for example how we may have different logic-model worlds creating distinct mathematical domains that nonetheless share core necessary structures present in any possible world. N, Z, Q, R, C etc and linked things come instantly to mind as such in-common structures as we just saw.

>> Design means there are choices.>>

10: Yes, and distinct possibilities are inherent in there being unique possible worlds. So, choice would exist connected to actualising one or the other of neighbours W and W’ or even both.

11: Choice, of course, is inherent in design.

>>What choices did the designer make regarding mathematics?>>

12: Choices connected to actualising particular worlds with structures such as a particular physics and cosmology. Some structural-quantitative aspects of a PW are in common, others will be distinct to particular worlds such as our own.

13: There is abundant evidence that our world sits at a deeply isolated operating point amenable to C-Chemistry, Aqueous medium, terrestrial planet in galactic and circumstellar habitable zone life.

14: As there is no reason to hold neighbouring but life-inhibiting worlds logically impossible of being there is good reason to hold that we thus see signs of design.

KF

ET: That’s the way the universe was designed.Designed means choices were made. If math could have been different how?

Just because you can say something stupid that doesn’t make it so.If math was part of the design then choices were made which means things could have been different. How could math be different?

To design or not to design is a choice. To have the laws that govern nature to be the way they are, was also a choice- to have intelligent observers or not, was a choice that affected that prior choice.I’m talking about mathematics which I say is invariant no matter what nature is like.

BornAgain77: Thus JVL is actually defending a necessitarian view of mathematics that the ancient Greeks also held. A fruitless view of mathematics that played a major role in preventing the rise of modern science since a necessitarian view of gives rise to the “Greek philosophers who pronounced on how the world should behave, with insufficient attention to how the world in fact did behave”.You may be right about the mindset most conducive to the rise of modern science, certainly the weight granted to people like Aristotle slowed things down. But I’m talking about mathematics and the Greeks were excellent mathematics. Arguably no major advancements were made after the Greek era for another 1000 years. They figured out that the square root of 2 is irrational! Euclid’s Elements are still studied and still true. And just about everyone knows the Pythagorean theorem. They may have slowed down science but they discovered the mathematics upon which science sits.

Kairosfocus: 12: Choices connected to actualising particular worlds with structures such as a particular physics and cosmology. Some structural-quantitative aspects of a PW are in common, others will be distinct to particular worlds such as our own.But what about the mathematics? Could the underlying mathematics be different? If you say yes then how? Can you give an actual example.

Kairosfocus @85

Excuse the digression, but one thing has always puzzled me, that may have already been solved by philosophers generations ago. This is the proposition that, if God is truly omnipotent, it would seem that He could create a world where the to us fundamental laws of logic and mathematics are different.

If not, the laws of logic and mathematics are ultimate realities prior to and out of the control of God. But He is supposed to be truly omnipotent.

Could He create if He chose a world reality where 2 + 2 = 5, where the laws of logic are different? Are there such world realities, forever inaccessible to humans?

This notion does not seem acceptable, so where is the flaw in this reasoning?

JVL asks,

Simple, and to repeat, there are an infinite number of different axioms that could have been chosen that could have given rise to an infinite number of different mathematical frameworks,

As Chaitin pointed out, “an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.”

For instance, the parallel postulate and/or axiom of Euclidian geometry does not hold for the Riemannian geometry and/or the four-dimensional Minkowski space that lies at the basis of relativity.

Thus the fact that the math that describes this universe ‘could have been different’ was in fact the way that it was. The math that actually describes the space-time of this universe is very different than Euclidian math and that difference between the two mathematical systems lies in the different axioms of each mathematical system. And again, to repeat, axioms are a matter of choice, not necessity,

And again, “an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.”

Thus JVL’s claim that math ‘just is’ and that math could not have been different, is simply a naively false claim for him to make. The math that describes this universe could have been infinitely different depending on then infinite number of axioms that God could have chosen to implement.

Of supplemental note:

BornAgain77: Simple, and to repeat, there are an infinite number of different axioms that could have been chosen that could have given rise to an infinite number of different mathematical frameworks,Can you come up with a consistent form of mathematics different from ours? One that works for the most basic problems?

As Chaitin pointed out, “an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.”Quite true, as per Godel’s work. But theorems are NOT axioms.

For instance, the parallel postulate and/or axiom of Euclidian geometry does not hold for the Riemannian geometry and/or the four-dimensional Minkowski space that lies at the basis of relativity.Yup, it’s like going from Newtonian mechanics to Einstein. But 2 + 2 still = 4. The area of a circle on a plane is the same. (Don’t tell

ETthat under non-Euclidian geometry parallel lines meet at infinity, he won’t like that.) But the axiom you’re throwing out was defined by MEN, it’s not an inherent or obvious rule to depend on. In other words, if God designed mathematics he did NOT come up with the parallel axiom, men did. In fact, since not using the parallel postulate means you can better model part of God’s creation then I would say that God was probably working with non-Euclidian geometry in the first place! Human’s thought parallel lines never meet and then changed their minds.Thus the fact that the math that describes this universe ‘could have been different’ was in fact the way that it was. The math that actually describes the space-time of this universe is very different than Euclidian math and that difference between the two mathematical systems lies in the different axioms of each mathematical system. And again, to repeat, axioms are a matter of choice, not necessity,But, again, the underlying arithmetic is the same. Algebra is the same. Number theory is the same. Throwing out the parallel postulate (which, again, was a human assumption) oddly enough works when modelling certain phenomena (and it was ‘discovered’ before there were applications) but that doesn’t change how numbers work together. Subtraction, addition, multiplication, division, exponents, logarithm, integrals, derivatives, etc, all that stuff still works.

Thus JVL’s claim that math ‘just is’ and that math could not have been different, is simply a naively false claim for him to make. The math that describes this universe could have been infinitely different depending on then infinite number of axioms that God could have chosen to implement.Okay, give me an example then of a consistent axiomatic mathematical system that would be completely different from ours but still work for real world problems. This is my point; I don’t hear anyone coming up with an example. You can talk and pontificate all you like but if you can’t come up with an example then maybe what you propose does not exist.

Doubter, the attributes of God are compossible and indeed bound up inextricably in one another. As any possible world will have a distinct identity as outlined certain core aspects of math flow from that and are necessary. The issue shifts as noted to there being the possibility of worlds, pointing to causally adequate world root, thus a second level of cause. In context, non core aspects of math can be explored through contingent logic model worlds, which opens up math fields of study and different physics for PWs. In all these the core is there. Have to go. KF

JVL, see the just above and earlier, you are again unresponsive to core points.one for RW now. KF

JVL:

Why do you keep saying that? You can’t prove it so stop being a strawman loser.

You are erecting a strawman and then attacking it like some sort of demented child.

JVL:

Meet @ infinity? Infinity is not a place. Look, JVL, you don’t understand the terminology. You don’t understand infinity. And you are totally clueless about design.

JVL has some demented and perverted view of design. I have already provided engineering examples in which choices could NOT be made. And then once we consider engineering STANDARDs, we can see there are plenty of times where choices could NOT be made in design.

JVL is ignorant of design. And he thinks his belligerent ignorance is an argument.

JVL in response to this fact, “axioms are a matter of choice, not necessity,” states that,

And yet if we were to choose different axioms then ‘all that stuff’ would not work.

In fact, the fact that basic arithmetic is incomplete was the main point of Godel first incompleteness theorem, i.e. “as long as your logical system is complicated enough to include addition and multiplication, then your logical system is incomplete.”

In short, JVL is simply completely wrong in his assumption that math could not have been different. All of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.

Kairosfocus: Doubter, the attributes of God are compossible and indeed bound up inextricably in one another. As any possible world will have a distinct identity as outlined certain core aspects of math flow from that and are necessary. The issue shifts as noted to there being the possibility of worlds, pointing to causally adequate world root, thus a second level of cause. In context, non core aspects of math can be explored through contingent logic model worlds, which opens up math fields of study and different physics for PWs. In all these the core is there. Have to goI just want to know if someone can present a consistent axiomatic mathematics that is significantly different from ours!

JVL, see the just above and earlier, you are again unresponsive to core points.one for RW now.I see you guys talking about different laws of physics and chemistry and different mathematics but I don’t see anyone giving me an example except non-Euclidean geometry. Throwing out the parallel postulate is just tossing a man-made axiom, an assumption about mathematics. I want to know how you could start from ground zero and get something different. Can you give me an example? If you can’t then how can you be sure one exists?

ET: Why do you keep saying that? You can’t prove it so stop being a strawman loser.Look, if you tell me you designed something then that means you made choices that could have been different. Like cars or bridges or bicycles or novels or landscapes or pottery or just about anything man-made. We can all see different ways you might have done something. You designed it, you made choices. I’m not sure the basic core of mathematics can be altered or different. I’m not sure there are choices that can be made. I’m not sure you can ‘design’ root-level mathematics. If you can then please give me an example.

Meet @ infinity? Infinity is not a place. Look, JVL, you don’t understand the terminology. You don’t understand infinity. And you are totally clueless about design.🙂 Sometimes I say things just to wind you up.

has some demented and perverted view of design. I have already provided engineering examples in which choices could NOT be made. And then once we consider engineering STANDARDs, we can see there are plenty of times where choices could NOT be made in design.Okay, fine. But you can at least design part of a car or a bridge or a wheel. You can make choices of how big the wheel is, how wide it is, what its made of, etc. I’m saying that I don’t think you can change the core of mathematics (arithmetic, algebra, probability, etc). If that’s true then I don’t think you can say that mathematics was ‘designed’ or ‘chosen’.

JVL is ignorant of design. And he thinks his belligerent ignorance is an argument.Look, if you design something then you must make choices between alternatives. At least at some level. I’m not sure there are choices in setting up mathematics. But if someone can come up with an example I’m happy to consider it.

Bornagain77: And yet if we were to choose different axioms then ‘all that stuff’ would not work.Your example of the Peano axioms is interesting but that was just an attempt to put our basic mathematics on the same kind of standing as Euclidean geometry (with its famous five axioms). They didn’t create something different. I’m asking: can you start with different axioms and come up with something different? Yes or no?

In fact, the fact that basic arithmetic is incomplete was the main point of Godel first incompleteness theorem, i.e. “as long as your logical system is complicated enough to include addition and multiplication, then your logical system is incomplete.”I’m not talking about whether or not you can deduce all theorems with a mechanistic approach starting with a set of axioms. I’m asking: can you create a whole new system of mathematics using different base axioms. Yes or no? If yes then an example please.

In short, JVL is simply completely wrong in his assumption that math could not have been different. All of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.Then show me a different mathematical system, a really different mathematical system, based on different axioms. Math is not a spectator sport: if you want to play you’ve got to put on a uniform and hit the field.

JVL- please shut up. You don’t know anything about design. And I have already told you about the choices. That you are a willfully ignorant troll doesn’t help you.

Whatever JVL, I am confident that the unbiased reader can now clearly see that you are wrong in your assumption that math ‘just is’.

“math ‘just is’”

JVL has proven itself quite the simpleton.

Andrew

If math can’t be different, as JVL claims, is this not further evidence for the fine tuning argument?

JVl, you have you answer, there are certain math structures that are pre axiomatic and will be in common to abstract logic model worlds erected through axiomatisations. Not to mention when we go on to sets of cosmos-building laws. KF

ET: please shut up. You don’t know anything about design. And I have already told you about the choices. That you are a willfully ignorant troll doesn’t help you.Bornagain77: Whatever JVL, I am confident that the unbiased reader can now clearly see that you are wrong in your assumption that math ‘just is’.Asauber: JVL has proven itself quite the simpleton.Look, it’s really simple. I assert that math has to be the way it is, at the basic level like arithmetic, algebra, probabilities, etc. I don’t think that part can be due to design.

I agree that axioms matter a lot. That’s the logical basis for any axiomatic system.

My challenge to you guys is: if you think mathematics was even partially designed then please proved and example of a designed mathematical system that is significantly different from ours at the basic level.

If you can’t do that then how do you know it’s possible to do so?

So far, all you’ve done is heap aspersions on me. Let’s see if you can establish your belief that mathematics could have been designed by providing a designed mathematics that differs from ours.

Mac McTavish: If math can’t be different, as JVL claims, is this not further evidence for the fine tuning argument?No, because you can’t fine tune something that is not tuneable.

Kairosfocus: you have you answer, there are certain math structures that are pre axiomatic and will be in common to abstract logic model worlds erected through axiomatisations. Not to mention when we go on to sets of cosmos-building laws.That sounds like you agree with me! That certain parts of mathematics are not design-able.

Thank you for that.

If that’s not what you mean then what pre-axiomatic math structures are you talking about?

JVL:

Even if it couldn’t be any other way doesn’t mean it wasn’t designed and isn’t part of the design.

Well deserved. Your “challenge” just exposes your clueless desperation. How can we show you math that doesn’t exist in our universe using terminology from our universe?

How does our inability to mimic the Designer of the universe have anything to do with math being designed in and for this universe?

JVL:

How do you know?

ET: Well deserved. Your “challenge” just exposes your clueless desperation. How can we show you math that doesn’t exist in our universe using terminology from our universe?If you can’t do it, how do you know it can be done?

How does our inability to mimic the Designer of the universe have anything to do with math being designed in and for this universe?If you can’t do it, how do you know it can be done?

Is having faith science? Or mathematics?

How do you know?Explain how you can fine tune something that is not tuneable?

All I want is for you to provide me an example of what you think is possible. If you can’t provide and example then how do you know it IS possible?

Math is not a spectator sport. You have to be able to ‘do it’.

JVL:

How can we show you math that doesn’t exist in our universe using terminology from our universe?Answer the question.At the start, by making it non-tunable.

ET: How can we show you math that doesn’t exist in our universe using terminology from our universe? Answer the question.How do you know it’s possible if you can’t show it? How do you know you’re not just making stuff up that doesn’t actually exist? “OOO, I can’t tell you but I know” just doesn’t cut it.

You don’t know if all the stuff you’re taling about is even possible. You can’t use your own ignorance of your own beliefs as proof you’re correct.

At the start, by making it non-tunable.How can you make something non-tunable? If you tuned it to be non-tunable why couldn’t you retune it later?

Of note, change the Peano axioms and you will have a different mathematical system.

Again, all of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity. That is exactly what made Godel’s incompleteness theorem so devastating to David Hilbert and others who wished for mathematics to be complete within itself.?

Again, JVL is completely wrong in his assertion that ‘math just is’.

This following video is also very interesting for revealing how Godel’s incompleteness theorem was brought about,

?

Bornagain77: Of note, change the Peano axioms and you will have a different mathematical system.Yup, you would. Show me an example.

Again, all of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.Yup, agreed. Show me an example of an axiomatic mathematical system that differs significantly from ours that works for some of our basic problems. Arithmetic, algebra, statistics, etc.

I don’t disagree with the theory, I just want to see an example that shows it is possible.

JVL

Are you claiming that the argument being made for the fine tuning of the universe is a flawed argument because there is no evidence that it can be tuned?

JVL, you are the one claiming that ‘math just is’. So for you to agree with the statement, “all of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.”,,,

For you to agree with that statement,,

,, is for you to concede that you are wrong in you belief that ‘math just is’

After conceding that you are wrong in your presupposition of ‘math just is’, you then wanted an example, to which I had already provided a reference in my post which stated,

So there is an example out there somewhere, and no, I will not dig it up for you. You can dig it up for yourself if you want. Personally, I am more than satisfied that you have conceded the primary fact that defeats your argument, i.e. “all of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.”,,,

Mac McTavish: Are you claiming that the argument being made for the fine tuning of the universe is a flawed argument because there is no evidence that it can be tuned?Ummm. .. . yeah. More or less.

Bornagain77: is for you to concede that you are wrong in you belief that ‘math just is’I agree that in general that a system depends on its axioms. What I am wondering is: is it possible for mathematics as we understand it to be significantly different from what we experience. And I’d like an example from those whose assert it could be something different.

So, what I am asserting is: I do not think that mathematics can be significantly different from what we know. So yes: I think it just is. Considering the discussion of axioms I think mathematics will always depend on the same basic axioms.

If I am wrong then someone should be able to provide a counter example. Can you provide such a counter example? Yes or no?

So there is an example out there somewhere, and no, I will not dig it up for you. You can dig it up for yourself if you want. Personally, I am more than satisfied that you have conceded the primary fact that defeats your argument, i.e. “all of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.”,,,I haven’t denied that. What I am asking is: can you come up with an axiomatic system of mathematics that differs greatly from what we have now? A system that deals with arithmetic and algebra and geometry and probability, etc.

So far, you haven’t found an example.

How can we show you math that doesn’t exist in our universe using terminology from our universe? Answer the question.The ignorance is all yours. The strawman you are whipping is proof that you are clueless.

Super tight specifications that do not allow for tolerances.

Strawman soup today, eh? It was designed and built to be non-tunable.

You can tune a piano but you can’t tuna fishJVL:

In this universe it can’t be. And even if can’t be any different in any verse it doesn’t mean it wasn’t designed. It is already very flexible.

LOL, JVL, do your own research, I gave you a big hint where to look. Myself, I am more than satisfied with your honest concession that you were wrong in your original presupposition of “math just is”. i.e. JVL: “Yup, agreed.”

You are just wasting my time after you conceded that axioms are a matter of choice, not necessity.

i.e. The game is over, the fat lady has sung, and the stadium lights are being shut off.

Mathematics is different from the real world. In the real world only positive integers exist but even these positive integers are abstractions that just exist in our heads. That does not mean that all the mathematical concepts that are used are not useful but they are abstractions. Maybe similar to Plato’s shadows.

In our universe there is no pi or e or square root of 2 or infinity whether infinitely big or infinitely small. And definitely not any imaginary or complex numbers.

All are incredibly useful. But all are mental abstractions. There is no such thing as a circle or right angle or polygon or even a straight line in the physical world. Only in our heads. That does not mean we don’t observe close approximations to these concepts but in reality they do not exist.

Mathematics is not a science but logical truisms. The modern world thrives on these abstractions and their logical underpinnings but that is all they are.

And how far is all this from the OP about zombies.

As to mathematics and fine-tuning. As mentioned previously, the parallel postulate and/or axiom of Euclidian geometry does not hold for the Riemannian geometry and/or the four-dimensional Minkowski space that lies at the basis of relativity.

And yet, although the universe is based on four-dimensional Minkowski space, we find that the universe is “actually very close to the most unlikely state of all, absolute flatness.”

As to the fine-tuning of the ‘most unlikely’ flatness, and as the following author comments, the universe must have been flat to 1 part within 1×10^57 parts over its entire 13.8 billion year history which, “seems like an insane coincidence”.

Since the universe is “ever-so-boringly flat. On large, cosmic scales, parallel lines stay parallel forever, interior angles of triangles add up to 180 degrees, and so on. All the rules of Euclidean geometry that you learned in high school apply.”,

And yet, as the author goes on to comment, “But there’s no reason for our universe to be flat.”

The author should be grateful that the universe is ‘ever-so-boringly flat’. If the universe were not so ‘ever-so-boringly flat’ science and technology would not be possible for humans.

Simply put, without some remarkable degree of exceptional, and stable, flatness for the universe, (as well as exceptional stability for all the other constants), Euclidean (3-Dimensional) geometry would not be applicable to our world. or to the universe at large, and this would make science and engineering for humans, for all practical purposes, all but impossible.

This ‘insane coincidence’ of flatness adds considerable weight to both Einstein’s and Wigner’s claim that the applicability of math to the universe is, by all rights, a miracle:

Thus in conclusion, although JVL blew off as inconsequential the fact that Euclid’s parallel postulate does not hold for the four-dimensional space time of relativity, the fact of the matter is that the ‘insanely’ finely tuned flatness of the four-dimensional space time of relativity allows us to apply Euclidian mathematics to the real world so as to enable us to practice science, engineering, and technology in the first place. In other words, the universe gives every appearance of having been designed so as to enable intelligent creatures to practice science.

And remember, the entire concept of a line is an axiom in mathematics, and axioms in mathematics are always the result of choices, not necessity.

Verse:

JVL

I always thought there was something flawed in the fine tuning argument with respect to design.

as to:

The only flaw is that you would give any credence whatsoever to JVL’s claim that fine-tuning of the constants of the universe had to be exactly the way they are. The constants, like mathematical axioms themselves, are certainly not derived by mathematical necessity:

As Luke Barnes noted, “Today, our deepest understanding of the laws of nature is summarized in a set of equations. Using these equations, we can make very precise calculations of the most elementary physical phenomena, calculations that are confirmed by experimental evidence. But to make these predictions, we have to plug in some numbers that cannot themselves be calculated but are derived from measurements of some of the most basic features of the physical universe. These numbers specify such crucial quantities as the masses of fundamental particles and the strengths of their mutual interactions. After extensive experiments under all manner of conditions, physicists have found that these numbers appear not to change in different times and places, so they are called the fundamental constants of nature.”

Bornagain77: VL, do your own research, I gave you a big hint where to look.I’m not going to research your assertion that basic mathematics can be very much different from what we have. That means your assertion is unsupported.

You are just wasting my time after you conceded that axioms are a matter of choice, not necessity.But that doesn’t support your assertion if you cannot construct an alternative form of mathematics the works by making axiom choices. I guess we’ll never know . . .

i.e. The game is over, the fat lady has sung, and the stadium lights are being shut off.You shouldn’t mix your metaphors so much.

I gave you a link. which referenced an example of a different system,

You refused to chase that example down. It is not on me to do your research for you. Especially when you have already conceded the main point under consideration, i.e. that mathematical axioms are always a matter of choice not mathematical necessity.

You can’t have it both ways JVL. You cannot claim that basic arithmetic had to be exactly the way it is, i.e. ‘math just is’, while at the same time conceding that the Peano axioms which underlie basic arithmetic itself are a matter of choice.

Moreover, as an atheist who believes in Darwinian evolution, and who therefore believes that you have no immaterial mind and/or soul, you have no explanation as to why humans are even able to grasp this, as you yourself admitted, ‘beyond space and time’ immaterial realm of mathematics. Whether you honestly admit it or not, that is a rather glaring hole in your entire argument for atheism.

The self-refuting holes in your arguments against design literally pop out with every post you write. The only thing that has been consistent in your argumentation is that you are against the inference to design no matter what type of argument you have to make, even if the arguments are blatantly self-contradictory.

This is NOT honest scientific inquiry on your part, but is a stubborn, dogmatic, refusal on your part to, no matter what the evidence says to the contrary, to budge from your a-priori atheistic bias against any type of inference to God.

Bornagain77:In the book you linked to:

On pages 67 and 68 the possibility of alternative arithmetics is discussed (I am unable to copy-and-paste passages for some reason). It is mentioned that one scheme is tantamount to creating extensions to standard arithmetic not rivals; in other words basically the same at the base level. Another approach talks about creating finite arithmetics which are useful under very limited conditions; not the sort of thing you would come up with first. You get those things AFTER you already have standard arithmetic. That section concludes with mentioning dropping the consistency requirement. Then there is a long discussion culminating in a fictional example. In the example different observers use arithmetic to calculate the result of some cosmological event. And get different results (pages 74 – 76).

First of all I asked if you could create a consistent alternate arithmetic. Secondly the example in the book is a bit daft because I do not see how a race of being could develop science to the high point given in the example with an inconsistent arithmetic? In the example they don’t even know their arithmetic is inconsistent until they compare their results from measuring different cosmic events and later comparing with beings on other planets. So, they have arithmetic consistent enough to build a high level of scientific sophistication but one that is inconsistent? Really? If someone can wrap their head around the example I’d love to hear about it. And, it seems to me, even the author assumed they already had consistent arithmetic like ours to start with.

As I said, all the finite arithmetic systems I have seen were derived AFTER standard arithmetic was in wide scale use. And they were derived by mathematicians. Witht he possible exceptions of some primitive tribes who never went on to develop any kind of science or business.

Sorry, I’m just not buying it. It all sounds like intellectual exercises on the fringes or derivations from that standard form just for limited and particular purposes. And mostly arrived at after standard arithmetic was mastered. I don’t see an alternative, consistent type of arithmetic that would solve the same kind of problems ours does.

Again the mathematics of our universe is FLEXIBLE. So flexible there doesn’t need to be any alternative. The CHOICE was to make it flexible so it can be used in a wide variety of scenarios.

ET: Again the mathematics of our universe is FLEXIBLE. So flexible there doesn’t need to be any alternative. The CHOICE was to make it flexible so it can be used in a wide variety of scenarios.How is it flexible? How is flexible baked into mathematics?

@jvl Yeah, how on earth could a race of beings on a planet have two space pineapples, and add another space pineapple, and not have three space pineapples? If you have 12 space pineapples, and you want to distribute them equally among three beings, how could you not get four space pineapples apiece? Nonsense of the highest order.

JVL you state:

So you agree that he gave an example but you disagree that it is consistent because it does not agree with ‘cosmic events’? Do you even read what you write?

So a system of mathematics can only be consistent if it agrees with cosmic events? But that is the entire point, there are consistent mathematical laws that don’t describe the universe. As Steven Weinberg, an atheist, told Richard Dawkins, “we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws of nature what they are rather than some other laws?’. And I don’t see any way out of that.”

Moreover, as I pointed out in post 124, (and you apparently ignored), the fact that we can even practice science in the first place is dependent on the ‘insanely’ fine-tuned flatness of the universe that allows everything to, mathematically, ‘make sense’ for us:

The universe, being the 4-D spacetime geometry that it is, simply did not have to be flat, and thus mathematics did not have to ‘make sense’ for us! i.e. There could very well have been no correlation between the math that we take for granted (i.e. Euclidian geometry) and the physical world!

You claimed that ‘math just is” and that the ‘fine-tuning just is”. You are wrong on both of your claims.

Retired Physicist:Yup, mathematics is not a spectator sport. Certainly it is appropriate for pure mathematicians to explore every single nook and cranny of the mathematical landscape but it doesn’t mean all of that theorising sheds any light on the practical, basic core of mathematics.

JVL:

The use of VARIABLES make it flexible. The fact that we do NOT need calculus to figure a grocery bill makes it flexible.

Your inability to think still isn’t an argument, Jerad

Bornagain77: So you agree that he gave an example but you disagree that it is consistent because it does not agree with ‘cosmic events’? Do you even read what you write?No, I say it’s inconsistent because the author of the books clearly states he is exploring a kind of arithmetic where the consistency axiom IS THROWN OUT! The author clearly has picked the example because the arithmetic is inconsistent.

Are you actually paying attention or just trying to score points? Did you actually read the section of the book you linked to?

Moreover, as I pointed out in post 124, (and you apparently ignored), the fact that we can even practice science in the first place is dependent on the ‘insanely’ fine-tuned flatness of the universe that allows everything to, mathematically, ‘make sense’ for us:Doesn’t the mathematics have to be consistent then? How can you understand the cosmos if you get everybody gets different answers from each other to simple, basic mathematical calculations?

The universe, being the 4-D spacetime geometry that it is, simply did not have to be flat, and thus mathematics did not have to ‘make sense’ for us! i.e. There could very well have been no correlation between the math that we take for granted (i.e. Euclidian geometry) and the physical world!But the math is consistent to itself. That’s the difference. You cannot model things if your mathematics is not consistent. Lots and lots of mathematics is developed well before an application is found. But when it looks like some obscure form of mathematics might reflect and uphold some new theory of physics it would all fall to pieces if the mathematics wasn’t consistent. Which is is in all the real world examples you cite.

Axioms in pure mathematics are arbitrary. Some very weird mathematical structures and approaches end up having real world applications. But all of that work initially came from a consistent arithmetic framework And I haven’t seen an alternative consistent arithmetic framework that can be built upon to create the wide variety of mathematics we have now that solves some really basic physical problems.

ET: The use of VARIABLES make it flexible. The fact that we do NOT need calculus to figure a grocery bill makes it flexible.Variables are placeholders for values that might change. That’s not part of the basic framework or mathematics. How the math actually works.

Why don’t you read through that book that

Bornagain77referenced and see if you can understand the example I discussed. Go on, give it a try.Whatever JVL, the authors both said that the universe did not have to ‘make sense’ to us mathematically. You disagreed. So what? You also disagree with both Einstein and Wigner.

I’ll let unbiased readers decide for themselves whether they want to give more credence to you, an atheistic troll on the internet, or to Einstein and Wigner. For me, the choice isn’t even close.

Wow. Jerad I understand that English confuses you. Variables make mathematics FLEXIBLE.

Why don’t you get an education that allows you to think. Then perhaps we can talk

Bornagain77: Whatever JVL, the authors both said that the universe did not have to ‘make sense’ to us mathematically. You disagreed. So what? You also disagree with both Einstein and Wigner.Wow, clearly you just don’t understand the mathematics. Incredible. You copy and paste stuff you think upholds your view and your really don’t understand what’s going on at all.

I have agreed that, in a purely abstract sense, mathematical axioms are arbitrary. Some mathematicians have created types of ‘arithmetic’ which are either inconsistent (as noted in the book you linked to) or limited (as also noted in the book you linked to). So, so far, no one has been able to show me an alternative, consistent form of arithmetic that differs significantly from ours that can be used to solve the same basic real-world problems.

But you thought: Oh, this hideous, awful atheistic materialist must be wrong; I’m going to find something that looks like it contradicts him.

I’m talking about mathematics, you seem to think that has something to do with world views and theology.

It doesn’t. It’s just mathematics. That is not subject to theology or philosophy or any world views.

ET: Wow. Jerad I understand that English confuses you. Variables make mathematics FLEXIBLE.Variables just take the place of unknown quantities. They don’t change the basic underlying mathematical structures. The can be replaced with real values or functions or . . . whatever they are standing in place of.

Clearly you just don’t understand what variables do. The don’t change basic, underlying mathematics.

Why don’t you get an education that allows you to think. Then perhaps we can talkI have done. Now I’m waiting for you to catch up.

I notice you haven’t even bothered to read the book excerpts that

Bornagain77linked to. Perhaps you should try and do that before you offer an opinion.Why doesn’t everyone try to define mathematics. It may be why people keep talking past each other.

I’ll give you a hint. No one can define it.

Ask yourself what is a number? I once wrote a paper on this for a philosophy class. For example what is the number three.

Jerry For example what is the number three.

That’s easy. It is 1/14th the answer to life, the universe and everything.

JVL, You claim that mathematics has nothing to do with the theology, i.e. the ‘miraculous’ and/or with God. You also claim I know nothing about mathematics since I think it does. (i.e. fallacious ‘argument to the man’) The quotes from Einstein and Wigner are unambiguous. THEY disagree with you. They hold it to be miraculous that mathematics should be applicable to the universe, and Einstein even went so far as to chastise ‘professional atheists’ in the process of calling it a miracle. I will take their word over your word any day of the week since you are merely an atheistic troll on the internet with, as far as I can tell from my limited interaction with you, an agenda. Seeking to score points no matter how dishonest you have to be, and in comparison to you, they, both Einstein and Wigner, are, frankly, both mathematical geniuses in their respective fields who’s shoes you are not worthy to tie.

Now define the number 17. And then define “1/14th” and life and universe.

LoL! @ JVL! Get a dictionary and look up the word “flexible”. To catch up with you would require I get a lobotomy.

Jerry:

My fav answer is a mod from my first Uni Math Prof, Harald Neiderreiter of Austria:

[the study of] the logic of structure and quantity.The first part is our part, where we can get partly creative.

The second is substance, connected to possible worlds and particularly logic-model worlds — including our actualised world. Where, it turns out there are Math facts that are self evident and/or discoverable that are antecedent to axiomatisations C19 – 20 style. Where, too, if a proposed axiomatic system is incompatible with core math facts it simply will gain no traction, often because it becomes an incoherent chaos.

Such would be rejected.

As for my comments above, I am pointing out that we need to ask how worlds become possible, given that utter nothingness would be permanent were it ever to obtain as non-being has no causal powers. Similarly, circular retrocausality is trying to pull an original world out of the not yet, i.e. from non being. Likewise, a proposed endlessly successive past of stages [years for simplicity] cannot be traversed stepwise to now. We are left with a finitely remote, necessary being world root capable of causing worlds with rational creatures capable of freedom to reason.

Such leads to huge logic of being consequences.

So, we need a reality root to get to possible worlds and the actual one. That in any possible world N, Q, Z, R, C will be with much consequent on that, is downstream of how do we get to possible worlds including an actual one with creatures capable of doing Mathematics.

KF

PS: See my onward discussion here https://journals.blythinstitute.org/ojs/index.php/cbi/article/view/62/59

Bornagain77:You are welcome to take whatever text or quotes you find most enlightening as definitive. The quotes and opinions are peripheral to the mathematics though.

I still haven’t seen a consistent, alternative form of mathematics that can handle all the simple and basic issues humans needed to deal with thousands of years ago. I do not think it’s possible to have a system of mathematics that meets those criteria markedly different from what we’ve got. I am open to any counter example anyone wishes to present but, so far, no one has presented one.

MMT, see the just linked, noting how N etc are necessary abstracta embedded in what it takes to get to a distinct possible world. Also, following von Neumann (another Austrian, there is a theory about a Martian settlement . . .):

{} –> 0

{0} –> 1

{0.1} –> 2

{0,1,2} –> 3. . .

{0,1,2,3 . . .} –> w, first transfinite ordinal.

And, oddly enough the logic of being import lurking behind such does point to the roots of reality, thus the meaningfulness of our observed cosmos.

KF

JVL, you are being evasive on central issues again. KF

ET: LoL! @ JVL! Get a dictionary and look up the word “flexible”. To catch up with you would require I get a lobotomy.I notice you haven’t addressed the book

Bornagain77linked to. Of course he won’t call you on it ’cause you guys scrupulously choose not to criticise each other. But I will assert that the mathematics in that book is above the level that you andBornagain77can deal with. You can prove me wrong, if you have the ability. I’m betting you won’t even try.I’ll wait and see what you do.

Kairosfocus: JVL, you are being evasive on central issues again.Really? Can you provide an example of a consistent system of arithmetic that is significantly different from ours that can still handle the same basic problems our system does?

This has nothing to do with theology. This has nothing to do with values. This is pure mathematics.

RP, 147 above may help. JB’s related article here may further help. KF

JVL, side tracking evasion pivoting on setting up and knocking over a strawman. I point you to 85 above. KF

JVL:

Am I supposed to care about this book? Does it have any affect on my life?

And yet we have had at it a few times. Strange, that.

Am I supposed to care what you assert? You can’t even grasp the language you use. You don’t seem to understand infinity. You may have taken more advanced mathematics than I have. It definitely hasn’t helped you form a coherent argument nor understand what other people are saying.

ET: Am I supposed to care about this book? Does it have any affect on my life?It may mean you’re not up to the conversation.

Am I supposed to care what you assert? You can’t even grasp the language you use. You don’t seem to understand infinity. You may have taken more advanced mathematics than I have. It definitely hasn’t helped you form a coherent argument nor understand what other people are saying.There is another interpretation. that you don’t quite grasp the concepts involved. Perhaps if you could be bothered to look at some of the references given we might be able to make a determination of your capacity.

Kf,

Mathematics is essentially logic. It will exist as such in any world we can dream of. Is there a world where logic does not hold?

I was in a PhD program in math and we had a discussion on just what math was and essentially what came out of it was that math is logic. None of the professors or students could define it otherwise.

I made the point above that the only numbers that exist are positive integers and in reality they are in our head too. They are not in nature though we can certainly count but for that we have to have a concept of what is meant by number. In our universe there are no negative numbers, no pi, no e, no rational or irrational numbers, nothing infinite nor anything infinitely small.

As I said above they are extremely useful but are just in our head. We can write all the equations, symbols and terminology we want but they are all just abstract creations. Extremely useful but not real.

Kairosfocus: JVL, side tracking evasion pivoting on setting up and knocking over a strawman. I point you to 85 aboveI have been very clear in my statements and questions. Perhaps you’d like to actually address the issues I have raised? Especially considering I find your comments in #85 above to be a bit off topic, to be honest.

As expected, JVL hand waves off Einstein and Wigner and pretends he has a more expert opinion than they on mathematics and how it relates to the universe. Hubris is too mild a term.

Bornagain77: As expected, JVL hand waves off Einstein and Wigner and pretends he has a more expert opinion than they. Hubris is too mild a term.🙂 It’s okay with me if you have consistently failed to address my questions and challenges with pointless references and digressions.

As I said before: your mathematics ability is clearly not up to the task. Being able to copy and paste just doesn’t cut it.

JVL responds with a lie, a ad hominem, and another hand wave. Pathetic.

Jerry, yes the logic of structure and quantity. KF

JVL, the questions have been digressions and have ignored substantial, relevant remarks. KF

JVL:

With you? No thanks.

Or you’re just horse’s arse.

I do NOT care about your irrelevant tangent. I have much better things to do.

It’s as if there are two different conversations- 1) What people say and 2) What JVL responds with which usually has nothing to do with 1.

ET, language. KF

As to the ‘miracle’ that directly faces us in the applicability of mathematics to the universe, (via Einstein and Wigner).

Ever since modern science was born in medieval Christian Europe, scientists have had a history of looking for ‘platonic perfection’ in our mathematical descriptions of the universe, and assuming the Mind of God to be behind that ‘platonic perfection that was being sought after’.

That is to say, that science has had a history of reaching for perfect agreement between the immaterial mathematics that might describe a certain facet of this universe and the experimental results that measure those mathematical predictions. And assuming God to be behind the assumed platonic perfection that was being sought after.

Copernicus, (who was heavily influenced by Platonic thinking), imagined (incorrectly) that the planets move in perfect circles (rather than ellipses).

Later, when Newton was challenged with the extreme mathematical difficulty of multiple orbits (perturbation theory), and for allowing God could adjust the orbits of the planets, was chastised by Leibniz, (and even by Laplace) for having “very narrow ideas about the wisdom and the power of God.”.. i.e. For having a narrow view of the perfection of God.

As a side-note, I hold that Newton, Leibniz, (and even Laplace himself), would be very pleased with what modern science has now revealed about the wisdom and power of God in setting up the solar system.

But anyways, back to the topic at hand, for most of the history of modern science in the Christian west, finding ‘platonic perfection’, i.e. perfect agreement, between our mathematical predictions for the universe, and our experimental measurements of those mathematical predictions, has been a very elusive goal. The primary example being Newton’s theory of gravity, (which I remind was based on Euclidean geometry), and the failure to describe the precession of Mercury’s orbit within the Euclidian geometry of Newton’s theory.

This lack of perfect agreement between our mathematical predictions for the universe, and our experimental observations of those mathematical predictions, all changed with the discoveries of the 4-dimensional spacetimes of Special Relativity & General Relativity, and the discovery of the infinite dimensional Hilbert space of Quantum Mechanics. That is to say, as far as experimental testing will allow, there is no discrepancy to be found between what the higher dimensional mathematical descriptions of Relativity and Quantum Mechanics predict and what our most advanced scientific testing of those predictions are able to measure.

As well, quantum electrodynamics (QED), which is a combination of special relativity and quantum mechanics, also now joins the list of perfect mathematical descriptions of the universe in which we can find no deviation from what the mathematics predict and what our best experimental testing can discern. In other words, as far as we can tell, ‘platonic perfection’ is reached for QED:

This point was driven further home with the discovery of the hypergeometric object of the amplitudhedron:

As Nima Arkani-Hamed himself, the discoverer of the amplituhedron, stated “It seems inconceivable that this intricate web of perfect mathematical descriptions is random or happenstance. This mystery must have an explanation.”,,,

And as was already mentioned previously in this thread, another very important place where ‘platonic perfection’ is now shown to be ‘perfectly reached’ in the universe, (as far as our most precise testing will allow), is for the ‘flatness’ of the universe.

Moreover, this ‘insane coincidence’ of ‘plantonic perfection’ being reached for the axiomatic ‘primitive object’ of the line just so happens to be necessary for us to even be able to practice math and science, (and apply technology in our world), in the first place:

Simply put, if the universe were not ‘ever-so-boringly’ flat (and if the universal constants were not also ‘ever-so-boringly’ constant), but the universe were instead governed by randomness, as atheists presuppose, or governed by some other of the infinitude of ‘platonic topologies’ that were possible, modern science and technology would have never gotten off the ground here on earth.

Nor, if platonic perfection were not present for the flatness of the universe would we have eventually been able to deduce the ‘platonic perfection’ that is revealed in the ‘higher dimensional’ mathematics that lay behind Relativity and Quantum Mechanics.

More interesting still, these findings of ‘platonic perfection’ for the higher dimensional mathematics that lay behind Relativity and Quantum Mechanics are VERY friendly to overriding Christian presuppositions of life after death as well as the presupposition of God upholding this universe in its continual existence.

For an example of just how friendly this ‘platonic perfection’ is to Christian presuppositions, let’s look at special relativity and general relativity in particular.

There are a couple of thought experiments that Einstein utilized to work out the basics of special relativity and then general relativity.

In the first thought experiment for special relativity, Einstein imagined that he was riding on a bus near the speed of light,

Whereas in his second thought experiment, which he termed ‘the happiest thought of my life’, Einstein imagined a man freely falling in an elevator:

And similar to when time, as we understand it, comes to complete stop in Special Relativity when we reach the speed of light, in General Relativity time, as we understand it, also comes to a complete stop when we reach what is termed to be the ‘event horizon’ of a black hole, As wikipedia states, “Travel to regions of space where extreme gravitational time dilation is taking place, such as near a black hole, could yield time-shifting results analogous to those of near-lightspeed space travel.”

It is important to point out that these ‘eternities’ found at both Special Relativity and General Relativity have fairly direct theological implications. As Dr. Richard Swenson states,

Einstein himself seemed to concede this theological implication of his theory when he, upon his good friend Michele Besso’s death, stated that, “Now he has departed from this strange world a little ahead of me. That signifies nothing. For those of us who believe in physics, the distinction between past, present and future is only a stubbornly persistent illusion.”

And in what was, basically, an extension of Einstein’s thought experiment for General Relativity, Kip Thorne worked out what would happen to a hypothetical astronaut who was unfortunate enough to fall into a black hole,

In short, what makes the eternity of General Relativity profoundly different than the eternity found at Special Relativity, is that the entropy associated with Special Relativity is extremely ordered whereas the entropy associated with General Relativity is extremely chaotic

In fact, gain in entropy, which is the primary reason why our material bodies grow old and eventually die in this universe,,,

,, gain in entropy is found to be greatest at black holes. As the following article stated,, ‘supermassive black holes are the largest contributor to the observable universe’s entropy.’

Thus the ‘eternity’ that is found at a black hole can rightly be called an ‘eternity of decay, death, and destruction’.

Needless to say, to those of us who are of, shall we say, a spiritually minded persuasion, this finding of an eternity of destruction and decay should be fairly sobering.

To continue on, the evidence from Special Relativity, (which is currently one of our most powerful theories in science), strongly supports the physical reality of a timeless eternity and of a heavenly dimension that exists above this temporal dimension. The timeless eternity aspect of both Special and General Relativity was already covered in this post. ,,, so to continue on, the only way it is possible for time not to pass for light, and yet for light to move from point A to point B in our universe, is if light is of a higher dimensional nature of time than the temporal time that we are currently living in. If this were not the case, then light would simply be ‘frozen within time’ to our temporal frame of reference.

And indeed that is exactly what we find. “Hermann Minkowski- one of the math professors of a young Einstein in Zurich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space.” In fact, Hermann Minkowski’s work in higher dimensional mathematics proved to be vital for Einstein in his eventual formulation of General Relativity.

One way for us to more easily understand this higher dimensional framework for time that light exist in is for us to visualize what would happen if a hypothetical observer approached the speed of light.

In the following video clip, at around the 2:40 minute mark, (a video which was made by two Australian University Physics Professors), we find that the 3-Dimensional world ‘folds and collapses’ into a tunnel shape as a ‘hypothetical’ observer approaches the ‘higher dimension’ of the speed of light.

Interestingly, as was visualized at the 3:00 minute mark of the preceding video, (i.e. all of the light concentrating into the direction of travel, i.e. the light visualized at the ‘end of the tunnel’ in the video), is termed to be the ‘headlight effect’

Now that we have outlined the basics of what we know to be physically true from special relativity, It is very interesting to note that many of the characteristics found in heavenly Near Death Experience testimonies are exactly what we would expect to see from what we now know to be physically true about Special Relativity.

For instance, many times people who have had a Near Death Experience mention that their perception of time was radically altered. In the following video clip, Mickey Robinson gives his Near Death testimony of what it felt like for him to experience a ‘timeless eternity’.

And here are a few more quotes from people who have experienced Near Death, that speak of how their perception of time was radically altered as they were outside of their material body during their NDEs.

As well, Near Death Experiencers also frequently mention going through a tunnel, towards an extremely brilliant light, to a higher heavenly dimension:

In the following video, Barbara Springer gives her testimony as to what it felt like for her to go through the tunnel towards ‘the light’:

And in the following audio clip, Vicki Noratuk, who has been blind from birth, (besides being able to ‘miraculously” see for the first time in her life during her Near Death Experience), Vicki also gives testimony of going through a tunnel at a ‘horrifically’ rapid rate of speed:

And in the following quotes, the two Near Death Experiencers both testify that they firmly believed that they were in a higher heavenly dimension that is above this three-dimensional world, and that the reason that they have a very difficult time explaining what their Near Death Experiences actually felt like is because we simply don’t currently have the words to properly describe that higher dimension:

That what we now know to be true from special relativity, (namely that it outlines a ‘timeless’, i.e. eternal, dimension that exists above this temporal dimension), would fit hand and glove with the personal testimonies of people who have had a deep heavenly NDEs is, needless to say, powerful evidence that their testimonies are, in fact, true and that they are accurately describing the ‘reality’ of a higher heavenly dimension, that they experienced first hand, and that they say exists above this temporal dimension.

I would even go so far as to say that such corroboration from ‘non-physicists’, who, in all likelihood, know nothing about the intricacies of special relativity, is a complete scientific verification of the overall validity of their personal NDE testimonies.

It is also interesting to point out that, although Special Relativity can be unified with Quantum Mechanics, that General Relativity simply refuses to ever be mathematically unified with quantum mechanics in any realistic way,

In fact, mathematically speaking, there is found to be an ‘infinite divide’ between General Relativity and Quantum Mechanics that forever prevents them from being unified mathematically.

Professor Jeremy Bernstein states the situation as such, “there remains an irremediable difficulty. Every order reveals new types of infinities, and no finite number of renormalizations renders all the terms in the series finite.”

Considering the ‘infinitely’ chaotic entropy associated with General Relativity, this mathematically ‘infinite divide’ between General Relativity and Quantum Mechanics reminds me very much of this quote from scripture concerning the rich man finding himself in hell and pleading with Abraham to get him out.

But anyways, to continue on, the ‘zero/infinity’ conflict between General Relativity and Quantum Mechanics has some fairly disturbing theoretical implications. Specifically, when theorists try to combine the two theories, then the resulting theory predicts that spacetime, atoms, and even the universe itself should all be literally blown apart.

https://uncommondescent.com/intelligent-design/at-quanta-how-gravity-differs-from-the-other-three-fundamental-forces/#comment-704725

And yet, despite both theories contradicting each other to the point of literally blowing the universe apart, quantum mechanics and general relativity are both tested to extreme levels of precision, (in fact, both general relativity and quantum mechanics are consider to be our most successful theories ever in the history of science), as was referenced previously,,,

And since quantum mechanics and general relativity are both tested to such an extreme level of precision, (and we can thus have a very high level of confidence that both theories are, in fact, true mathematical descriptions of reality), and since Godel’s incompleteness theorem itself requires something to be ‘outside the circle’ of mathematics,,,,

,,, then it is fairly safe to assume that there must be something very powerful that must be holding the universe together in order to keep it from blowing itself apart. ,,,

For the Christian this theoretical finding from our very best theories in science, (i.e. that something very powerful must be ‘outside the universe’ that is holding this universe together), should not be all that surprising to find out. Christianity, a couple of millennium before the zero/infinity conflict between the two theories was even known about, predicted that Christ is before all things, and in him all things hold together,,,

Dr. William Dembski in this following comment, although he was not directly addressing the Zero/Infinity conflict between General Relativity and Quantum Mechanics, offers this insight into what the ‘unification’ of infinite God and finite man might look like mathematically:

Moreover, if we rightly let the Agent causality of God ‘back’ into the picture of modern physics, as the Christian founders of modern science originally envisioned,,,, (Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders of modern science),,, and as quantum mechanics itself now empirically demands (with the closing of the free will loophole by Anton Zeilinger and company), rightly allowing the Agent causality of God ‘back’ into physics provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead provides an empirically backed reconciliation, via the Shroud of Turin, between quantum mechanics and general relativity into the much sought after ‘Theory of Everything”. Here are a few posts where I lay out and defend some of the evidence for that claim:

To give us a small glimpse of the power that was involved in Christ’s resurrection from the dead, the following recent article found that, ”it would take 34 Thousand Billion (trillion) Watts of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.”

Verse:

@JVL 158 heavens to betsy there is a lot of jabbering where there is little substance.

RP & JVL:

As by direct import of reference, after a late intervention, I am being targetted for dismissal without serious examination of the substance (over years, an all too familiar tactic in dealing with design thinkers . . . ) I again point you to 85 above and to the onward linked note here and JB’s more popular level article here.

I particularly clip from 85:

Clearly, the issue is NOT, whether one can propose an alternative arithmetic. We have on the table several frameworks that get us to Arithmetic, I usually favour von Neumann’s approach. No alternative axiomatic framework that is inconsistent with long known, pre-axiomatisation facts (a core of which are self evident of order || + ||| –> ||||| which we conveniently symbolise 2 + 3 = 5) would be generally accepted. Similarly, as I showed in my paper the answer to Wigner is that as there is a core of mathematics — logic of structure and quantity — that pivots on requisites of distinct identity of any PW W marked apart from a close neighbour W’, then there is a core trans-world applicability of that core, which embraces the structured sets . . . hence, many familiar key relationships, operations and functions . . . N, Z, Q, R, C etc. This structure, quantity and logic are a cluster of abstract necessary entities and structured relationships that lead to what Wigner marvelled at.

However, that does not end the matter, as I just clipped: how do we get to possible worlds?

Not from utter non-being, nor from a transfinite past succession of finite duration stages [years, for simple short], nor from circular retrocausality. That leaves a bill of requisites for the world root: independent being [so, necessary], causally adequate to worlds such as ours existing with freely thinking creatures capable of doing Math [i.e. rational, responsible, morally governed, significantly free], finitely remote.

A familiar — but too often these days, unwelcome and/or unfashionable — figure looms as the only truly serious candidate. Which, is the real problem. Math and linked logic of being are pointing where many refuse to go.

As at now, the two of you are in danger of slipping into the zero credibility, unserious carping, sneering commenter ilk. Do you really want to go there?

Please, do better than that.

KF

PS: On traversal of the transfinite, there was a three years long series of exchanges here at UD. The matter is readily resolved once it is recognised that a lot of talk about number lines and continua makes better sense if we accept that people — such as HS Math teachers — are often implying the hyperreals not the reals, R*/*R being mileposted by the hyperintegers. It is then trivial to see that stepwise ascent from a transfinitely remote claimed actual past cannot span a transfinite intervening range. And there is no evading that the structure of Z mileposting R includes the direct import that it cannot be spanned in stepwise succession, hence the use of ellipses of continuation L-ward and R-ward: { . . . -2,-1,0,1,2 . . .}. Much of the debate, per fair comment, boiled down to refusal to admit the hyperreals and/or to accept that Z’s structure implies that spanning of the transfinite supertask.

What do you get when you cross an elephant with a grape? |elephant||grape|sin(theta).

I am happy to let the whole matter drop. I’m just here to talk about the mathematics not the theology or philosophy. Discussing axiomatic systems is not theology or philosophy.

JVL, you raised a question that goes beyond axiomatisation and raises the sorts of issues I addressed from 85. Perhaps, you have not seen that the Godel results relativised any axiomatisation of a reasonably complex body of mathematics? Axiomatisation is incomplete or incoherent, and there is no constructive process to build a known coherent axiomatisation. The grand axiomatisation agenda of 100+ years ago has long since been dead. As for links to logic of being and to reality roots, they are inherent in mathematics once the Wigner challenge of the bridge to physics is on the table. Indeed, historically a lot of mathematics arose from physics and to address physics. Logic of being issues include what accounts for a world involving rational, responsible, significantly free, thus morally governed creatures. KF

Kairosfocus: Axiomatisation is incomplete or incoherent, and there is no constructive process to build a known coherent axiomatisation.I don’t think that’s exactly what Godel’s incompleteness theorems say.

You seem to be using the word ‘coherent’ in place of the clearer word ‘consistent’. Neither theorem says axiomatisation is incomplete or inconsistent: the first theorem says that IF system is consistent then it will be incomplete but it does not say that a complete system will be incoherent. The second theorem says the consistency of axioms cannot be proved within their own system which is roughly consistent with your phrase that there is no constructive process to build a known consistent axiomatisation. Anyway, my point is that the subtle points matter. A lot of people ascribe things to Godel that aren’t the case so it’s important to get it right.

Logic of being issues include what accounts for a world involving rational, responsible, significantly free, thus morally governed creatures.Nothing to do with mathematics so I won’t comment further.

“What do you get when you cross an elephant with a grape? |elephant||grape|sin(theta).”

One of my very favorite math/physics jokes.

I am sensing a bromance…

JVL:

I note from your clip:

With my addition that we speak of complex domains, that is essentially what I said. Inconsistency and incoherence here effectively mean the same. Note here, the principle of explosion. You are making up an objection out of nothing.

And BTW, once we see that Mathematics is in effect substantially the logic of structure and quantity, logic of being has everything to do with Mathematics and its foundations, as well as with the existence of creatures able to do mathematics with some confidence that they are in fact rational. Those things then make issues of axiomatisation and what comes before such — to which axiomatisations answer — highly relevant. With Godel’s work a capital example.

KF

Kairosfocus: With my addition that we speak of complex domains, that is essentially what I said. Inconsistency and incoherence here effectively mean the same. Note here, the principle of explosion. You are making up an objection out of nothing.I am insisting that correct and proper terminology is used. I don’t think that inconsistency and incoherence mean the same thing and I encourage you to use the accepted forms to avoid misunderstanding.

Those things then make issues of axiomatisation and what comes before such — to which axiomatisations answer — highly relevant. With Godel’s work a capital example.Whatever. You would do better getting your points across if you wrote more plainly.

Eugene Wigner, who rightly considered the applicability of mathematics to the universe to be a ‘miracle’, won a Nobel prize for his work in quantum mechanics in 1963,

Here is Wigner commenting on the key experiment that led Wigner to his Nobel Prize winning work on quantum symmetries,,, “As the observer is replaced by another observer (working elsewhere, looking at a different direction, using an other clock, perhaps being lefthanded), the state of the very same particle is described by another vector, obtained from the previous vector by multiplying it with a matrix. This matrix transfers from one observer to another.,,,”

Wigner’s insights into the foundations of quantum mechanics, continue to drive breakthroughs,

For instance of Wigner’s insights into the foundations of quantum mechanics continuing to drive breakthroughs, Wigner’s thought experiment, “Wigner’s friend’, was recently experimentally realized in 2019,

“Wigner’s friend” thought experiment made its first appearance in this following 1961 paper where Wigner stated, “”It will remain remarkable, in whatever way our future concepts may develop, that the very study of the external world led to the scientific conclusion that the content of the consciousness is the ultimate universal reality” –

And in 1970 Wigner further stated that,,

The experimental realization of Wigner’s claim that “the content of the consciousness is the ultimate universal reality”, was foreshadowed, ‘philosophically’, by other giants in quantum mechanics,

In fact, Wigner himself considered the philosophical argument for the primacy of consciousness to be more powerful than the fact that materialism is experimentally found to be incompatible with quantum theory,

But anyways, in his 1960 paper where he considered that the applicability of mathematics to the universe to be a miracle, Wigner stated that, “We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity.,,, The two theories operate with different mathematical concepts: the four dimensional Riemann space and the infinite dimensional Hilbert space,?”

Since I have already covered, in posts 168 through 170, how the “four dimensional Riemann space” of Relativity is very friendly to Christian presuppositions, I will now cover how the infinite dimensional Hilbert space is also very friendly to Christian presuppositions,

In its ‘uncollapsed’ state, a particle, and/or a photon, is mathematically described as being in an infinite dimensional state,,,

,, an infinite dimensional state that also takes an infinite amount of information to describe properly.

Now, saying something is in an infinite dimensional state to me, as a Christian Theist, certainly sounds very much like the theistic attribute of omnipresence to me.

And then saying something takes an infinite amount of information to describe, as a Christian, certainly sounds very much like the Theistic attribute of Omniscience to me.

Now all this is pretty much exactly what we would expect to see under Christian presuppositions. But, on the other hand, under Atheistic materialism and/or naturalism, and the presuppositions therein, there simply is no rational explanation for why we should find these infinite dimensional/infinite information mathematical definitions to be as they are.

Moreover, the basics of quantum wave collapse dovetail perfectly into some of the oldest philosophical arguments that were made by Aristotle and Aquinas for the existence of God, and even offers empirical confirmation for those ancient philosophical arguments. Michael Egnor states that ‘Aristotle 2,300 years ago described the basics of collapse of the quantum waveform (reduction of potency to act),,,’

Here is a technical explanation and video of Aquinas’ First way argument for God where you can, at your leisure, see just how well the argument from motion dovetails into what we are seeing in quantum mechanics

Or to put Aquinas’ argument much more simply “The ‘First Mover’ is necessary for change occurring at each moment.”:

Again, all this fits hand in glove with Christian presuppositions about infinite and almighty God sustaining this universe in its continual existence,,,

Thus, Christians, despite what atheists may claim, certainly have no problem with the findings of modern science. In fact, despite their claims to the contrary, it is the atheist himself who finds his foundational beliefs about reality to be directly challenged by the findings of modern science.

Why Atheists would fight tooth and nail against what is such a wonderful thing, i.e. that God is really real, I have no idea. Frankly, I find the basics of quantum mechanics much easier to understand than why atheists would fight so hard against what Is such a wonderful realization, i.e., that God is really real!

Such irrational hatred of God, who they claim does not exist, is simply completely unreasonable.

JVL, first, I gave a summary in a blog, not a detailed theorem statement. In that context, incoherence takes in inconsistency and its immediate corollary effects per principle of explosion. A “complete” axiom system for a complex enough domain will be inconsistent; immediately, per explosion, the system is incoherent and so unsafe; we for cause routinely use reductio ad absurdum as a means of disproof by contradiction. That is, we see here disintegration and disjointedness of a system. Your tangent game is duly noted as making mountains out of nothing. And, it is clear enough that you refuse to look at the logic of being issues that directly connect to the mathematics, once we recognise that substantially, Math is the logic of structure and quantity. A Possible Worlds approach, as I linked, is fruitful on that, drawing out necessary facts of math that are antecedent to axiomatisation. As a human endeavour, it is again fruitful: the study of the substance. This instantly leads to how do we get to creatures capable of freely reasoning so they can credibly, confidently explore and study that substance. That again points to roots of reality and matters ontological. KF

PS: Statements

First Incompleteness Theorem: “Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.” (Raatikainen 2015)

Second Incompleteness Theorem: “Assume F is a consistent formalized system which contains elementary arithmetic. Then F [stroke-entail] Cons ( F ) .” (Raatikainen 2015)

Kairosfocus: first, I gave a summary in a blog, not a detailed theorem statement. In that context, incoherence takes in inconsistency and its immediate corollary effects per principle of explosion.Principle of explosion? What is that?

A “complete” axiom system for a complex enough domain will be inconsistent; immediately, per explosion, the system is incoherent and so unsafe; we for cause routinely use reductio ad absurdum as a means of disproof by contradiction.The first incompleteness theorem DOES NOT say that any complete system will be inconsistent. It just doesn’t. It says: If a (logical or axiomatic formal) system is consistent, it cannot be complete.

The second incompleteness theorem says, roughly: The consistency of axioms cannot be proved within their own system. That doesn’t mean the system is complete or inconsistent.

Proof by contradiction doesn’t work that way. If, according to the first theorem: C (consistent) -> -K (not complete) . You can attempt to prove that by contradiction but you then have to demonstrate that K -> -C. If that’s what you’re trying to say then please make things clearer instead of like this:

Then F [stroke-entail] Cons ( F )Your tangent game is duly noted as making mountains out of nothing.I am trying to make sure the mathematics is represented correctly. If I think you’ve misrepresented it then I will say so. It’s nothing person. You do the same when I say something you find incorrect.

And, it is clear enough that you refuse to look at the logic of being issues that directly connect to the mathematics, once we recognise that substantially, Math is the logic of structure and quantity. A Possible Worlds approach, as I linked, is fruitful on that, drawing out necessary facts of math that are antecedent to axiomatisation. As a human endeavour, it is again fruitful: the study of the substance. This instantly leads to how do we get to creatures capable of freely reasoning so they can credibly, confidently explore and study that substance. That again points to roots of reality and matters ontologicalI think I’ll just stick to what the established mathematics actually says if that’s okay.

JVL states:

Save, of course, for when ‘established mathematics’ says that the origin of life, and subsequent evolution of life, by unguided processes is mathematically impossible, Then, of course, ‘established mathematics’ can be safely ignored by JVL.

JVL, your grudging retreat tells us the balance on merits. You and those in the penumbra of attack sites cannot evade the issue of where possibility of worlds comes from, especially worlds with creatures with rational, thus morally governed, freedom to confidently do Mathematics. That tells us a lot. KF

Bornagain77: Save, of course, for when ‘established mathematics’ says that the origin of life, and subsequent evolution of life, by unguided processes is mathematically impossible, Then, of course, ‘established mathematics’ can be safely ignored by JVL.That’s someone applying mathematics to a particular situation. They may or may nt be doing so correctly. Personally I don’t think evolution via unguided processes has been ruled out and certainly not by some mathematical argument.

Kairosfocus: your grudging retreat tells us the balance on merits. You and those in the penumbra of attack sites cannot evade the issue of where possibility of worlds comes from, especially worlds with creatures with rational, thus morally governed, freedom to confidently do Mathematics. That tells us a lot.Oddly enough, I wasn’t even addressing that issue. I was just talking about the mathematics.

JVL:

Great. We await your refutation of “Waiting for TWO Mutations”. Because that paper definitely rules out unguided processes ability to account for the diversity of life via a mathematical argument.

JVL,

“Personally I don’t think evolution via unguided processes has been ruled out and certainly not by some mathematical argument.”

Of course you don’t because, as I pointed out, you believe math can be safely ignored whenever it conflicts with your atheistic worldview.

i.e. When the ontology of math points to God, you ignore it. Likewise, when the implications of math point to God, you also ignore them.

Such denial of facts is rampant throughout arguments from Darwinian atheists.

Such a mindset is called ‘denialism’, i.e. the denial of reality, and the denial of reality is certainly not a coherent argument, as you seem to think that it is, but is instead considered a mental illness.

ET: Great. We await your refutation of “Waiting for TWO Mutations”. Because that paper definitely rules out unguided processes ability to account for the diversity of life via a mathematical argument.There have been plenty of discussions of that paper and its ramifications; I don’t think I can add anything significant. I do note, however, that mainstream biologists are not fleeing the ship of unguided evolution because of that paper. Food for though eh?

Bornagain77: Of course you don’t because, as I pointed out, you believe math can be safely ignored whenever it conflicts with your atheistic worldview.Or, it’s because I disagree with your use and interpretation of the mathematics.

i.e. When the ontology of math points to God, you ignore it. Likewise, when the implications of math point to God, you also ignore them.I’m not ignoring anything; I simply disagree with your interpretation of the mathematics.

Such denial of facts is rampant throughout arguments from Darwinian atheists.And they would say you’re mistinterpreting the mathematics.

Such a mindset is called ‘denialism’, i.e. the denial of reality, and the denial of reality is certainly not a coherent argument, as you seem to think that it is, but is instead considered a mental illness.It’s not denialism if I am right is it?

Why does it bother you so much that I disagree with you? Who cares? I don’t particularly care if you agree with me or not. I find it interesting to know how you see the data and the math but I don’t expect (nor am I trying) to change you or your view.

JVL,

The evasiveness continues, so let’s roll the tape to part of why I intervened, your comment at 79 above:

H’mm, it looks a whole lot like at that point you were interested in logic of being and reality root issues, once you could assert confidently that Math stands independent of any world-designer.

So, your retreat from that assertion once challenged on those subjects you are suddenly no longer interested in is as Mr Spock says, “interesting.”

As, once a serious logic of being challenge was put up in response to your attempt to imply that those who suggested above that God is responsible for the Mathematical framework of reality run into the roadblock of core Mathematics having independent necessary character you retreated to a fallback of only being interested in the Math.

Only, the tape sez different.

(From 85 on I first rebalanced the exchange, as there are structural and quantitative aspects of reality framework to any/all worlds and particular fine-tuned aspects relevant to a viable world amenable to C-chem, aqueous medium, terrestrial planet in galactic and circumstellar habitable zone life. With further constraints to get to significantly free, rational — thus, morally governed — creatures capable of credibly, confidently doing Mathematics and similar intellectual endeavours.)

You were asking also for a different Arithmetic, presumably a completely alien axiomatised framework.

I showed, by pointing and summarising from published work, that

there are Math realities antecedent to any axiomatisation (which, since Godel, has had a bit of the shine taken off the new ball).andthat such things . . . e.g. N,Z,Q,R,C etc with linked relationships, structures, properties . . . are tied to what it takes per logic of being for there to be a distinct possible worldThus, the directly tied — so, highly relevant and even decisive — logical issue is,

how are such PW’s possible? How does the P get there?That, takes us to reality root, and in particular, we see how on logic of being:(This last is best seen by using the hyperreals mileposted by hyperintegers. Where, say HS Math teachers and the like . . . Engineers, Physicists in many cases [from Newton etc on], etc . . . using the intuitive number line on balance, are better understood as speaking intuitively in the hyperreals context. Such even arguably rehabilitates a good part of Euler’s thinking etc. Infinitesimals, suitably tamed, are back. Arguably, as part of the framework structure-quantity infrastructure for all PW’s. Where, once an infinitesimals cloud surrounds 0, *0*, we then can infinitestimally alter any r in R by vector displacement of the cloud *0* to superimpose on r yielding *r*, an infrastructure closer to r than a similarly shifted 1/n for any n in N and its negative -1/n. This is tied to nonstandard analysis and the ubiquity of Calculus in physics, including our habitual treatment of infinitesimals as a valid meaning of dr. This is of course directly connected to Wigner’s marvelling, as what is in any PW applies to our world, and extends to any coherent suggested framework for a world.)

Such leaves one serious candidate in the room:

the P in PW gets there through a finitely remote, causally independent — thus necessary — reality root being framework to any world.Mathematical entities framework to any PW are not independent of there being a reality root.In that context, your retreat into of you are just interested in the Math, is an interesting result. Indeed, on the just rolled tape, it is a disguised retreat.

Of course, with implications for your credibility in arguments you have been making here at UD.

KF

JVL, and disagreeing for the sake of disagreeing, minus any coherent argument to the contrary, and being nonchalant about the fact that your belief is not rooted in reality, i.e. “Who cares?”,,, is suppose to be different from the mental illness of denialism how exactly?

As mentioned previously, denialism, i.e. the denial of reality, is rampant in the arguments used by Darwinian atheists.

Although the Darwinian atheist firmly believes he is on the terra firma of science, (in his appeal, even demand, for methodological naturalism), the fact of the matter is that Darwinists are adrift in an ocean of fantasy and imagination with no discernible anchor for reality to grab on to:

Thus, although the Darwinian Atheist firmly believes he is on the terra firma of science (in his appeal, even demand, for methodological naturalism), it would be hard to fathom a worldview more antagonistic to modern science, indeed more antagonistic to reality itself, than Atheistic materialism and/or methodological naturalism have turned out to be.

BA77, you ask an excellent question which ties in with the bold assertions as just tape-rolled, then suddenly retreated from once challenged. Mental illness is maybe too strong, worldview induced blind spots is more specific. KF

@JVL The only math I’ve seen on this website is ET’s horrendous misunderstanding of set theory.

Kf, “Mental illness is maybe too strong, worldview induced blind spots is more specific.”

Nope, not too strong at all. To point out the obvious fact that Darwinian atheists are in the grip of the mental illness of Denialism is to hit the nail squarely on the head.

As alcoholics and drug addicts must come to grips with their own denialism, their own mental illness, that leads to their destructive lifestyles, in order to make a successful recovery, so to atheists, in order to ‘make a recovery’, must come to grips with their own denialism. i.e. their own mental illness that has destructive effects in their own personal lives, (and on society at large, i.e. abortion and the horrors of socialist/atheist ‘utopias’, i.e. Hitler, Stalin, Mao, etc.. etc..),

Of related interest, Thomas Nagel, who recognized the devastating implications of the hard problem of consciousness for Darwinism,,,,

,,,, although Nagel knew Darwinism must be false because of the ‘hard problem’ of consciousness, none-the-less, rejected God simply because God was a “a psychologically uncomfortable truth” for him. i.e. full blown Denialism!

Might I be so bold as to further suggest that Nagel’s guilty conscious is what compels him to try to hide from God?

I mean, you could’ve guessed this

https://www.psypost.org/2020/07/covidiot-study-lower-cognitive-ability-linked-to-non-compliance-with-social-distancing-guidelines-during-the-coronavirus-outbreak-57293

RP, first, you have obviously not monitored years of mathematical discussions here at UD. Second, on fair comment you have given half truth in order to belittle and denigrate; on the contrary to your suggestions in this thread, there is summary discussion and there are links to elsewhere where summary can be filled in, as I just exemplified again. Further to this the mention of hyperreals, infinitesimals and infinitesimally altered reals is an allusion to model theory and to linked nonstandard analysis. This includes how that brings the calculus firmly into the embrace of algebra, as JB has argued in these pages and elsewhere. Also, the intuitive number line, arguably is about the hyperreals not the reals, I have gone so far as to suggest these are more relevant to general math than the reals, at minimum as setting conceptual context in which we work, including habitual usage of Physicists that looks really sloppy without that context; well do I recall the dichotomy between routine use of dr, curly dr and improper d-bar [think d’q in thermodynamics] in Physics and the repeated R-driven, limits and epsilon-delta formulation in math that dr was not a number, worse dr/dt is not a ratio but a limit as abbreviated, only it LOOKS like it can be treated like algebraic fractions etc. I suspect also that you wish to dismiss cosmological fine tuning, which would be ill advised. KF

RP, you have posed a tangent, again one suggestive of the notorious Dawkins theme, ignorant, stupid, insane or wicked. In fact, it is notorious that the cognitively challenged can often be resistant to change (especially change where in a few weeks to a couple of months there was major flip-flopping and this tied to evidence of lying by medical authorities . . . undermining their credibility across the board). I note, personally, as one with asthma, prolonged wearing of masks is a struggle that is debilitating. Far more robust people than I am, speak of how it wears them down as they do heavy physical work. Then, there are the debates over just how effective such are at filtering in praxis, with what mechanisms. I favour electrostatic and van der Waals type forces so passing through a microfibre-forest raises odds of sticking to a fibre . . . with the “fuzz” on cloth threads or felted matrices highly significant . . . then being bound more tightly through polarisation, native or induced. On which, washing with detergent pulls out the trapped particles, also breaking up bilipid layers and perhaps hydrolysing proteins etc. Distancing at 6 feet was subject to a debate and raises issues that goggles are necessary, recall sneezes can entrain a spreading cloud up to the whole nine yards, including going over supermarket shelves and the issue of long suspended particles. Think, on modern split unit air conditioning, too. KF

RP:

And another coward who doesn’t understand infinity.

JVL:

Willful ignorance is rampant with evolutionary biologists. They don’t even know how to test the claims of their own position! No one uses unguided evolution for anything. It is a useless heuristic.

Mainstream biologists don’t even know what makes an organism what it is! How pathetic is that?

Food for thought, indeed…

Unguided evolution is untestable nonsense. The only reason probability arguments exist is because there isn’t any way to test its claims. Evolutionists just lie, bluff and equivocate their way through life. Theirs is the most pathetic existence.

It is very telling that evos are afraid to compare to see which side has the science an which side has the nonsense. I offered a $10,000 challenge @ the swamp. At first it was taken and then the coward ran away when the debate terms were laid out

KF:

RP is just another insipid troll. He is just like all of the others who can only spew false accusations and innuendos but never support its trope. RP will definitely never even try to support the claim that I have a “horrendous misunderstanding of set theory”. That’s because RP is an ignorant coward who thinks false accusations are enough.

F/N: Just for emphasis, the von Neumann construction of the Naturals, with order type w:

{} –> 0

{0} –> 1

{0,1} –> 2

{0,1,2} –> 3

. . .

{0,1,2 . . . } –> w

w is first transfinite ordinal, of cardinality aleph null. beyond as copiously discussed previously, we can construct the hyperreals and the surreals.

DV, I will be looking at some interesting issues that give a very different view on what the Greeks esp Pythagoreans and Platonists etc were up to. Number patterns and how they connect to deep structures and phenomena of reality.

KF

Retired Physicist@ 197I could.

And, continuing the ‘why am I not surprised’ theme:

New study identifies a psychological factor linked to Trump supporters’ vindictiveness.

Two things

First, guessing is often ignoranceHans Rosling showed that the more educated one was the more ignorant one was. So I would not use polls of behavior of anything as proof of something especially about the wisdom of the so called educated. Apparently chimpanzees give more accurate guesses about our world than do the educated. So what is one person’s guess is often ignorance. Read Factfulness. http://bit.ly/2HQZCS4

For example, is this evaluation of mask usage accurate? Seems pretty damning of the use of masks, not so much for face shields. https://bit.ly/2CvpJ0l

Second, I reiterate mathematics exist only in our heads and is essentially logic. The only numbers that exist in our world are possitive integers and even this concept requires an abstraction from the real world. Enumeration or quantity are so essential to our existence that we fail to realize it. You can point to a tree or a river but you can not point to any number.QED Is so natural to us that we don’t understand it is all in our minds. So when we use the term infinity either as a large analogy or an extremely small analogy it is just that. an analogy to something large or small. Not something that actually exists.

When this is done mathematics is better understood and why logic is built into us and so important for our existence.

RP and Seversky, linked to articles that have nothing to do with the topic at hand. That is called evasion.

Moreover, Seversky linked to an article whose headline reads,”New study identifies a psychological factor linked to Trump supporters’ vindictiveness”,,,

All I have to say after 3 years of the false Russian Collusion narrative, is that “YOU HAVE GOT TO BE KIDDING ME” Democrats, simply because they lost the 2016 election, turned into the most vindictive spoiled brats they could possibly be. Falsely targeting President Trump and a host of people associated with President Trump. i.e. Flynn, Stone, etc.. etc.., Besides using the CIA and FBI to illegally spy on resident Trump, they literally turned Congress, which use to be one of the most respected bodies in America, into a circus because of their antics. Republicans have been overly restrained to an absurd degree in not punishing the Democrats to the full extent of the law that were responsible for orchestrating such antics.

Myself, since integrity is apparently scarce to non-existent among the Democrats who brought this on the nation, I wish they would hold the Democrats who orchestrated this farce of a circus responsible for their crimes, to the full extent of the law, so that Democrats in the future would seriously think twice before putting the nation through such antics again.

Kairosfocus: As, once a serious logic of being challenge was put up in response to your attempt to imply that those who suggested above that God is responsible for the Mathematical framework of reality run into the roadblock of core Mathematics having independent necessary character you retreated to a fallback of only being interested in the Math.That’s because I want to be polite and not get into an argument about your beliefs wHich I don’t share. I don’t feel the need to dissuade you of your view. I’ve stated mine and that’s enough.

Thus, the directly tied — so, highly relevant and even decisive — logical issue is, how are such PW’s possible? How does the P get there? That, takes us to reality root, and in particular, we see how on logic of being:What are PWs anyway?

(This last is best seen by using the hyperreals mileposted by hyperintegers. Where, say HS Math teachers and the like . . . Engineers, Physicists in many cases [from Newton etc on], etc . . . using the intuitive number line on balance, are better understood as speaking intuitively in the hyperreals context. Such even arguably rehabilitates a good part of Euler’s thinking etc. Infinitesimals, suitably tamed, are back. Arguably, as part of the framework structure-quantity infrastructure for all PW’s. Where, once an infinitesimals cloud surrounds 0, *0*, we then can infinitestimally alter any r in R by vector displacement of the cloud *0* to superimpose on r yielding *r*, an infrastructure closer to r than a similarly shifted 1/n for any n in N and its negative -1/n. This is tied to nonstandard analysis and the ubiquity of Calculus in physics, including our habitual treatment of infinitesimals as a valid meaning of dr. This is of course directly connected to Wigner’s marvelling, as what is in any PW applies to our world, and extends to any coherent suggested framework for a world.)I do not see what any of the above has to do with theology but I guess it does for you.

Bornagain77: JVL, and disagreeing for the sake of disagreeing, minus any coherent argument to the contrary, and being nonchalant about the fact that your belief is not rooted in reality, i.e. “Who cares?”,,, is suppose to be different from the mental illness of denialism how exactly?I’m not inclined to get involved with something I consider to be a theological argument which you find comforting and supportive. I’m not here to dissuade you of your long held and deeply rooted beliefs.

Retired Physicist: The only math I’ve seen on this website is ET’s horrendous misunderstanding of set theory.You might very well think so, I couldn’t possibly comment.

Nope, not too strong at all. To point out the obvious fact that Darwinian atheists are in the grip of the mental illness of Denialism is to hit the nail squarely on the head.I guess poisoning the well of discourse is okay if you agree with the sentiments expressed.

you have posed a tangent, again one suggestive of the notorious Dawkins theme, ignorant, stupid, insane or wicked.As opposed to openly calling your opponents insane?

So now the truth = poisoning the well. You have to be in denial if you think that nature can produce coded information processing systems. And that is a hallmark of Darwinian atheists.

So RP ran away instead of trying to support its cowardly accusation. Vey telling, that

ET: Willful ignorance is rampant with evolutionary biologists. They don’t even know how to test the claims of their own position! No one uses unguided evolution for anything. It is a useless heuristicUnguided evolution is untestable nonsense. The only reason probability arguments exist is because there isn’t any way to test its claims. Evolutionists just lie, bluff and equivocate their way through life. Theirs is the most pathetic existence..No indication of how organisms are ‘designed’ to evolve -> no design. No design -> it’s all down to unguided processes.

Since you claimed there is a mechanism, some kind of programming the guides organisms to evolve, can you point to that mechanism and explain how it works, where it is stored and how it’s encoded in organisms?

RP is just another insipid troll. He is just like all of the others who can only spew false accusations and innuendos but never support its trope. RP will definitely never even try to support the claim that I have a “horrendous misunderstanding of set theory”. That’s because RP is an ignorant coward who thinks false accusations are enough.There is no need to support what you’ve already clearly demonstrated with your own comments and statements

ET: So now the truth = poisoning the well. You have to be in denial if you think that nature can produce coded information processing systems. And that is a hallmark of Darwinian atheists.That is your opinion. But that’s all it is. For some reason, thousands, if not millions, of working biologists disagree with you.

It’s a fact, not an opinion. And not one working biologist can refute what I said. Not one can demonstrate nature can produce coded information processing systems. They don’t even know how to test the claim.

JVL, you still failed to provide a coherent argument, and thus your ‘disagreeing’ is no more than ‘denialism’ by a different name.

JVL:

Read “Not By Chance” and “the Evolution Revolution”. Your ignorance is not an argument.

That is the “logic” of a moron.

I proved that you don’t understand infinity and you don’t grasp the implications of set subtraction.

Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

ET: It’s a fact, not an opinion. And not one working biologist can refute what I said. Not one can demonstrate nature can produce coded information processing systems. They don’t even know how to test the claim.I wonder why your opinion is not the one promulgated in millions of research papers and seminar presentations let alone thousands of books both technical and for the general public. Weird that. I guess almost everyone who actually studies biology professionally disagrees with you. Oh well.

Bornagain77: you still failed to provide a coherent argument, and thus your ‘disagreeing’ is no more than ‘denialism’ in a different name.I am under no obligation to get involved in what I consider a theological argument. I disagree with you and for some reason that bothers you immensely. Why not just leave it?

Strange that out of all those alleged working biologists no one can come up with a scientific theory of evolution! And again, they don’t even know what determines form. How pathetic is that?

JVL:

And yet there isn’t any support for blind watchmaker evolution, anywhere. Your working biologists appear to be a bunch of dolts. They don’t even use unguided evolution for anything

Bornagain77@ 196Atheism is nowhere classified as an addictive disorder and there is no evidence that it leads to destructive lifestyles. There is plenty of evidence, however, that absolutist beliefs, such as those of religions or political ideologies, can lead to destructive effects on many personal lives.

And disagreeing with your religious beliefs does not indicate pathological denialism. By that logic I could, with equal justification, argue that your persistence with your religious beliefs in the face of contradictory argument and evidence is also denialism. However, my position is that, while I may disagree with them, your religious beliefs are your own and we are both free to express our respective views.

Evos always try to bluff their way through any discussion. JVL isn’t any different. It must suck to be such a desperate fool.

Et: Read “Not By Chance” and “the Evolution Revolution”. Your ignorance is not an argument.You can’t explain the basic precepts? Why is that? Everyone else brings their evidence to the table.

I proved that you don’t understand infinity and you don’t grasp the implications of set subtraction.You didn’t ‘prove’ anything except that you don’t understand real set theory.

Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.You’re really funny when you double and triple down on something that is clearly incorrect based on over a century of published and well established mathematics as can be easily verified by anyone willing to have a look.

Strange that out of all those alleged working biologists no one can come up with a scientific theory of evolution! And again, they don’t even know what determines form. How pathetic is that?Even Dr Behe admits there is a theory of unguided evolution. Did someone say denialism?

And yet there isn’t any support for blind watchmaker evolution, anywhere. Your working biologists appear to be a bunch of dolts. They don’t even use unguided evolution for anythingAgain, if you can’t establish your claim that organisms are ‘designed’ to evolve then it must all be down to unguided processes. So, can you support your claim? Where is the designed programming in organisms? How does it interact with development? How is it encoded?

Evos always try to bluff their way through any discussion. JVL isn’t any different. It must suck to be such a desperate fool.I’m asking you if you can support your own claim that organisms are ‘designed’ to evolve. So far, you can’t.

Oh well.

Atheism is incoherent desperation.Too funny, change the topic instead of defending your own claims.

Atheism is incoherent desperation.

JVL, when you defend atheism, as you have done in this thread, you are, by default, making a Theological argument.

For you to deny that you are doing so is just more proof that you are in the grip of denialism.

JVL:

I have. Your willful ignorance gets in the way, every time.

Like a punk you are a liar.

Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.I made my case. JVL ignored it and tried to use the very thing being debated to win the debate. You can’t be any more ignorant than that.

Why is it that no one can link to this alleged scientific theory of unguided evolution? Why can’t anyone say when it was published and who the authors were?

Why do I always get evos lying about the theory as if their lies mean something? How pathetic are you, JVL?

Seversky at 223, after I listed these studies,

After I listed those studies, Seversky has the audacity to state, “there is no evidence that it (Atheism) leads to destructive lifestyles.”

And there you have it folks, the mental illness of denialism displayed in an atheist in all its full blown glory. 🙂

JVL:

I have. And when compared to what you spew my side is by far more coherent.

Bornagain77: When you defend atheism, as you have done in this thread, you are, by default, making a Theological argument.Not in the course of a discussion about mathematics. Math has NOTHING to do with theism. Nothing.

^^^^ Pathetic, for you to claim that math has nothing to with God, you must, by necessity, show that math can exist independently of God. It is, by default, a theological argument that you making. Denying it, just proves my point about you suffering from the mental affliction of denialism.

Moreover, contrary to what you want to believe, you are VERY far from ever proving that math can exist independently of God:

Again, the ONLY reason probability arguments exist with respect to unguided evolution, is because there isn’t any way to actually test its claims. That means unguided evolution is outside of science. And that is why there isn’t any scientific theory of unguided evolution.

ET: I have. Your willful ignorance gets in the way, every time.Not everyone on this thread will have seen your defence. Better go over it again.

Repeating something in bold doesn’t make it true.

I made my case. JVL ignored it and tried to use the very thing being debated to win the debate. You can’t be any more ignorant than that.It’s not under debate because it’s proven mathematics. And you never found a fault with the proof. QED.

Why is it that no one can link to this alleged scientific theory of unguided evolution? Why can’t anyone say when it was published and who the authors were?We don’t bother any more because every time someone tries you just deny what is said.

Why do I always get evos lying about the theory as if their lies mean something? How pathetic are you, JVL?No one is lying. You just don’t like the cases being presented. But that doesn’t mean the cases weren’t presented. Nor does it mean the cases are false.

I have. And when compared to what you spew my side is by far more coherent.Go on, let’s see it again. Remember the questions: where is the ‘designed’ evolution encouraging programming stored? How is it encoded? How does it affect development and affect mutations?

Again, the ONLY reason probability arguments exist with respect to unguided evolution, is because there isn’t any way to actually test its claims. That means unguided evolution is outside of science. And that is why there isn’t any scientific theory of unguided evolution.Gosh, I don’t think anyone else brought up probability arguments just now? I wonder what

ETis thinking . . . . first he says that paper, Waiting for Two Mutations (which is a probability argument) shows something about unguided evolutionary theory. Then he says probability arguments are rubbish. You know, I wonder whyETbelieves that paper anyway since the authors were testing unguided evolutionary processes whichETthinks you can’t test. It’s all kind of convoluted and weird.Bornagain77: ^^^^ Pathetic, for you to claim that math has nothing to with God, you must, by necessity, show that math can exist indepently of God. It is, by default, a theological argument that you making. Denying it, just proves my point about you suffering from the mental affliction of denialism.Sorry I disagree with you and that I don’t want to get caught up in a Bible-quoting argument. It is NOT a theological argument. You just want it to be.

Moreover, contrary to what you want to believe, you are VERY far from ever proving that math can exist independently of God:If there is no God then math came from someplace else.

JVL:

What I said is true. Clearly you are just a pathetic loser.

Evos are lying. Anyone who says that nature produced the genetic code is a liar. No one has presented any cases in that regard. You are lying.

I never said probability arguments are rubbish. What’s wrong with you?

Clearly you are just a pathetic liar and troll

Good luck with that

To repeat,’ Moreover, contrary to what you want to believe, you are VERY far from ever proving that math can exist independently of God:

I challenge anyone to make the case that I have a horrendous misunderstanding of set theory. If no one steps up to even try then they should be banned for being pathological liars and losers

JVL, your own words at 79 speak for themselves. Also, that you did not follow enough above to see that PW is possible worlds. That may also explain why you failed to see that Mathematics, substantially, being logic of structure and quantity would tie to how necessary mathematical entities will be framework to PWs, thus universally applicable. Thence, how do we get the P in PW, i.e. a logic of being, ontological question. Ontology being a subdiscipline of metaphysics, one of the main foci of philosophy. BTW, so is logic. And yes, meta questions raised by Mathematics and other disciplines are by definition matters of philosophy. It is unsurprising that you would mislabel meta issues of Mathematics as “theology,” that palpably being a dismissive sneer on “beliefs.” BTW, every worldview option — the stuff of metaphysics — necessarily has core first plausible beliefs that are antecedent to proofs, they are how you get to proofs. The issue is comparative difficulties and strengths and it so happens that PW framing allows a powerful answer to the Wigner challenge. KF

Of related interest, to JVL statement: “If there is no God then math came from someplace else.”

Not only would math not have a basis if God did not exist, but, since the entire concept of ‘personhood’ itself is immaterial and therefore must be based in the personhood of God, then JVL himself would not exist as a real person if God did not really exist:

But hey, don’t take M. Anthony Mills’ word for it, here are leading atheists themselves denying that they really exist as real persons,

The claim that our sense of self, that is to say, our conscious experience, is just a neuronal illusion is simply insane. As David Bentley Hart states in the following article, “Simply enough, you cannot suffer the illusion that you are conscious because illusions are possible only for conscious minds. This is so incandescently obvious that it is almost embarrassing to have to state it.”

BA77 (& attn RP et al):

The direct import of such a claim of our being under grand delusion is to discredit rationality itself. This definitely rises above mere gaps or blind spots in worldviews and is patently, manifestly self-falsifyingly absurd. To cling to such rather than recoiling in abject defeat implies that one finds the consequences of a sounder view unacceptable. So, one clings to the absurd, like a security blanket.

And that is indeed seriously irrational.

Worse, it is but one of many ways in which atheistical materialism is absurdly self-referentially incoherent.

In this context “insane” may be a bit over the top but it is fair comment,once the homework behind it has been done.

KF

Kf as to ““insane” may be a bit over the top”,,

And yet from the horse’s mouth,

Nope, the word ‘insane’ fits exactly. Just because Coyne is a professor doesn’t change just how insane that statement actually is.

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Mathematics is the product of measurement and expression, i.e. something must become specified among alternatives. You know this, but ignore it.

BornAgain are you capable of doing any level of math?

Calculus 2? Ordinary differential equations? Partial differential equations?

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That’s a silly question, and you know it.

RP can you do any level of mathematics without measurement and symbolic expression; can you do any level of mathematics without specifying something among alternatives?

@upright biped i’m guessing the answer is no.

RP, can you make a coherent argument? I am very sure the answer is no.

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Are you actually unsure if you can do mathematics without specifying something among alternatives, or is “guessing” just a rhetorical maneuver to depreciate the obvious answer?

ET: What I said is true. Clearly you are just a pathetic loser.Evos are lying. Anyone who says that nature produced the genetic code is a liar. No one has presented any cases in that regard. You are lying.So, given the evidence you just say the thousands of researchers are lying? That’s your counter-argument?

I challenge anyone to make the case that I have a horrendous misunderstanding of set theory. If no one steps up to even try then they should be banned for being pathological liars and losersYou disagree with one of the most basic precepts of modern set theory.

Bornagain77: To repeat,’ Moreover, contrary to what you want to believe, you are VERY far from ever proving that math can exist independently of God:Okay. I’ll leave it then.

Not only would math not have a basis if God did not exist, but, since the entire concept of ‘personhood’ itself is immaterial and therefore must be based in the personhood of God, then JVL himself would not exist as a real person if God did not really exist:But you just can’t leave it alone can you? Me disagreeing with you, that you just cannont tolerate.

Kairosfocus: your own words at 79 speak for themselves. Also, that you did not follow enough above to see that PW is possible worlds.Why can’t you just speak plainly?

That may also explain why you failed to see that Mathematics, substantially, being logic of structure and quantity would tie to how necessary mathematical entities will be framework to PWs, thus universally applicable. Thence, how do we get the P in PW, i.e. a logic of being, ontological question. Ontology being a subdiscipline of metaphysics, one of the main foci of philosophy. BTW, so is logic. And yes, meta questions raised by Mathematics and other disciplines are by definition matters of philosophy. It is unsurprising that you would mislabel meta issues of Mathematics as “theology,” that palpably being a dismissive sneer on “beliefs.” BTW, every worldview option — the stuff of metaphysics — necessarily has core first plausible beliefs that are antecedent to proofs, they are how you get to proofs. The issue is comparative difficulties and strengths and it so happens that PW framing allows a powerful answer to the Wigner challengeJust repeating yourself over and over again doesn’t make you right. Or, I’m afraid, coherent.

RP, you have ignored the substantive issue on the table to play at credentials. That tells us something, and not to your advantage. From 79 a challenge was issued which bridges mathematics and ontology. A response was on the table since 85 (see onward here), which you have evaded, while trying to belittle. I would suggest that as Math proper a reasonable senior high school or freshman exposure to core math would be adequate to follow the substantive math of the von Neumann construction and cascade N,Z,Q,R,C, R* and it is easy enough to pick up on the possible worlds context, including how logic of structure and quantity emerges from the principle of distinct identity of a PW. Thus we see how an answer to Wigner’s wonder emerges: necessary, framework entities obtain in any PW, so will be relevant through logical necessity not cause-effect bonds. Beyond, the attempt to infer to Math independent of a causal root of reality runs into: where do possible worlds come from. Non-being fails, circular retrocausality fails, infinite descent from an unbounded past is a supertask. That leaves one serious candidate: finitely remote, causally capable, necessary being reality root. KF

Upright BiPed: Mathematics is the product of measurement and expression, i.e. something must become specified among alternatives. You know this, but ignore it.I don’t ignore that but that has nothing to do with theology.

RP, I most likely have far more experience working with math and applying it to the real world than you do.

I worked as a technician helping build Chemical factories in the Texas area.

This is the math that I had to be familiar with in order to qualify for, and do, that job:

In fact, in college, I was required to build a PID controller from scratch, i.e. from the component level up. It was either pass or fail. In other words, you did not graduate from that college until you successfully built that PID controller. It was the most challenging, and nerve wracking, class that I have ever taken.

And even though you probably know the math RP, I still don’t think you could have done my job. Besides the math, I had to be extremely knowledgeable in troubleshooting many other areas, i.e. electronics, chemistry, hydraulics, pneumatics, etc.. etc..

Frankly, I would not have given two cents for anyone who tooted their own horn as being smarter than everyone else as you do, but the respect that I received and gave to others in that job was every bit earned. Book learning could only get you so far in that job, but in the field, in the real world of applied science, it was the common sense solutions to extremely complicated problems that most often earned you the most respect from others in that job.

Do you have that required common sense to do that job? The only way to find out is to throw you in the water and see if you can swim, i.e. can do the job. I doubt it. I’ve seen many people fail at trying to do that job after they got out of college. There is something about being in the field that just can’t be learned in the classroom. That something is common sense. And in that area of having common sense, I have not seen much coming from you.

Retired Physicist: BornAgain are you capable of doing any level of math? Calculus 2? Ordinary differential equations? Partial differential equations?In my experience:

BornAgain77hasn’t actually shown any experience with mathematics above the basic level. He’s good at copying and pasting references. For lots of different things.Bornagain77: In fact, in college, I was required to build a PID controller from scratch, i.e. from the component level up. It was either pass or fail. In other words, you did not graduate from that college until you successfully built that PID controller. It was the most challenging, and nerve wracking, class that I have ever taken.Okay, I stand corrected. Always happy to revise my stance with the addition of new data.

ETlikes to think he’s good at math and, a few times when I’ve pushed him, has come up with some good answers. After quite a few proddings. As you’ve noted, his understanding of set theory is severely flawed; but there is no way he’s ever going to back down from that stance as he’s decided to die on that hill a long time ago.Upright Bipedis quite good on philosophical discussions and topics but mathematics . . . .I’m not so sure.Kairosfocuscertainly does has some good basic mathematical knowledge but he’s prone to throw out tons of jargon and irrelevant comments; I think maybe he was taught in a very old and out dated fashion and that has affected his approach to communicated mathematical ideas.I could be very wrong but those are my impressions.

JVL:

What evidence? Stop bluffing.

What evidence is there that unguided, blind and mindless processes can produce a ribosome? How can we test for such a thing?

Liar. I disagree with something that no one uses for anything. And the reason I disagree is because basic set subtraction warrants my disagreement. You are just too dim to grasp what I post.

Again, I only disagree with an insignificant and useless part of set theory. To say otherwise is a blatant lie. JVL has steadfastly refused to answer my challenges and can only falsely accuse, as cowards are want to do.

F/N: Normal math level to work with PID controllers, familiarity with Laplace Transforms and associated s-domain block diagram algebra [z-domain is related, for the discrete time case], poles and zeros of a rational, complex frequency domain function, the transfer function. Even with tricks and tools such as the heavy rubber sheet model, you need to understand transient behaviour, circular frequency and cycle frequency as well as frequency response. The transfer function is of course the image of unit area impulse response; this can be used to draw it out of noise and responses thereto. Generally, do not hit a system in a real world situation with an impulse . Familiarity with ODE’s is a given, indeed that is what you are manipulating . . . that auxiliary equation or D operator is a thinly disguised Laplace Transform. Way back the get the idea concept was, sophisticated logarithms. Someone with that background and required basic intelligence will be able to access and appreciate the mathematical thinking in baseline special relativity and quantum mechanics. With persistence and good references, should be able to appreciate more advanced topics. Of course, such an autodidact will have limitations, but such will not be relevant to what is on the table substantially from 85 on, which answers the challenge in 79. KF

I challenge anyone to make the case that I have a horrendous misunderstanding of set theory. If no one steps up to even try then they should be banned for being pathological liars and losersStill waiting. More nonsensical accusations just prove that JVL is a coward, liar and bluffing loser.

JVL, and again, disagreeing without presenting a coherent argument defending your position is no different than straight up ‘denialism’, i.e. a mental illness!

ET: What evidence? Stop bluffing.What evidence is there that unguided, blind and mindless processes can produce a ribosome? How can we test for such a thing?As you like to say: your ignorence of the evidence is not an argument.

Liar. I disagree with something that no one uses for anything. And the reason I disagree is because basic set subtraction warrants my disagreement. You are just too dim to grasp what I post.You are in stark contrast with every single math publication produced in the last century. No one takes your view seriously. Why you bother I just can’t fathom.

Again, I only disagree with an insignificant and useless part of set theory. To say otherwise is a blatant lie. JVL has steadfastly refused to answer my challenges and can only falsely accuse, as cowards are want to do.Welcome to obscurity. No one takes you seriously or uses your system. No one.

It doesn’t matter what you think. You are incorrect.

You have already made the case yourself and NO ONE has come to your defence. No one.

Still waiting. More nonsensical accusations just prove that JVL is a coward, liar and bluffing loser.I’m good being correct.

Kairosfocus: Normal math level to work with PID controllers, familiarity with Laplace Transforms and associated s-domain block diagram algebra [z-domain is related, for the discrete time case], poles and zeros of a rational, complex frequency domain function, the transfer function. Even with tricks and tools such as the heavy rubber sheet model, you need to understand transient behaviour, circular frequency and cycle frequency as well as frequency response. The transfer function is of course the image of unit area impulse response; this can be used to draw it out of noise and responses thereto. Generally, do not hit a system in a real world situation with an impulse . Familiarity with ODE’s is a given, indeed that is what you are manipulating . . . that auxiliary equation or D operator is a thinly disguised Laplace Transform. Way back the get the idea concept was, sophisticated logarithms. Someone with that background and required basic intelligence will be able to access and appreciate the mathematical thinking in baseline special relativity and quantum mechanics.You really do not make sense. I can’t even parse most of what you write. Just speak clearly and plainly.

ET, I appreciate that you take a heterodox view of set theory. There are difficulties with that view, but they do not substantially alter the key point in 85 above. Though, it is much harder to hammer home to the determined, that finite stage step traversal of the transfinite is impossible, a supertask, as we saw four years ago. That is what needs to be answered. Of course, I see that tamed infinitesimals thus transfinite hyperreals and infinitesimally altered reals are very useful. For concepts, surreals. Likewise, there is transfinite induction that goes beyond limits of induction on N. KF

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I made no comment about theology; my issue with you (among others) is your claim that math exists outside of an observer. Mathematics requires the specification of something among alternatives (i.e. measurement and symbolic expression), so do have an argument that supports this assertion? You tell us that mankind learned mathematics by counting – i.e. matching our symbolic expressions to the quantity of objects in a set. Additionally you seem to suggest that if that scenario were repeated elsewhere, the symbolic expressions might certainly be different, but the math itself would be the same. Whatever else that argument may be, it is not an argument that math exists outside the measurement and expression of an observer.

JVL:

You coward. The ignorance is all yours.

Liar. I disagree with something that no one uses for anything. And the reason I disagree is because basic set subtraction warrants my disagreement. You are just too dim to grasp what I post.Liar.

Again, I only disagree with an insignificant and useless part of set theory. To say otherwise is a blatant lie. JVL has steadfastly refused to answer my challenges and can only falsely accuse, as cowards are want to do.No one uses what I am disputing for anything. No one.

I don’t care what you say. All you can do is use the thing being disputed to try to settle the dispute. How stupid is that?

I only dispute an insignificant and useless part of set theory. And at least I understand the implications of set subtraction. All JVL has is its cowardly accusations and ignorance when it comes to debate tactics.

So to claim anything else about my knowledge of set theory is a cowardly lie.

Bornagain77: JVL, again, disagreeing without presenting a coherent argument defending your position is no different than straight up ‘denialism’, i.e. a mental illness!How do you know the laws of mathematics are mutable at all? You don’t. That’s all just a supposition on your part because your conception of the ‘creator’ of the universe dictates that they have control over all things.

I think mathematics is invariant. God or no God we have to work with the mathematical structures. And that means that ‘God’ did not create them. I may be wrong but I see not evidence to contradict that belief.

Show me an example of God affecting mathematics. Just one. And not something that you just find ‘amazing’ or ‘beautiful’. I mean something really clearly divinely influenced.

KF, set subtraction proves there are difficulties with Cantor’s view. If all people have is to Jedi hand-wave away the implications of set subtraction, then they have left mathematics behind.

And the fact that no one uses the concept that all countably infinite sets have the same cardinality for anything, tells me all I need to know about that Jedi hand-wave. Arguments from authority don’t stand a chance in the octagon.

Upright Biped: I made no comment about theology; my issue with you (among others) is your claim that math exists outside of an observer.Show me a counter example.

JVL:

That doesn’t follow. This is the problem, JVL. Your posts prove that you don’t understand logic and reasoning.

ET: Liar. I disagree with something that no one uses for anything. And the reason I disagree is because basic set subtraction warrants my disagreement. You are just too dim to grasp what I post.Your basic set subtraction is not used by anyone, ever, for infinite sets. Why do you keep embarrassing yourself with this futile line or argumentation?

Liar. Again, I only disagree with an insignificant and useless part of set theory. To say otherwise is a blatant lie. JVL has steadfastly refused to answer my challenges and can only falsely accuse, as cowards are want to do.I have and you just deny anything that runs counter to your view.

No one uses what I am disputing for anything. No one.Now who’s a denialist?

No one is going to agree with you just because you type it in bold.

I don’t care what you say. All you can do is use the thing being disputed to try to settle the dispute. How stupid is that?Find a fault in a proof. Can you do that? If you can’t then there is no dispute.

Find a fault in a proof. Can you do that?

I only dispute an insignificant and useless part of set theory. And at least I understand the implications of set subtraction. All JVL has is its cowardly accusations and ignorance when it comes to debate tactics.Find a fault in a proof. Can you do that?

So to claim anything else about my knowledge of set theory is a cowardly lie.You can’t find a fault in the proofs which establish what you dispute. You lose.

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You want “counter examples” to mathematics existing outside of an observer? Hello?

Instead of incoherence, let’s try out what you actually

do sayas an argument instead. Let’s match our symbols with the quantity of objects in a set, as you suggested upthread.How many moons are in our sky at night?

Answer: One

Okay … explain to me how mathematics exists outside of measurement and expression here. Surely you are not arguing that math exist merely because a single moon exist in the night’s sky?!?

JVL:

Wow, what a devastating refutation- not.

More lies. I have challenged you to show that the concept is useful and you have failed.

No one uses what I am disputing for anything. No one.YOU. YOU have FAILED to demonstrate that the concept under dispute is used or useful. Clearly you are just a punk.

Set subtraction proves there is fault with the inferences from the proof. JVL is still too dim to grasp what that means.

There isn’t anything in set theory that prevents set subtraction from being used with infinite sets. You have to be a special type of coward to even try that BS argument.

The only thing I dispute is the concept that all countably infinite sets have the same cardinality. And no one uses the concept that all countably infinite sets have the same cardinality for anything. No one.

For years I have asked JVL to produce something showing the concept is used and useful. For years JVL has been the typical coward, refusing the challenge.

Upright Biped: Okay … explain to me how mathematics exists outside of measurement and expression here. Surely you are not arguing that math exist merely because a single moon exist in the night’s sky?!?Of course not. That would be incredibly stupid.

Why don’t you show me a consistent system of mathematics that works for basic problems like arithmetic that is significantly different from ours. Are you sure one exists?

ET: Wow, what a devastating refutation- not.It’s quite true though.

More lies. I have challenged you to show that the concept is useful and you have failed.Deny, deny, deny. Strange that no one is coming to your defence on this. I wonder why?

No one uses what I am disputing for anything. No one.Your ignorance is not an argument.

YOU. YOU have FAILED to demonstrate that the concept under dispute is used or useful. Clearly you are just a punk.Your ignorance is not an argument.

Set subtraction proves there is fault with the inferences from the proof. JVL is still too dim to grasp what that means.You never found a fault with any of Cantor’s proofs. You lose.

There isn’t anything in set theory that prevents set subtraction from being used with infinite sets. You have to be a special type of coward to even try that BS argument.You never found a fault with any of Cantor’s proofs. You lose.

The only thing I dispute is the concept that all countably infinite sets have the same cardinality. And no one uses the concept that all countably infinite sets have the same cardinality for anything. No one.Your ignorance is not an argument.

For years I have asked JVL to produce something showing the concept is used and useful. For years JVL has been the typical coward, refusing the challenge.Deny, deny, deny. Oh hey, listen . . . . do you hear that? That stark silence? That’s the silence of NO ONE coming to your defence on this issue. Not

Kairosfocus, notBornagain77, notUpright Biped. NO ONE. They’re leaving you to twist in the wind. Being wrong.Welcome to reality.

Oh, and by the way . . .

Are you going to provide evidence, as in hard physical evidence, that organisms are ‘designed’ to evolve? As in evidence of where such programming exists.. How it’s encoded. How it affect development. People want to know if you can uphold your claim. So far, there’s a lot of disappointment.

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And how would that relieve you of the fact that mathematics requires measurement and symbolic expression?

– – – – – – – – – – – – – – – –

EDIT … unless of course, you are simply arguing that mathematics exists because there is a single moon in the night’s sky – a position you’ve summed up as “incredibly stupid”.

Upright Biped: And how would that relieve you of the fact that mathematics requires measurement and symbolic expression?What? Sigh. What does that have to do with the question of whether or not math is independent of any possible creator?

You keep arguing on some odd fringe of mathematics. I hope you enjoy it. But the real fun is actually doing the work. As well you know.

.

lol

Just for the fun of it, I did a word search on this page for the phrase “any possible creator”. I found it only appears on this page once, in comment #277.

Your argument, JVL, is that mathematics exists outside any mind, any observer, any intelligent agent whatsoever —

“it just is”as you say.For that to be so, it would require math to exist without the need to specify something among alternatives, without measurement, and without expression. You are now down to arguing that math exist because a single moon orbits in the night sky. Surprise surprise.

– – – – – – – – – – – – – –

Your argument is not only incoherent but pointless, JVL, and has been since the start of this conversation. The problem here is that you’ve already proven yourself incapable of doing an “about face” — i.e. you are are unwilling to admit mistakes to those who point them out to you (certainly not uncommon) but most unfortunate of all, you are equally unwilling to just walk away.

The only thing I dispute is the concept that all countably infinite sets have the same cardinality. And no one uses the concept that all countably infinite sets have the same cardinality for anything. No one.YOU are the ignorant one here, JVL. I noticed no one has come to your defense. No one. Stark silence, you loser.

According to the paper “Waiting for TWO Mutations” that is the only thing that can explain the diversity of life. But you are too stupid to understand that. And that is not my problem.

For years I have asked JVL to produce something showing the concept is used and useful. For years JVL has been the typical coward, refusing the challenge.To refute that claim all JVL had to do was show us how it is used. So it is very telling that he bailed like a coward

Earlier in the thread Jerry stated,

Later in the thread at post 264 Upright Biped states:

The fact that math is immaterial, and that it takes an immaterial mind to even think about immaterial mathematics in the first place, is certainly not that hard to understand. As Dr. Egnor once commented, “What is the physics behind the Pythagorean theorem? After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds. There is no real triangle in which the sum of the squares of the sides exactly equals the square of the hypotenuse. That holds true for all of geometry. Geometry is about concepts, not about anything in the natural world or about anything that can be described by physics. What is the “physics” of the fact that the area of a circle is pi multiplied by the square of the radius? And of course what is natural and physical about imaginary numbers, infinite series, irrational numbers, and the mathematics of more than three spatial dimensions? ”

And as Eugene Wigner once commented, “thought processes and consciousness are the primary concepts, that our knowledge of the external world is the content of our consciousness and that the consciousness, therefore, cannot be denied.”

In short, consciousness is the primary prerequisite of all possible prerequisites for any coherent ‘mathematical’ model of reality to be put forth. To postulate anything other than consciousness as the primary substratum of reality is self-negating, As William J Murray once stated, “Mind must be postulated as the unobserved observer, the uncaused cause simply to avoid a self-negating, self-conflicting worldview. It is the necessary postulate of all necessary postulates, because nothing else can come first. To say anything else comes first requires mind to consider and argue that case and then believe it to be true, demonstrating that without mind, you could not believe that mind is not primary in the first place.”?

Moreover, we no longer have to rely solely on these powerful philosophical arguments that immaterial Mind must precede immaterial math itself, but we can now support the fact that Mind must be primary by appealing to advances in quantum mechanics, Specifically, numerous experiments have all concluded that “Material reality does not exist without an observer”

Moreover, the math of quantum mechanics requires for us to make a choice in what we will measure before reality can be said to be brought into existence. As Stephen Weinberg, an atheist, stated, “In quantum mechanics these probabilities do not exist until people choose what to measure,,, Unlike the case of classical physics, a choice must be made,,,”

In fact Weinberg, again an atheist, rejected the instrumentalist approach precisely because “humans are brought into the laws of nature at the most fundamental level” and because it undermined the Darwinian worldview from within. Yet, regardless of how he and other atheists may prefer the world to behave, quantum mechanics itself could care less how atheists prefer the world to behave.

For instance, this recent 2019 experimental confirmation of the “Wigner’s Friend” thought experiment established that “measurement results,, must be understood relative to the observer who performed the measurement”.

My question for JVL and RP is this, “why in blue blazes does a supposedly deterministic mathematical equation even care what I, as a person, choose to measure?” Mathematical equations, by definition, can’t care about people, Only a person can care about another person. Thus, it follows from logical necessity, that the Mind of God must be behind the mathematics of quantum mechanics.

As the Bible said thousands of years before quantum mechanics was even discovered,

Supplemental note:

JVL, if you cannot understand what I summed up about ET, then you are unfamiliar with instrumentation and control, and perhaps with linked Mathematics. Though, I am surprised if you are unfamiliar with Laplace Transforms (close cousins of both Fourier Transforms and Z-transforms), all of which are connected to the complex frequency domains. For years, I lived more in that domain than in our day-to-day time domain (and yes, there are t-domain techniques too). As an applied physicist who played both sides of the street (and an educator), I took time to draw up some conceptual bridges. KF

PS: I am also quite confident that what I wrote here and summarised then augmented above is both coherent and well warranted. However, it may well cut across your own worldview first plausibles. Let me clip — nope real mess, just read it there and respond on points. Otherwise for cause we call your dismissive bluff.

ET, kindly turn down rhetorical voltage. KF

If JVL is going to get away with lying what choice do I have?

Can you tell me what the concept of all countably infinite sets have the same cardinality is used for?

UB, core structure and quantity connected to logic of being will exist in any possible world. The question then is how possible gets there; what makes a PW possible. That connects to logic of being and the root of reality. JVL, here, confuses ontology with theology. S/he also seems to imagine a power of blind chance and mechanical necessity that is patently unwarranted. Conveniently, twice over. Of course the study requires a rational, free observer. KF

UB, 276:

This actually does show how a PW embeds the substance of structure and quantity, here first a countable discrete object and it s being of a definite size, shape and location for starters. We then find out that what is must be compatible with everything else that is, and that to be distinct and identifiable there must be core characteristics of distinction. This brings out logic through the principle of distinct identity.

No PW is possible, then, without embedding a logic of structure and quantity that in part is trans-world, i.e. necessary and framework to any world. This includes N,Z,Q,R,C,R* etc. Where, already at abstract level vectors are present from Z on, with invitation to spaces.

Does that suggest that Mathematics is an independent realm of necessary entities? No, it is a consequence of being a possible world that core structures and quantities will be present, as key abstracta. The issue pivots on what I pointed out from 85 on: what makes a world possible?

JVL et al refuse to go there but we may freely do so: utter non-being has no causal capacity, circular retrocausation is the same from a different angle, traversing a beginningless past of “years” is an infeasible supertask. That leaves on the table just one serious option: a finitely remote root of reality, where in any world with creatures sufficiently rationally and responsibly free to do math, they will be governed morally by first duties of reason. Even objectors, to argue are forced to appeal to same. That is, they are self evident.

That further constrains the root, as we are such creatures, i.e. our existence implies the root is inherently good and so too utterly wise. That is philosophy, and it naturally arises from asking about what it means to be rational. It is interesting that the objectors here, at this npoint, tend to support views that undermine credibility of rationality required to do math.

No wonder berlinski suggested there are no arguments against God that are not arguments against math.

KF

ET, it is part of the coherence of Mathematics, inter alia it connects to the further implication of different transfinite cardinalities such as continuum. That connects to any number of properties in NZQRC etc. And BTW, cardinality of a number is a scaling metric, countability meaning, can be put in 1:1 correspondence with N or a subset thereof. Transfiniteness emerges from the endless continuation property of N as a structured set. So, if N and another set S can be endlessly matched, S has the same cardinality and can be transformed into N, it is N in another form so to speak, insofar as this property is concerned. For example: {0,1,2 . . . } x2 element by element is {0,2,4 . . .}. This means, we have to broaden our understanding of cardinality once sets become transfinite. And the transfinite opens up the world of the infinitesimal, thus calculus. And arguably the epsilon delta limit approach simply manages the infinitesimal by exploiting its scale. Continuum and limits are inextricably tied to the transfinite. Just, it is hard to manage. KF

No, it isn’t part of any coherence and no it doesn’t connect anything.

Again, no one uses the concept that all countably infinite sets have the same cardinality. The concept is useless. And no one can demonstrate otherwise. Notice I am NOT saying infinity is useless.

Cantor’s diagonal just shows that two sets are countably infinite. It says nothing about the cardinality. Set subtraction can prove the cardinalities are not the same.

ET, I have summarised uncontroversial facts. KF

ET: Cantor’s diagonal just shows that two sets are countably infinite. It says nothing about the cardinality.Countably infinite sets all have the same infinite cardinality; aleph-nought.

Set subtraction can prove the cardinalities are not the same.Nope. Find a mistake in a proof that the set of all even integers has the same cardinality as the set of all integers. If you can’t find a mistake then the proof holds. QED

Kairosfocus: I have summarised uncontroversial factsThank you!!

ET, if you have made a massive breakthrough in infinite set theory, you are due for a Fields medal and the accompanying $15,000. So can you tell us what mathematicians you have contacted or publications you have prepared to publish in? Because if the answer is zero that suggests you know you’re full of it.

RP, why do you think your cowardly comments mean something? The fact that the concept I am disputing is useless says it all, really. But then again you are clearly too dim to grasp that fact.

JVL:

Repeating your trope isn’t going to make it so.

Set subtraction can prove the cardinalities are not the same.JVL:

Yes, it can. And no amount of your whining and handwaving will ever change that fact.

Kairosfocus- You have failed to show how the concept that I am disputing is used. Your “summary” is pure double-talk

Again, no one uses the concept that all countably infinite sets have the same cardinality. The concept is useless. And no one can demonstrate otherwise. Notice I am NOT saying infinity is useless.Cantor’s diagonal just shows that two sets are countably infinite. It says nothing about the cardinality. Set subtraction can prove the cardinalities are not the same.Everyone can see that no one has refuted my claim that the concept is useless

ET: Repeating your trope isn’t going to make it so.It is true. And will stay that way unless you can find a fault in a pertinent proof.

Set subtraction can prove the cardinalities are not the same.Find a mistake in a proof.

Yes, it can. And no amount of your whining and handwaving will ever change that fact.If you can’t find a mistake you lose.

Welcome to real mathematics. It’s not a spectator sport.

Kairosfocusagrees with me.Everyone can see that no one has refuted my claim that the concept is uselessEveryone can see you can’t find a mistake in a proof that says you’re wrong. And I and

Kairosfocshave told you how it is used and is fundamental in mathematics. You just deny, deny, deny.My example of two different counters refutes the notion that all countably infinite sets have the same cardinality. And all anyone can do is demonstrate they do not understand infinity.

I know JVL doesn’t understand infinity. KF thinks that a set with infinite elements can be handed in all at once- hint, it cannot.

So perhaps we need to start with the concept of infinity…

Earth to JVL- how many times do I have to explain the proof to you? Why do you think that your willful ignorance is an argument? And why do you think you can use the very thing being debated to try to settle the debate? Are you really that daft?

JVL:

No, he did no such thing. Clearly you are just a desperate fool.

Again: Let A = {1,2,3,4,5,…}; Let B = {2,4,6,8,10,…}; Let C = {1,3,5,7,9,…}

A – B = C. If A and B had the same cardinality A – B would = {}

So, ET, you have contacted zero mathematicians to tell them about your amazing breakthrough. And there are intelligent design leaning mathematicians like Edward Grandville Sewell that we can talk to.

What does Dr. Sewell think of your math?

ET,

I’m late to the party, so you might have already answered this question. Given two _arbitrary_ sets A and B (not necessarily integers or what have you), how do you decide whether they are equinumerous? (that is, whether they have the same cardinality).

Of course you can make sense of statements such as “{2, 4, 6, …} is half the size of {1, 2, 3, …}”, and that’s sometimes useful, but I think the others are talking about the absolute “sizes” of arbitrary sets where B may not be a subset of A and vice-versa.

Hi DaveS- A system would have a standard that everything is relative to.

Earth to RP, what part of “it’s a useless concept” are you too dim to understand?

ET: Earth to JVL- how many times do I have to explain the proof to you? Why do you think that your willful ignorance is an argument? And why do you think you can use the very thing being debated to try to settle the debate? Are you really that daft?Hey, I’m not the one that denies well over a century of well established and used mathematics. For those who haven’t seen the proof:

Let A = {1, 2, 3, 4, . . . . } Let B = {2, 4, 6, 8 ,. . . . }

Match the first element of A with the first element of B: 1 (in A) 2 (in B)

Match the second element of A with the second element of B: 2 (in A) 4 (in B)

Match the third element of A with the third element of B: 3 (in A) 6 (in B)

And so on.

Every element of A has a match with one and only one element of B. Every element of B has a match with one and only one element of A. You tell me an element of A and I can tell you what element of B it’s matched with. You tell me an element of B and I can tell you what element of A it’s matched with. It’s called a one-to-one correspondence.

No element of either set is unmatched. They only way two sets can have complete one-to-one correspondence is if they have the same number of elements. Sets A and B are clearly infinite and we’ve just seen that they are the same size. Any infinite set that can be put into a one-to-one correspondence with A (the set of positive integers is said to be countably infinite with cardinality aleph-nought.

Everyone on the planet except

ETaccepts this as proof sets A and B (and C) are countably infinite with cardinality aleph-nought. It can also be shown that the rational numbers are likewise countably infinite. But not the reals. The reals cannot be put into a one-to-one correspondence with the positive integers (set A).IF

ETis right and Set A and set B are NOT the same size then he should be able to find at least one element in either set that doesn’t have a match in the other set. But he can’t find such an element. Thats’ why his ‘set subtraction’ doesn’t work. It’s not consistent with the rest of set theory.LoL! @ JVL:

If it isn’t used it isn’t established. Cantor is not infallible. Ser subtraction works. Your cowardice doesn’t change that.

With set subtraction I found infinite unmatched elements. You lose.

And most people would agree with me. Only the people who think they are math experts disagree.

DaveS: I’m late to the party, so you might have already answered this question. Given two _arbitrary_ sets A and B (not necessarily integers or what have you), how do you decide whether they are equinumerous? (that is, whether they have the same cardinality).Technically speaking: they are the same size if their elements can be matched up one-to-one. But think ot it like counting. When you’re trying to see how big a set of things is you count them. That’s putting the elements of the set into a one-to-one correspondence with a subset of the positive integers.

1 the first element of the set

2 the second element of the set

3 the third element of the set

And so on.

When you run out of elements of the mystery set you know how many elements it has because the last elements is matched with your count.

When working with infinite sets you have to be more careful to make sure your matching is tight with nothing left out before deciding if the sets have the same size.

Of course you can make sense of statements such as “{2, 4, 6, …} is half the size of {1, 2, 3, …}”, and that’s sometimes useful, but I think the others are talking about the absolute “sizes” of arbitrary sets where B may not be a subset of A and vice-versa.Yes. Another reason

ET;s ‘set subtraction’ doesn’t work is because he can’t compare the sizes of sets B and C. In fact, he can’t compare lots of sets. His ‘method’ only works for two sets where one is a subset of the other. But how does that work when comparing the positive integers with the polynomials with rational coefficients? You can’t ‘subtract’ one set from another. So you have to use element matching to see if those two sets are the same size.Like I said, well established and well used mathematics. You couldn’t do power series without it.

Two counters- A and B. Counter A counts every second. Counter B counts every other second. Both counters start at the same time. Counter A will ALWAYS AND FOREVER have more counts, ie elements, than counter B. At EVERY finite point in time- meaning for infinity. Counter B will NEVER equal counter A.

Now watch as JVL bastardizes the English language or just ignores it

ET: With set subtraction I found infinite unmatched elements. You lose.Using your set A and B and my matching tell me an element of either set with is unmatched. Support your claim.

ET: Now watch as JVL bastardizes the English language or just ignores itYou can’t find an unmatched element of set A or B using my matching. That means the sets are the same size. They have to be.

It’s not a counter or a time thing. It’s just a question of lining up both sets to see if they match up, one-to-one all the way down the line.

ET: And most people would agree with me. Only the people who think they are math experts disagree.Most people don’t understand the mathematics. I’m not an expert but I know basic axiomatic set theory. This stuff is in chapter one of any real set theory book. Go check it out. Look it up on Wikipedia. It’s everywhere and easy to find.

As predicted, JVL ignores the refuting post. How typical and cowardly of you, JVL.

Why would I use JVL’s matching when it is then very thing that I am disputing? How much of a desperate fool are you JVL?

Again, I know what set theory says. And I also know that I am well within my rights to dispute it. Especially since I can refute it. Just because JVL can ignore my refutations just makes my case.

Two counters- A and B. Counter A counts every second. Counter B counts every other second. Both counters start at the same time. Counter A will ALWAYS AND FOREVER have more counts, ie elements, than counter B. At EVERY finite point in time- meaning for infinity. Counter B will NEVER equal counter A.Cantor did not understand relativity. Cantor was not infallible.

ETwill not be able to find an unmatched element of set A or B using my matching no matter what he says. But he won’t back down or admit he’s in disagreement with any mathematician you ask.Anyone can check this stuff out by going to your local University library and looking at a book on set theory. A proper, university textbook not some primary school thing. Or you can read all about it on Wikipedia. It’s easy to find and see.

For those who have taken Calculus you might recall doing Taylor and MacLaurin power series. Remember how you had to match the index with the coefficients and come up with a formula? You were setting up a one-to-one correspondence with the positive integers. And any electrical or acoustical will tell you that power series are incredibly pervasive.

This is all well established, well used and absolutely non-controversial mathematics. When Cantor first starting mucking about with such things lots of people did think he was a bit wrong in the head. But not any more. Now he is lauded as on of the seminal mathematicians of all time.

And

ETcan’t find an unmatched element or an error in any proof done by Cantor or anyone else working in this area.ET,

Then I think you’re talking about something very different from JVL, KF, RP, etc.

Do you agree that it’s reasonable to say that {1, 2, 3, …} and {10, 20, 30, …} have the “same number of elements” in _some_ sense? Those two sets obviously have a striking similarity. You could obtain the second set by simply adding a “0” each element of the first set. And this trivial alteration of symbols should not change the total number of elements involved.

Similarly, {a, aa, aaa, …} and {xxx, xxxx, xxxxx, …} also have the same number of elements according to the same reasoning.

Wow, all JVL can do is repeat his oft-refuted trope.

Why would I use JVL’s matching when it is then very thing that I am disputing? How much of a desperate fool are you JVL?You can dispute it by finding an element of either set that is unmatched. Can you find such an element, yes or no?

Again, I know what set theory says. And I also know that I am well within my rights to dispute it. Especially since I can refute it. Just because JVL can ignore my refutations just makes my case.You always have to righ to look foolish when you can’t support your own claims and methods.

Again, can you find an unmatched element, yes or no?

Cantor did not understand relativity. Cantor was not infallible.This has nothing to do with relativity.

Can you find an unmatched element, yes or no?

Wow, all JVL can do is repeat his oft-refuted trope.It’s not my fault you cannot find an unmatched element in my scheme. That means the sets are the same size. QED

JVL YOU are looking foolish by ignoring my example that refutes you:I addressed your example by saying this has nothing to do with time or counters running at different speeds.

Can you find an unmatched element, yes or no? You said you found some, let’s see them.

Your ignorance is not an argument.This has nothing to do with relativity. This has to do with set theory. And proving that two sets have the same number of elements which I have done. And you can’t find a mistake in my proof. You can’t find an unmatched element. But you continue to whine and moan and declare you are right.

Keep digging your hole deeper and deeper if you so choose. But don’t blame others because you look a fool.

Two counters- A and B. Counter A counts every second. Counter B counts every other second. Both counters start at the same time. Counter A will ALWAYS AND FOREVER have more counts, ie elements, than counter B. At EVERY finite point in time- meaning for infinity. Counter B will NEVER equal counter A.This has nothing to do with how fast something is happening, the time something happens or any of that stuff. This has to do with taking two sets and lining them up one-to-one. Which I have done.

Yes, daves, I know I am talking about something different. Look @ my example in 316.

JVL YOU are looking foolish by ignoring my example that refutes you:

You lose

JVL:

Your ignorance is not an argument.

DaveS: Do you agree that it’s reasonable to say that {1, 2, 3, …} and {10, 20, 30, …} have the “same number of elements” in _some_ sense? Those two sets obviously have a striking similarity. You could obtain the second set by simply adding a “0” each element of the first set. And this trivial alteration of symbols should not change the total number of symbols involved.That is correct.

DaveSgets it.ETjust denies, denies, denies.daves:

And set subtraction demonstrates the differences.

ET,

It would then seem that there isn’t so much a disagreement here, but rather that the interlocutors are talking past each other?

JVL, why do you think your ignorance and cowardice mean something? Why can’t you nor anyone else show us how the concept of all countably infinite sets have the same cardinality is used?

Yes, daves. That JVL ignores what I post and prattles on, is evidence of that.

ET,

I will say that when people talk about “cardinality” of sets, they always understand it in the way JVL explained.

Your concept of the two “counters” makes sense, but people don’t use the term “cardinality” in connection with it.

Therefore your usage is non-standard.

ET: JVL, why do you think your ignorance and cowardice mean something? Why can’t you nor anyone else show us how the concept of all countably infinite sets have the same cardinality is used?I and

Kairosfocushave told you that it’s fundamental to the foundations of set theory and therefore modern mathematics. But you ignore that.I mentioned, in passing, that it underlies and puts on a firm foundation the ability to work with infinite series including power series which lead on to Laplace transforms and Fourier transforms. But you dill deny that as well no doubt.

And, finally, it doesn’t matter if it’s used or not. It’s still true. You don’t get to say it’s rubbish just because you don’t know how it’s used.

Does any use Fermat’s last theorem? Or the Four Colour theorem? No one used Topology for quite a while until physics caught up. Lots and lots of Number Theory is pure mathematics with no real world applications whatsoever.

You can’t find an unmatched element in my matching between sets A and B. Therefore they must have the same number of elements. It doesn’t matter how fast you count them or any of that. All that matters when you’re talking about size is how many elements there are. Your example is not pertinent. But you cry and whine that I haven’t addressed it. How many times do you have to have it explained?

Deny, deny, deny. You can’t be wrong so everyone else, over a century of mathematicians, textbooks, papers, etc got it wrong. But you got it right. Uh huh.

DaveS: I will say that when people talk about “cardinality” of sets, they always understand it in the way JVL explained.Your concept of the two “counters” makes sense, but people don’t use the term “cardinality” in connection with it.

Therefore your usage is non-standard.See,

DaveSgets it. Didn’t take long either. Not years and years likeET.Yes, daves, I know my usage is non-standard. I never said that it wasn’t. Both my counter example and set subtraction support my point of view. All anyone else can do is repeat the very thing that I am disputing. “People” don’t use cardinality at all. Go out on the street and take a poll.

JVL:

Your words are HOLLOW and meaningless.

And you are full of it.

That JVL has to ignore my counter example says it all, really.

ET,

Then why not state your point using standard vocabulary? That would help others to understand it.

ET: All anyone else can do is repeat the very thing that I am disputing.In mathematics people ‘dispute’ things by finding mistakes not just stomping their feet and claiming they’re right. Can you find a mistake? Can you find an unmatched element? If you can’t then how can sets A and B have different sizes?

“People” don’t use cardinality at all. Go out on the street and take a poll.You don’t use it so it’s not true? How does that follow?

Your words are HOLLOW and meaningless.So you whine and complain that no one has explained to you how the concepts are used and then when someone explains it to you you deny what’s been said?

And you are full of it.It’s not my fault you don’t understand the applications within mathematics.

That JVL has to ignore my counter example says it all, really.I didn’t ignore it. I told you determine the size of sets has NOTHING to do with counters clicking at different speeds. That’s stupid. It has to do with seeing if two sets can be put into a one-to-one correspondence. But you’ll claim I ignored it again because you can not admit you can’t find an unmatched element in set A or B in my matching EVEN THOUGH you said you had found loads. Can’t name one though can you?

Use your set subtraction to compare the cardinalities of the positive integers and the polynomials with rational coefficients. What, you can’t do that. Gosh, I guess ‘set subtraction’ is pretty useless isn’t it. I wonder if anyone actually uses it when comparing sets that are infinite and where one is not a subset of the other . . .. gosh, nope, they don’t!! I guess it doesn’t work. What a shame.

daves- I have beaten this to death. My point is that there are different densities of infinity with respect to a set’s elements. Set subtraction and the counter example demonstrate this. Different densities is the very reason why Cantor said there are different infinities- one for the countably infinite and one for the non countably infinite.

There are and have been objections to Cantor’s axiom of infinity: https://en.wikipedia.org/wiki/Controversy_over_Cantor%27s_theory

JVL:

And yet all YOU do is stomp your feet and claim that you are right.

JVL:

That is just stupid. As I said, you do not understand infinity.

Jvl:

You did NOT explain anything. You just spewed gibberish.

ET: And yet all YOU do is stomp your feet and claim that you are right.Still can’t find a mistake or an unmatched element in set A or B can you? And too afraid to admit it.

My point is that there are different densities of infinity with respect to a set’s elements.Great, compare the ‘densities’ of the positive integers and the positive primes and show us how it works.

Set subtraction and the counter example demonstrate this. Different densities is the very reason why Cantor said there are different infinities- one for the countably infinite and one for the non countably infinite.There’s a lot more than two! Which is also easy to find.

EThas been shown the proof that the cardinality of the reals is NOT the same as the cardinality of the counting numbers. That proof takes off from the proof that the rational numbers DO have the same cardinality of the counting numbers (aleph-nought).EThas also been shown a proof that any infinite subset of a countably infinite set is also countably infinite. And he cannont find a mistake in that proof or any proof.He can ‘dispute’ all he wants. But if he can’t find a mistake then the proofs stand. That’s how it works.

There are and have been objections to Cantor’s axiom of infinity:Go on, explain what the objection are, in your own words.

And yet all YOU do is stomp your feet and claim that you are right.I am right. I’ve demonstrated it over and over again. I’ve shown you the proofs. You cannot find a mistake in any of the proofs AND, more pertinently, you cannot find an unmatched element of set A or B. But you won’t admit that you can’t find an unmatched elements so you keep trying to deflect attention away from that question.

So, again, can you find an unmatched element in set A or B in my matching scheme? Yes or no?

That is just stupid. As I said, you do not understand infinity.Everyone else agrees with me.

You did NOT explain anything. You just spewed gibberish.If you think I’ve ‘spewed gibberish’ then you have demonstrated that you don’t understand the mathematics.

Keep digging the hole you’re standing in. It’s very amusing. I suspect there are some people laughing at you as we speak.

ET, I note that the key problem in every case has been the structural importance of the ellipsis. Countable endlessness has cardinality aleph null, which is a degree of transfiniteness, not the same as 5 or 3. I am sure x –> 2*x –> 2x is uncontroversial, so take N:

{0,1,2 . . .}

x*2 for all elements:

{0,2,4 . . .}.

These two sets have the same cardinality

now do 2*x +1:

{1,3,5 . . .}

Again, the same cardinality.

The property/structure of endless continuation makes the key difference from a finite chain.

In effect, thanks to never running out on the series, the evens and the odds are transmuted forms of N.

Similarly, and relevant to earlier debates strike off k elements:

{k,k+1,k+2 . . .}

is again a transmuted form, shifted right to k on, take away k from each element and we have {0,1,2 . . .}

And more.

From this, we see that the properties are inherent.

This is why one definition of a transfinite set is that a proper subset can be placed in full correspondence with it.

KF

PS, you can construct an abstract, logic model world on different premises but where it goes is a problem, and whether it is as useful is another.

ET,

If you clarify that you are talking about densities, and not claiming that {1, 2, 3,…} and {2, 4, 6, …} have different cardinalities, then everything would be fine.

Kairosfocus: Countable endlessness has cardinality aleph null, which is a degree of transfiniteness, not the same as 5 or 3. I am sure x –> 2*x –> 2x is uncontroversial, so take N:{0,1,2 . . .}

x*2 for all elements:

{0,2,4 . . .}.

These two sets have the same cardinality

now do 2*x +1:

{1,3,5 . . .}

Again, the same cardinality.Yup, yup. Thank you.

This is why one definition of a transfinite set is that a proper subset can be placed in full correspondence with it.See,

Kairosfocusgets it.DaveS: If you clarify that you are talking about densities, and not claiming that {1, 2, 3,…} and {2, 4, 6, …} have different cardinalities, then everything would be fine.In fact, there is a way to handle the ‘densities’ of infinite sets. But I’m afraid the math is beyond

ET‘s capabilities.Again, set subtraction proves there is something wrong with then INFERENCE from Cantor’s proof. That JVL cannot grasp that is on him, not me.

Nothing in what KF said has anything to do with using the concept that all countably infinite sets have the same cardinality. He is just repeating Cantor

daves:

They are the same thing. Set subtraction demonstrates there is a difference in the number of elements, ie cardinality.

JVL:

I know. I was just providing an example. But clearly that, too, is over your head

Yes, I was shown that decades ago. And I understand it. It is the very basis of my claim.

No one can show us anyone using the concept for anything. No one can present an example of how to use the concept that all countably infinite sets have the same cardinality. No one

JVL, if you really want to make this personal I suggest meeting me and getting it over with. YOU are NO ONE to challenge me. YOU have proven to be ignorant of logic and reasoning.

So stuff it

If someone wants to believe that one set (A) has ALL of the elements in another set (B), PLUS set A has infinite elements B does NOT have, yet they have the same cardinality, ie the same number of elements, I don’t care. Just don’t try to get me to drink your BS.

ET: Again, set subtraction proves there is something wrong with then INFERENCE from Cantor’s proof. That JVL cannot grasp that is on him, not me.You’ve proved nothing and you haven’t been able to find a fault in anyone’s proof or find an unmatched element of set A or B under my scheme.

Nothing in what KF said has anything to do with using the concept that all countably infinite sets have the same cardinality. He is just repeating CantorBecause it’s correct. And you haven’t been able to prove otherwise.

They are the same thing. Set subtraction demonstrates there is a difference in the number of elements, ie cardinality.Nope, as established by proofs you have failed to disprove.

Yes, I was shown that decades ago. And I understand it. It is the very basis of my claim.Not true at all. You don’t even understand what you’ve claimed. Too funny.

No one can show us anyone using the concept for anything. No one can present an example of how to use the concept that all countably infinite sets have the same cardinality. No oneIt has been shown, you just deny, deny, deny. AND the truth of it doesn’t depend on an application. You lose, twice over.

JVL, if you really want to make this personal I suggest meeting me and getting it over with. YOU are NO ONE to challenge me. YOU have proven to be ignorant of logic and reasoning.Ooo, I’m scared now! Physical threats, that’s how you do mathematics. Too funny. You have been shown to be ignorant of well established and used mathematics and you think you can win with fisticuffs? What a buffoon.

If someone wants to believe that one set (A) has ALL of the elements in another set (B), PLUS set A has infinite elements B does NOT have, yet they have the same cardinality, ie the same number of elements, I don’t care. Just don’t try to get me to drink your BS.You’re very welcome to NOT be able to get your head around well established, well used and (mostly) non-controversial mathematics. Knock yourself out.

AND, let’s say it again:

You have NOT found a fault with any proof that establishes the results you dispute.

You have NOT found an unmatched element in either set A or set B under my matching even though you said you had found unmatched elements. I guess that was just bluffing and hoping no one would call you on it.

Your ideas run counter to what has been published in hundreds, thousands of paper, textbooks, etc over the last century.

Kairosfocusagrees with me as well,DaveSgot the issue easily. You just can’t admit you have been wrong for several years. And when it’s been shown to you over and over and over again you make physical threats. What a great example of doing mathematics you present.Can you find an unmatched element in set A or B? Yes or no?

Can you find a mistake in any of the proofs that have established the mathematics you dispute? Yes or no?

ET,

You seemed to agree above that they are not the same.

By one way of reckoning, {10, 20, 30, …} has density 1/10 that of {1, 2, 3, …}, while the operation of adding a zero, which associates 1 to 10, 2 to 20, etc., preserves the number of elements, so that the cardinalities of {1, 2, 3, …} and {10, 20, 30, …} are equal.

Now you are saying that your “counter” method is the only valid way to do this.

DaveS- The densities and the cardinality are directly linked. If the cardinalities are equal then set subtraction should verify an validate that claim. It doesn’t.

The set {1,2,3,4,5,…} has EVERY element in the set {10,20,30,40,50,…} PLUS it has infinitely more elements. If you want to believe that they have the same cardinality, I don’t care. The reason what you believe is counter-intuitive is because it is nonsense

Earth to JVL- You have no clue. You request that I use my own words to describe something and yet all YOU can do is parrot a dead guy stuck in the 19th century. You are a sick person.

And you are welcome to believe something that is patently false. I will gladly join the over 6 BILLION people who agree with me

daves:

‘The counter method is just a clear example that demonstrates an inference from Cantor’s proof is incorrect. In mathematics all it takes is ONE example that goes counter to the claim to ruin the claim

ET,

But now you have to swallow some very counterintuitive consequences yourself. Tacking a zero onto the end of each numeral decreases the number of elements by a factor of 10. Also, placing decimal points to the left of each zero, as in 5 -> 50 -> 5.0, increases the number of elements by a factor of 10, and we’re back to where we started. That’s too magical for my tastes.

What? How is it too magical to end up where you started if your process takes you there? There isn’t anything counterintuitive about ending up where you start if that is the path you take. Tack a zero on and then take it away. Where did you think you would end up? It would be very magical to not end up where you started.

All I am saying, daves, is the bijective function that maps the one-to-one correspondence becomes the relative cardinality.

ET,

The rest of us are not talking about “relative” cardinality. The cardinality of a set, as we understand it, is absolute. The notion that simply adding a dot to each numeral changes the cardinality of the set is just unacceptable.

Major Face Palm- come in major face palm.

I agree. However, cardinality refers to a number. Infinity isn’t a number, it’s a journey. That is where relativity comes in.

That “dot” is a decimal point and has meaning in mathematics. It actually does something. The notion that one set has all of the elements contained in another, PLUS elements the other doesn’t, and still have the same number of elements, is lunacy. And lunacy is unacceptable.

But that is moot as you think it’s magical to add a zero, take it away and end up where you started. That is unacceptable.

🤦

Edit: The number we are presently discussing is ℵ0.

ET is right.

Infinity is not a number. Its an absurdity.

Andrew

ET: Earth to JVL- You have no clue. You request that I use my own words to describe something and yet all YOU can do is parrot a dead guy stuck in the 19th century. You are a sick person.It doesn’t matter to me if you can’t explain something you support. It doesn’t matter to me if you can’t find an unmatched element in sets A or B under my matching. It’ doesn’t matter to me if you can’t find a mistake in the proofs of theorems which contradict your statements.

And you are welcome to believe something that is patently false. I will gladly join the over 6 BILLION people who agree with meWelcome to the losers’ club.

‘The counter method is just a clear example that demonstrates an inference from Cantor’s proof is incorrect. In mathematics all it takes is ONE example that goes counter to the claim to ruin the claimBut you haven’t found the counter example because you THINK the rate at which the counters tick means something. It doesn’t. That is not the issue.

What? How is it too magical to end up where you started if your process takes you there? There isn’t anything counterintuitive about ending up where you start if that is the path you take. Tack a zero on and then take it away. Where did you think you would end up? It would be very magical to not end up where you started.Pure gibberish.

All I am saying, daves, is the bijective function that maps the one-to-one correspondence becomes the relative cardinality.What’s the relative cardinality of the prime numbers then? Go on tell us.

That “dot” is a decimal point and has meaning in mathematics. It actually does something. The notion that one set has all of the elements contained in another, PLUS elements the other doesn’t, and still have the same number of elements, is lunacy. And lunacy is unacceptable.Speaking of lunacy.

Let’s recap:

You haven’t been able to find an unmatched element in sets A or B under my matching.

You haven’t found a fault in any proof supporting the accepted mathematics.

You cannot specify the ‘relative’ cardinality of the prime numbers.

Have I forgotten something?

That isn’t a number, daves. It’s a contrivance.

Asauber: ET is right.Infinity is not a number. Its an absurdity.Welcome to the mathematics deniers’ club.

“Welcome to the mathematics deniers’ club.”

JVL,

Hey, I think rearranging symbols is very, very real.

Andrew

I am claiming that your “matching” is bogus. I have explained ad nauseum why your “matching” is bogus. That you still refuse to grasp that says it all.

And no, I will never be a member of your club, loser.

Asauber: Hey, I think rearranging symbols is very, very real.As long as you don’t expect anyone to take you seriously.

What? How is it too magical to end up where you started if your process takes you there? There isn’t anything counterintuitive about ending up where you start if that is the path you take. Tack a zero on and then take it away. Where did you think you would end up? It would be very magical to not end up where you started.JVL:

Only to an imbecile.

“As long as you don’t expect anyone to take you seriously.”

JVL,

I don’t take you seriously, either, so we are even steven.

Andrew

ET: I am claiming that your “matching” is bogus. I have explained ad nauseum why your “matching” is bogus. That you still refuse to grasp that says it all.It’s not ‘bogus’. It works. It does what it claims. It contradicts your assertions and claims. Let’s recap, again:

You claimed to have found lots of unmatched elements under my matching between sets A and B but you haven’t specified a single unmatched element.

You haven’t found a single fault in any proof of any mathematical theorem. At all.

You proposed the idea of ‘relative cardinality’ but you cannot specify the relative cardinality of the primes.

ET: What? How is it too magical to end up where you started if your process takes you there? There isn’t anything counterintuitive about ending up where you start if that is the path you take. Tack a zero on and then take it away. Where did you think you would end up? It would be very magical to not end up where you started.More gibberish. And, it doesn’t address the issues on the table:

What is the relative cardinality of the primes?

Can you find a fault in any of the mathematical proofs which contradict your claims?

Can you find an unmatched element in sets A or B under my matching scheme?

As to infinity in mathematics, Gödel’s incompleteness theorems were ultimately a cumulation of the work of Georg Cantor in trying to bring a systematic understanding of infinity into mathematics. In short, Georg Cantor was trying to ‘tame infinity’ so as to make it mathematically useful.

As the beginning of the preceding video made clear, this endeavor by Cantor to ‘tame infinity’ was very much a theological quest for Cantor.

In fact, in the following article Cantor is quoted as saying that, “From me Christian philosophy will be offered for the first time the true theory of the infinite.”

As the preceding video also touched upon, Cantor ultimately failed in his endeavor to ‘tame infinity’. In fact, the preceding video is also not too subtle in its hint that Cantor’s mental illness in his later life was directly associated with his endeavor to try to ‘tame infinity’.

As the following article states, “Cantor spent the last thirty-five years of his life in a vain effort to prove this., (i.e. that all the possible orders of infinity could be counted,), He died in 1918 in a mental hospital.”

And although Cantor failed to in his effort to completely ‘tame infinity’, none-the-less, he developed some very useful tools in mathematics which later proved to be very useful to Gödel in his work on bringing incompleteness to fruition,,

Cantor would have been very pleased with Gödel’s results. As to following article states, “Gödel demonstrated that mathematics was intrinsically incomplete. Gödel was reportedly concerned that he might have inadvertently proved the existence of God, a faux pas in his Viennese and Princeton circle.”

Indeed Cantor would be very pleased with Gödel’s work. The Theistic, even Christian, implications of incompleteness are obvious,,,, as mentioned previously in this thread in these following articles,,,

Of supplemental note, Gödel’s work was recently extended to Quantum Physics and “challenge the reductionists’ point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description.” (i.e. the reductive materialism of Darwinian evolution is, via the extension of incompleteness to quantum physics, proven to be false!)

Also of supplemental note, Kurt Gödel, like Cantor, was also an adamant Christian. Specifically, a ‘baptized Lutheran’. Moreover, Gödel was convinced that there must be an afterlife by pure reasoning, A belief in the afterlife that he said was derived independently of any theology.

JVL:

Between A and B the set C is unmatched.

How much do you want to ante up? It has to be at least $10,000 US.

Does anyone else think it is impossible to find the relative position of the primes as compared to the naturals? The squares is easy enough. The cubes. The cubes relative to the squares and the naturals. The cubes relative to the primes. The primes relative to the squares.

It all can be one.

JVL’s matching is bogus because in the case of the naturals vs the evens, you are forcing a 1 to be “matched” with a 2. The way I call it we have the natural matching. The 2’s match. The 4’s match. And so on. That is the SAME matching used throughout set theory to determine if one set is a subset of another. Or if there is a union between two sets.

At least with me we get consistency from bottom to the top.

ET,

I believe this “relative cardinality” of the primes (to {1, 2, 3, …}) has already been computed. It’s available on a number of wikipedia pages (for much less than $10,000).

Thanks daves. JVL just wants to make this personal. For that I charge $10,000 US.

ET: Between A and B the set C is unmatched.This is just dumb. We’re not talking about set C at all. Now, if you mean the odd numbers in set A then I showed you how they are matched to elements in set B. I guess I have to show the scheme again because some people just can’t understand it.

A = {1, 2, 3, 4, 5, 6, 7 . . . . . .} B = {2, 4, 6, 8, 10, 12, 14 . . . . }

1 (in A) 2 (in B)

2 (in A) 4 (in B)

3 (in A) 6 (in B)

4 (in A) 8 (in B)

5 (in A) 10 (in B)

6 (in A) 12 (in B)

7 (in A) 14 (in B)

And so on.

CLEARLY all the elements of A have a partner in B, even and odd numbers.

How much do you want to ante up? It has to be at least $10,000 US.Just do it if you can.

Does anyone else think it is impossible to find the relative position of the primes as compared to the naturals? The squares is easy enough. The cubes. The cubes relative to the squares and the naturals. The cubes relative to the primes. The primes relative to the squares.Do it then. (“relative position of the primes”?)

It all can be one.We’re waiting to see you do it.

JVL’s matching is bogus because in the case of the naturals vs the evens, you are forcing a 1 to be “matched” with a 2. The way I call it we have the natural matching. The 2’s match. The 4’s match. And so on. That is the SAME matching used throughout set theory to determine if one set is a subset of another. Or if there is a union between two sets.We’re not checking to see if one set is a subset of the other! We’re seeing if they’re the same size? And there is no preference or rules on how the matching is done. If you can come up with a scheme and it works then you’re done.

At least with me we get consistency from bottom to the top.And you can’t handle a bunch of cases. What’s the cardinality of the polynomials with rational coefficients? What’s the cardinality of the primes?

And you still haven’t found any unmatched elements in my scheme between A and B.

DaveS: I believe this “relative cardinality” of the primes (to {1, 2, 3, …}) has already been computed. It’s available on a number of wikipedia pages (for much less than $10,000).Well, link to it then!

HInt: the primes have the same cardinality as the positive integers, that being aleph-nought. They are both countably infinite sets. AND there is an easy to find theorem which says any infinite subset of any countably infinite set is also countably infinite, i.e. with cardinality aleph-nought.

Can I have my $10,000 please as my answer is correct and can be verified on many websites and textbooks. Or just phone up your local mathematics department at a university. I take checks.

ET,

I am not merely blindly quoting (esp. without attribution!), I am showing that once one defines an exhaustive 1:1 mapping between sets P and Q one defines a function . . . and yes this stuff connects to what a function is . . . so one can transform one set into another.

The key with transfinite sets is that the ellipsis [and things beyond such as continuum] imply inexhaustibility of any case by case process.

So, we TRANSFORM N into the evens and the odds or even k on continuation thereby showing these have the same scale as N, Aleph null, first order, inexhaustible countability.

Power sets come in and there is a debate as to pinning c, continuum to a member of that chain. Using ordinals — there we go on how pervasive the influence of this work was — we can get a chain of transfinite integers and can go on to fill in a continuum, in principle. The infinitesimal cloud around 0 — I have represented *0* — can be transferred to any hyper-integer and that then extends to [0,1) and its mirror (-1,0]. Infinitesimally altered numbers are everywhere and are utterly dense. Indeed, there are vastly more densely packed in infinitesimally altered numbers than real numbers, as the transfinite extension of the reals will show.

That is, we can translate from the intuitive but wrong sense of greater cardinality of sets as a whole to greater densities in sampled intervals. That is the density idea is that some types of numbers are far more common in a given interval than other types. Integers are less dense than reals but more dense than evens or odds or squares etc. But because of inexhaustibility, the cardinalities can be the same, here, first order countable but inexhaustible values.

Could that be a way forward?

In which context, we can speak of “subtraction” in set theoretic terms as say, the evens are the complement to the intersection of the naturals and the odds. But this does not do away with countability or inexhaustibility so we can make a 1:1 match betwen naturals and evens, or even transform the naturals into the evens.

So, we have a counterintuitive but valid result.

KF

AS, infinity is indeed not a number, but a concept, beyond finite bound. Immensus in the Athanasian creed, beyond bounding finite measure. Indeed, in + finite means not finitely bounded. God is infinite, his powers and attributes are maximally great, confined only by the logic of compossibility i.e. they are all so together so are coherent. And God is not absurd. Infinity is not absurd with numbers either, we can properly conceive, construct and represent then manipulate transfinite quantities and structures, then use the 1/x catapult to get infinitesimals and by shifting the cloud around 0 –*0* for convenience — we infinitesimally alter any number. This points to calculus. And ultimately it is the infinitesimals and infinitesimally altered numbers that are the most densely present, indeed, they are the most familiar form of the transfinite at work, from Calculus. Which is always a main goal. Newton’s h, dx, dt, dr and onward extensions are absolutely vital to any number of disciplines, even when disguised under epsilon delta limit approaches. Nonstandard analysis is truly liberating. KF

AS, infinity is indeed not a number, but a concept, beyond finite bound. Immensus in the Athanasian creed, beyond bounding finite measure. Indeed, in + finite means not finitely bounded. God is infinite, his powers and attributes are maximally great, confined only by the logic of compossibility i.e. they are all so together so are coherent. And God is not absurd. Infinity is not absurd with numbers either, we can properly conceive, construct and represent then manipulate transfinite quantities and structures, then use the 1/x catapult to get infinitesimals and by shifting the cloud around 0 –*0* for convenience — we infinitesimally alter any number. This points to calculus. And ultimately it is the infinitesimals and infinitesimally altered numbers that are the most densely present, indeed, they are the most familiar form of the transfinite at work, from Calculus. Which is always a main goal. Newton’s h, dx, dt, dr and onward extensions are absolutely vital to any number of disciplines, even when disguised under epsilon delta limit approaches. Nonstandard analysis is truly liberating. KF

PS: Do not overlook the ubiquity of sequences and series in modern mathematics, which involve running indices, often from N.

Weird a double post.

KF,

I respectfully disagree. God is beyond human understanding, other than what He has revealed to us. So Because God doesn’t work to fix infinity. It’s still an absurdity.

Andrew

KF,

Introducing infinity into ideas like the progression of time causes paradoxes, doesn’t it? Why do you think that is?

Andrew

JVL,

Sorry, I should have used the standard term, density. I believe that by “relative cardinality” ET means a type of density, and this density of the primes in {1, 2, 3, …} is zero by the Prime Number Theorem. I do agree that the cardinality of the primes is aleph-0.

Kairosfocus: Weird a double post.You ARE special! Even the website thinks what you have to say is worth repeating!! 🙂

DaveS: Sorry, I should have used the standard term, density.Ah yes, that is something completely different! And has nothing to do with the size of the sets.

I believe that by “relative cardinality” ET means a type of density, and this density of the primes in {1, 2, 3, …} is zero by the Prime Number Theorem.I agree with that result, obviously ’cause it’s correct. And no, that’s not what

ETis thinking. He’s been saying the same thing for years.I do agree that the cardinality of the primes is aleph-0.DaveS: 2 points.

KF:

Wow, transform one set into another- like alchemy or magic? That isn’t mathematics

Earth to JVL a “1” does NOT match a “2”. A “2” matches a “2”.

No wonder you are ignorant of science.

JVL:

YOU can’t because you are too dim to think beyond your own arse. And if you want to make this personal then I suggest we meet and get it over with. How desperate of a coward are you?

ET,

The idea is that these transformations should not affect the cardinality of the set itself. We take this as axiomatic.

Suppose you have a large jar full of marbles. Take each marble out and draw a dot on it with a Sharpie, and place the “dotted” marbles in a new jar. The total number of marbles does not change.

Any theory of cardinality where this principle is violated is going to have problems.

Edit:

To continue the analogy, suppose you have a large (infinite) jar containing tickets labeled 1, 2, 3, and so on. Remove the tickets one at a time, cross out the original number, and write 2 times the original number minus 1. Then place the renumbered tickets in a new jar.

Does the number of tickets change? Obviously not.

Edit 2:

This is a concrete illustration, and we are really talking about abstract concepts which do not occupy space. Therefore there is nothing stopping us from considering a jar with infinitely many “marbles” or tickets inside.

Again, cardinality refers to the number of elements. Infinity is not a number, it’s a journey.

The number of marbles in the jar is finite.

If you want to believe that one set that has ALL of the elements of another, PLUS infinite elements NOT in the other set but still they both have same number of elements, I don’t care. I am not going to drink that BS. Cantor’s diagonal just proves both sets are countable. That some people take it to mean they also have the same cardinality is their wrong inference.

Infinity is NOT magic, it’s a journey. That is why the counter example is relevant- it exemplifies the journey. And that is also why relativity is also relevant.- it looks at the journey from a proper perspective.

ET,

Regarding Cantor’s diagonalization argument, it shows that the set of real numbers

cannotbe put in one-to-one correspondence with {1, 2, 3, …}. Hence the real numbers and {1, 2, 3, …} donothave the same cardinality. I would have assumed you agreed with this because your two-counter method also shows the set of real numbers is much larger than the set of natural numbers.PS to my #392: In the ticket/jar illustration, all the renumbered tickets have distinct numbers on them; if there were some “collisions”, then my analogy would break down.

Small technical note here, dx, dt, etc are Leibniz’s notation, not Newton. Newton used apostrophes. f’(x), f’’(x) etc.

ET: Earth to JVL a “1” does NOT match a “2”. A “2” matches a “2”. No wonder you are ignorant of science.The values or labels of the elements do not matter. If you don’t like those two sets then try these:

A = {1, 2, 3, 4, 5 . .. . . } and B2 = {-2, -4, -6, -8, -10 . . . . }

Clearly B and B2 are the same size. And here’s my new matching:

1 -2

2 -4

3 -6

4 -8

etc.

Same result: both sets are the same size, both are countably infinite, both have cardinality aleph-0.

OU can’t because you are too dim to think beyond your own arse. And if you want to make this personal then I suggest we meet and get it over with. How desperate of a coward are you?You can’t handle some cases I have presented to you. You’re childish bully-boy threats are laughable and not the way mathematics is done.

If you want to believe that one set that has ALL of the elements of another, PLUS infinite elements NOT in the other set but still they both have same number of elements, I don’t care. I am not going to drink that BS. Cantor’s diagonal just proves both sets are countable. That some people take it to mean they also have the same cardinality is their wrong inference.There is, in fact, a theorem which proves that any infinite subset of a countably infinite set is also countably infinite with the cardinality aleph-0. You can not find a fault with the proof of that theorem so it stands as truth.

Infinity is NOT magic, it’s a journey. That is why the counter example is relevant- it exemplifies the journey. And that is also why relativity is also relevant.- it looks at the journey from a proper perspective.It’s not magic, the ways to deal with it were elucidated by Cantor and others. Relativity has to do with physics not mathematics.

All your questions have been considered and answered. You just keep denying the truth.

You’ve been asked to find some unmatched elements in my scheme for sets A and B, you haven’t been able to do so. You seem to think that only your matching is valid which is clearly not the case if you looked in any university level set theory book or just checked with the tons of online resources that confirm what I am saying. You just keep denying.

You’ve been asked to apply your method of relative cardinalities to the prime numbers which you have failed to do. You have been asked to apply your method to the set of all polynomials with rational coefficients which you have failed to do. Your method barely works AND every mathematician in the world disagrees with you. But you just keep denying.

You have been asked over and over and over again to find a fault or mistake in the proofs of the pertinent theorems and you have not been able to do so. But you just keep denying.

DaveS: Regarding Cantor’s diagonalization argument, it shows that the set of real numbers cannot be put in one-to-one correspondence with {1, 2, 3, …}. Hence the real numbers and {1, 2, 3, …} do not have the same cardinality. I would have assumed you agreed with this because your two-counter method also shows the set of real numbers is much larger than the set of natural numbers.DaveSgets it. It’s pretty straightforward. ButETwill just keep denying.ET: Infinity is NOT magic, it’s a journey. That is why the counter example is relevant- it exemplifies the journey. And that is also why relativity is also relevant.- it looks at the journey from a proper perspective.Put the integers in a box in ascending order. Put the evens in a box in ascending order. Take one out of each box at a time and match them together. Repeat. You have to count the elements of both sets at the same speed. As has been explained over and over and over again. But you just keep on denying.

I think ET just gets off on arguing with people, nobody would pursue this silly nonsense for years without contacting mathematicians. He knows he’s wrong he’s just getting some kind of kick out of it.

Retired Physicis: I think ET just gets off on arguing with people, nobody would pursue this silly nonsense for years without contacting mathematicians. He knows he’s wrong he’s just getting some kind of kick out of it.Maybe, but why all the threats and abuse? He’s much worse on his own site where there are no moderators except himself.

I didn’t know he had his own site, I can’t imagine why anybody would go there.

But hey, there are people who have sexual interests that involve them getting dominated and abused, I don’t understand those people but I suppose you have to be wired that way to understand it. Maybe he gets off on some kind of public humiliation, he certainly seems to seek it out.

If he actually believed he was correct he would seek out mathematicians so that he could be awarded his Fields medal and recognized as a world-class mathematician. The fact that he doesn’t seek out mathematicians and doesn’t care what they think suggests that he knows he’s full of it.

RP,

I suspect ET is beyond the age limit (40 years) for a Fields Medal.

Why don’t you transform a set of infinite integers into food and feed the world!

What? You can’t? Go figure…

daves:

That’s because the reals are NOT countably infinite.

JVL:

Values matter in mathematics. Only a dolt would think otherwise.

DaveS 20 years ago I knew a Swedish guy who was one of the codiscoverers of wavelets, and unfortunately those math people are super arrogant, despite being super dumb with the ageism. What’s the deal with 40 years? At 41 you shouldn’t be recognized for an amazing discovery? So stupid.

If you want to believe that one set that has ALL of the elements of another, PLUS infinite elements NOT in the other set but still they both have same number of elements, I don’t care. I am not going to drink that BS. Cantor’s diagonal just proves both sets are countable. That some people take it to mean they also have the same cardinality is their wrong inference.I have nothing else to say about this matter.

Eh? I thought you don’t accept that Cantor’s diagonalization argument is a valid proof?

RP,

Yeah, I think it’s an odd requirement in this day and age. I guess that’s what Fields wanted, and apparently there hasn’t been pressure to remove it.

WTF daves? I said Cantor’s diagonal is proof the sets are countable.

You guys don’t even know how to read for comprehension. Why should anyone believe your asinine math?

@DaveS I was consulting for an engineering company in North Carolina about 15 years ago, and a guy said oh you’re in physics, my son said he went into math because the physics people are the people who are too stupid to be mathematicians. I responded something to him like OK that’s great, because they were paying me more than anybody’s ever paid me in my life. All I wanted to say was ‘Albert Einstein was in physics, and he figured out the photoelectric effect, Brownian motion, special relativity, and general relativity, he could have legit won 4 Nobel prizes, and you think everybody who is in math is smarter than that guy?’

People who believe in conspiracy theories do so because they are intellectually insecure, but I’m starting to think there are some math people in that group too.

RP:

That doesn’t follow. I am not on your asinine agenda. And seeing that the concept I am disputing is not used and is useless, why bother?

Still waiting for the transformation of infinite integers into food….

Holy moly This all got me thinking about my friend Susan who works at a UF hospital and so I messaged her and she just messaged me that the hospital she works at in Gainesville is at 100% capacity.

ET @ 412,

Well, it isn’t. How do you know the set of real numbers is

notcountably infinite? That’s what the diagonalization proof shows.daves:

That’s what I said. Again, if you cannot read for comprehension there is no way I would trust your math.

Why don’t you transform a set of infinite integers into food and feed the world!Oh oh, starting off not making sense is bad.

Values matter in mathematics. Only a dolt would think otherwise.NOT when you’re just counting how many things are in a set. Then, the only thing that matters is how many there are. But, this has been explained to you over and over again and you just keep denying.

I’m okay with you being completely and utterly wrong, provably wrong. I can live with that.

WTF daves? I said Cantor’s diagonal is proof the sets are countable.You guys don’t even know how to read for comprehension. Why should anyone believe your asinine math?Countably infinite. And all countably infinite sets have the same cardinality. If they didn’t you could find an unmatched element in my matching scheme, which you cannot do. But you just keep on denying.

That doesn’t follow. I am not on your asinine agenda. And seeing that the concept I am disputing is not used and is useless, why bother?Unsuccessfully disputed. You never found a mistake or a counter-example. You lose. But you keep on denying.

Still waiting for the transformation of infinite integers into food….I’m still waiting for you to find even one single unmatched element of sets A and B (or sets A and B2) under my scheme.

I’m still waiting for you fo find the relative cardinality of the primes. I’m still waiting for you to find the cardinality of all polynomials with rational coefficients.

I’m still waiting for you to find a fault with the proof that an infinite subset of a countably infinite set is also countably infinite and therefore has the same cardinality, aleph-0.

Instead you just deny, deny, deny. Over and over and over again.

ET,

I don’t see how these can be reconciled. You first say the proof shows “the sets” are countable, then you say it shows the set of real numbers is not countable.

Oh my- the proof can only show that the sets are countable or not.

Wow, my friend Susan is an administrator, and she just told me this

Don’t get sick right now friends.

JVL- it is NOT YOUR scheme. YOU can only parrot the work of others. You cannot find a fault with set subtraction. You lose.

JVL:

OK then. Start counting then elements in {1,2,3,4,5,…} and let us know when you are finished.

JVL still doesn’t understand infinity

JC 112 deaths here in Florida from it and it’s noon.

One good thing that has happened is two months ago nobody here was wearing a mask except doctors and nurses, and now everybody’s wearing a mask.

ET,

And it shows that the set of real numbers is uncountable. It doesn’t show that some set is countable.

Anyway, apparently you believe that Cantor successfuly showed that

Ris uncountable (which is a positive thing).Edit: In particular, it doesn’t show that “all countably infinite sets have the same cardinality”—that’s an elementary consequence of the definitions.

ET: JVL- it is NOT YOUR scheme. YOU can only parrot the work of others. You cannot find a fault with set subtraction. You lose.I’m happy to use the correct work of others. I like the truth.

I’ve found fault after fault. It can’t address lots of situations. It disagrees with proven results, proofs for which you can find no fault. And it’s not used for infinite sets for determining cardinality. It’s the wrong tool for the job.

But you just keep on denying. Over and over and over again.

OK then. Start counting then elements in {1,2,3,4,5,…} and let us know when you are finished.JVL still doesn’t understand infinityStill can’t find a mistake in any proofs. Still can’t find an unmatched element. Still can’t find some ‘relative cardinalities’.

JVL- the only fault with set subtraction is YOU. Good luck with that.Funny you can’t use it to answer a couple of my questions then. Funny that NO ONE uses it to check the cardinality of infinite sets. Except for you. Funny that it gives contradictory answers to proven mathematics, proofs which you cannot find fault with.

Deny, deny, deny.

The only fault with my counter example is also JVL.It doesn’t work! It runs counter to proven mathematics, proofs which you cannot find fault with.

Deny, deny, deny, deny.

I never doubted that. You guys have serious issues.

JVL- the only fault with set subtraction is YOU. Good luck with that.

The only fault with my counter example is also JVL.

daves:

Or an elementary misunderstanding.

ET: Or an elementary misunderstanding.Deny, deny, deny. Deny well established and proven mathematics without being able to find a fault with any theorem you disagree with. Deny, deny, deny.

Still waiting to see if you can:

Find an unmatched element between sets A and B using my perfectly acceptable scheme.

Find a mistake in any theorem in set theory.

Find the ‘relative cardinality’ of the prime numbers.

Find the cardinality of the set of all polynomials with rational coefficients.

Here’s another one: find the cardinality of the roots of unity.

Or this: find the cardinality of the complex numbers whose modulus is less than one.

Go on, prove us wrong. Our views are falsifiable but so far you haven’t been able to falsify them. You just deny, deny, deny.

ET,

Let’s assume that A and B are both countably infinite sets. Then there exist bijections f: A -> N and g: B -> N (where N = {1, 2, 3, …}). The function g^{-1} ∘ f (the composition of g inverse and f) is a bijection between A and B, so A and B have the same cardinality.

daves- the bijective function would be/ represent the relative cardinality. The fact said function exists tells us there is a difference between the two sets.

Is JVL saying that mathematicians are too stupid to be able to determine the relative cardinality of the primes with respect to all positive integers?

Wow

ET: daves- the bijective function would be/ represent the relative cardinality. The fact said function exists tells us there is a difference between the two sets.Doesn’t have a clue about the mathematics. Not a clue.

Is JVL saying that mathematicians are too stupid to be able to determine the relative cardinality of the primes with respect to all positive integers?I KNOW what the cardinality of the primes is. YOU made up the notion of ‘relative cardinality’ so it’s ups to you to show you can use it not the people who think it’s rubbish.

And, guess what? You can’t find the relative cardinality of the primes. You can’t even support your own idea.

I didn’t make the claim, you did. I don’t have to prop up your rubbish idea, you do. Can you? Looks pretty clear that you can’t. But you’ll keep avoiding admitting you can’t.

You’re going to deny, deny, deny. As usual.

ET,

It looks like you’re following Rudy Guiliani’s strategy now.

Is {deny, deny, deny, . . . } an infinitely countable set? What about a nested set of denials?

Sorry, just couldn’t resist. 😉

-Q

ET, functions routinely transform one set into another. KF

AS, I was quoting the Athanasian creed, the most technical of the three commonly referenced creeds. As for scripture, start with Isa 40 on independence of being and the common declaration of eternality. God is necessary thus eternal being himself. Among other cases, consider the point, nothing shall be impossible with God or the question, is there anything too hard for the Lord. Further, in fact the Scriptures do talk of testimonies to God in us and in the world, noting that those who dismiss God do so in the teeth of evidence, cf Rom 1. We can know and should acknowledge some things about God and ourselves in relation to him from reason and sound conscience reflecting on our inner morally governed rationality and the wonders of the world without; note here, Ac 17. But that is of course limited. Authentic scripture and the living edition of God’s word himself, teach us much more. KF

Q, at simple level, a set is a collection of distinct objects that are such that we can determine what’s in and what’s not. A key set is the empty one. What’s in is nada, of course. Chaining collecting that set and successors gives us the counting numbers. This specifically excludes cases where that decision cannot be made. For Mathematics, an axiomatised framework was built up from contemplation of set facts and results after being duly chastened by certain challenges. Insofar as the strings are distinguishable and collected, that is a set, and the ellipsis says endless repetition. KF

“nothing shall be impossible with God”

KF,

Which is my point. Unicorns are not impossible with God. But is it reasonable to think they exist and have magical properties on top of that?

Andrew

ET, that sets may have the like cardinality does not imply having the same elements and only the same elements. It means they can somehow be matched 1:1, member by member, and of course with countable sets, to N or a subset of N. You have already seen what happens with N, the evens and the odds. Endless continuation is a key factor. And that is tied to the point that a transfinite set can be matched 1:1 with a proper subset, without exhaustion. That is a conceptual hurdle similar to understanding complex unity, the nature of a system, quantization or relativity. A paradigm shift is called for. KF

KF:

And those functions demonstrate the differences between the two sets.

AS, I suspect within 100 years unicorns will exist, through genetic engineering; the market is obvious. Magical properties, no. That nothing is impossible with God implies, nothing compossible with his character. KF

daves:

Make your case. Or admit that your “strategy” is bald assertions and false accusations

ET, naturals, odds and evens etc are different in membership though there is overlap. All three share the same cardinality, first, countable, inexhaustible. Where O UNION E = N. KF

JVL:

Says the loser who cannot read for comprehension.

Why do all cowards just think they can falsely accuse someone as if it means something?

“I suspect within 100 years unicorns will exist’

KF,

Great. I’m glad you have a vivid imagination. Nothing to do with whether or not infinity is absurd.

Andrew

P.S. And you didn’t answer this question I asked above: “Introducing infinity into ideas like the progression of time causes paradoxes, doesn’t it? Why do you think that is?”

AS, not imagination, marketing. The genes can doubtless be manipulated, to grow a horn. Rhinos already have such, though technically a hair IIRC. KF

PS: And infinity is not absurd, it means, beyond finite limit. With the hyperreals we have the infinitely large and the infinitely small, quite readily. E.g. any number we can count to k can be exceeded, so we see that the set N has no identifiable upper limit. There is no last k so k+1 is infinity. The infinitesimals are v useful in workaday math. They have been since the days of the ancient Greeks actually.

Yes, KF, I know what mainstream says. Just repeating it isn’t going to change anything.

ET,

I have been making my case. You just haven’t engaged with my posts.

ET, I didn’t merely repeat, i showed why I hold what views I do. But, we can leave it at that. KF

daves, how can I be making your case seeing that I have agreed with much of what you have said?

Yes, KF, I understand why you hold the views that you do. I also held them @ one time in my life. Then I came to a better understanding of infinity.

“k+1 is infinity”

Sorry KF. k+1 is not infinity. It’s some number +1.

Andrew

ET: Says the loser who cannot read for comprehension. Why do all cowards just think they can falsely accuse someone as if it means something?Hey, it’s not my fault you have demonstrated your misunderstanding of mathematics over and over and over again. I’ve told the truth and I’ve told you how you can properly dispute it. But you haven’t managed to do that.

Yes, KF, I know what mainstream says. Just repeating it isn’t going to change anything.But you haven’t been able to refute any proof of any theorem. But you just keep denying over and over and over again.

ET:Okay, let’s try this:

I’ve told you how you can falsify the standard mathematical views on infinity. You just have to find a fault or flaw in one of the many proofs of the theorems supporting that view. If you can do that, you win.

Now, how can someone falsify your view of relative cardinalities? Something that is possible and not just you spouting off some impossible task. What would it take to get you to admit your view is incorrect?

Asauber: Sorry KF. k+1 is not infinity. It’s some number +1.It depends on what ‘k’ is doesn’t it? What did

Kairosfocussay ‘k’ represented?