Intelligent Design

Funny Stuff Over at TSZ

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Over at The Skeptical Zone Elizabeth Liddle writes:

Barry Arrington [says] A=A is infallibly, necessarily true.  What does this claim even mean? . . .  Is his claim even coherent?

Really folks.  You can’t make this up.  She wrote that.  If I made this stuff up someone would accuse me of lying.  But she really wrote that.

Fortunately, not everyone at The Skeptical Zone is a complete idiot.  Kantian Naturalist replies:

It means that every object is necessarily identical with itself.   Which is true, and in a certain sense of “self-evident”, self-evidently true.

Why do they kick against the goads with such vehemence?  Not only do they make fools of themselves, they seem eager to do so.  It really does beggar belief.

 

 

 

 

 

 

 

42 Replies to “Funny Stuff Over at TSZ

  1. 1
    mike1962 says:

    Liz “Well, no – fuzzy logic is a very useful logic system, and A is sometimes only approximately equal to A, or may equal A if it passes some threshold of probability of being A”

    Uh, no. In fuzzy logic A is still always equal to A.

    A may be approximately equal to B or something else, but A is always equal to itself.

  2. 2
    kairosfocus says:

    BA,

    if we cannot find willingness to agree that say a bright red ball on a table is itself and not something else, it is no surprise that forever after we see all sorts of intractable objections.

    We are here dealing with manifestations of a root of irrationality in our civilisation that leads some to say truth is falsity and falsity truth, light is darkness and darkness light, good is evil and evil good, and more.

    Such, in the end is diagnostic of a spiritual state and that kind goeth not out save by scripture:

    Jesus, Matt 6:22 “The eye is the lamp of the body. So, if your eye is healthy, your whole body will be full of light, 23 but if your eye is bad, your whole body will be full of darkness. If then the light in you is darkness, how great is the darkness!

    Paul, Eph 4:17 Now this I say and testify in the Lord, that you must no longer walk as the Gentiles do, in the futility of their minds.

    18 They are darkened in their understanding, alienated from the life of God because of the ignorance that is in them, due to their hardness of heart. 19 They have become callous and have given themselves up to sensuality, greedy to practice every kind of impurity.

    20 But that is not the way you learned Christ!— 21 assuming that you have heard about him and were taught in him, as the truth is in Jesus, 22 to put off your old self,[f] which belongs to your former manner of life and is corrupt through deceitful desires, 23 and to be renewed in the spirit of your minds, 24 and to put on the new self, created after the likeness of God in true righteousness and holiness.

    25 Therefore, having put away falsehood, let each one of you speak the truth with his neighbor . . .

    Isaiah, Is 5:20
    Woe to those who call evil good
    and good evil,
    who put darkness for light
    and light for darkness,
    who put bitter for sweet
    and sweet for bitter!
    21
    Woe to those who are wise in their own eyes,
    and shrewd in their own sight!

    So, we have two ways before us and must choose this day what and Who we will serve. For none may serve two masters.

    KF

  3. 3
    Aleta says:

    I’ve always liked the saying attributed to Wittgenstein: “A thing is what it is, and not another thing.”

  4. 4
    kairosfocus says:

    M62, I think there may be a problem of confusing partial set membership . . . a way of characterising degrees of an attribute . . . with identity. For a temp controller the thermometer indicating T, may be 70% warm, 10% cold and 20% hot but the thermometer indicating T is indeed its own distinct thing. Then the programmed control action may weight the degrees as given and come up with the control action relative to a set target, which “crisp” action will then be again its own distinct thing. At no point have we asserted A is not itself. And BTW the degree of memberships needs not sum to 100% nor follow neat smooth curves. Long stories. KF

  5. 5
    kairosfocus says:

    Aleta, a good summary. KF

  6. 6
    bFast says:

    Even in the weird quantum world, where the existence of A may not be determined until it is examined, the A on both sides of the = go through the same phases of “probability”.

    A=A. Certainly most usually. However, I have failed to find even any exception case. (The finding of some strange exception case does not nullify the general case, however.)

  7. 7
    Mung says:

    I thought that Elizabeth was asking an honest question. She got a bunch of nonsense in return. The psychology of UD. The psychology of Barry. etc.

    She then asked for people who think A=A means something to weight in. At which point KN offered his wisdom.

    But then Elizabeth went on to ignore it. Which calls into question my original assumption, lol.

    Do they really not understand the law of identity? Or is it just that the truth doesn’t matter, esp. if it’s declared at UD.

  8. 8
    Mung says:

    Aleta: I’ve always liked the saying attributed to Wittgenstein: “A thing is what it is, and not another thing.”

    Yes. The “and not another thing” is what was missing from what was offered by KN at TSZ. To me this is not just a statement of logic, but one of ontology. It’s not something decided by our epistemology, which is the mistake Elizabeth makes.

    To say that a thing exists is to assert the law of identity. No wonder we here at UD take it to be fundamental to rationality. Foundational, even.

    But as has been pointed out, self-evident truths are not self-evident to everyone. But who ever said otherwise. So I think we still have a duty to make the case.

    And in asking her question, Elizabeth shows that she’s ignored the posts where that case has been set out. Surely, if she is going to critique the views set out here at UD that is part of her intellectual duty.

  9. 9
    mike1962 says:

    Instant Karma’s gonna get ya.

    Wake up people

  10. 10
    Box says:

    Mung: To me this is not just a statement of logic, but one of ontology. It’s not something decided by our epistemology, which is the mistake Elizabeth makes.

    To say that a thing exists is to assert the law of identity.

    Is to say that a thing exists, to say that it has autonomous existence? When we say that a red balloon “exists”, do we say that its existence does not depend on anything else than what the red balloon seems to be?

  11. 11
    kairosfocus says:

    Box, existence is just that, it is not a declaration that an entity is non-contingent and autonomous. Do you exist? Are you non-contingent? KF

  12. 12
    kairosfocus says:

    Mung, the issue on the table is foundations of rationality. Disagreement after disagreement has been chased back, and we are at the root level now. Lo and behold, we find that a lot of objection to design thought is coupled to problems with first principles of right reason. As in, ouch. To find oneself in opposition to first truths of reason must be hard, especially when giving up such opposition looks like heading where you don’t want to go. KF

  13. 13
    Brent says:

    Liz “Well, no – fuzzy logic is a very useful logic system, and A is sometimes only approximately equal to A, or may equal A if it passes some threshold of probability of being A”

    Just how would one know that “A is only approximately equal to A” unless one knew precisely what A REALLY was?

    These people are actually working hard at being stupid. Being industrious isn’t always a good thing.

  14. 14
    Box says:

    KF,

    //For clarity: my position is that A=A //

    KF: existence is just that, (…)

    ….

    KF: (…) it is not a declaration that an entity is non-contingent and autonomous.

    So your fine with an “A” that is an aspect of a single, dissociable whole? For instance, can a thought be an “A” and its thinker be part of “not-A”? Do properties of a balloon , like “redness”, have their own identity distinct from the balloon? Is the balloon part of e.g. “not-redness”?

  15. 15
    News says:

    Most “skeptics” in the sense used at TSZ are progressives. All progressives aim at power, not fact. No fact can be allowed that limits their power. even if the fact is as simple as A=A or 2+2 makes 4. Understanding and dealing with that reality saves a lot of lives, if we go by the last 150 years.

    Failure to understand and deal with that gives us the politician who deals out minor exemptions from their rule (he will agree that A is A as long as we understand that he must knuckle under to any popular figure who doesn’t agree). We can go on with this as long as we like. But the bill will come in anyway. And it will be much higher.

  16. 16
    News says:

    Most “skeptics” in the sense used at TSZ are progressives. All progressives aim at power, not fact. No fact can be allowed that limits their power. even if the fact is as simple as A=A or 2+2 makes 4. Understanding and dealing with that reality saves a lot of lives, if we go by the last 150 years.

    Failure to understand and deal with that gives us the politician who deals out minor exemptions from their rule (he will agree that A is A as long as we understand that he must knuckle under to any popular figure who doesn’t agree). We can go on with this as long as we like. But the bill will come in anyway. And it will be much higher.

  17. 17
    kairosfocus says:

    Box, a bright red ball is distinct from redness which can be in many other things in pure or blended forms. The ball is contingent. Its redness is contingent based on what it happens to be made of or is coated with. Even its degree of roundness is contingent — hit it with a cricket bat . . . and that stitched overlapping seam is quite a departure from being a sphere. The ball and red things are part of the world which expresses the one and the many — yet another fundamental question. Is a thought distinct from a thinker? Plainly, yes their properties are such as precludes identity. The thinker produces and expresses the thought, speaks or writes, it is passed down and voila 2300 years on we are talking about Ari’s laws of thought. Long after he passed on. KF

  18. 18
    Box says:

    KF: Is a thought distinct from a thinker? Plainly, yes their properties are such as precludes identity.

    So, according to you, a thought is distinct from a thinker. I find your position absurd.

    KF: The thinker produces and expresses the thought, speaks or writes, it is passed down and voila 2300 years on we are talking about Ari’s laws of thought. Long after he passed on.

    It’s hard to believe, but you are actually arguing that Ari’s thoughts are really distinct from Ari!
    This sentence is a representation in matter of a thought of mine, but is not my thought. Same goes for all instantiated versions of Ari’s laws of thought.
    Why do you conflate a thought and its representation and pretend that you can posit “identity” as some easy substitute for “existence”?

  19. 19
    Virgil Cain says:

    (borrowing from News)- Most “skeptics” in the sense used at TSZ do not apply their skepticism equally. For example they don’t apply it to evolutionism nor abiogenesis.

  20. 20
    kairosfocus says:

    Box,

    thinkers are distinct from thoughts, we are not even the same kind of thing. Thinkers create thoughts which they can share with others, they are not identical with their thoughts.

    Perhaps it is a subtlety of language?

    Aristotle was a man, as he would put it a rational animal.

    One of his activities was to think, and to teach what he thought.

    We can mark a significant set of differences between the two. Thus, we can see the thoughts as having a distinct identity, say a string of sentences expressing key propositions.

    They are not equal to the man, and they took origin from his mental activity.

    But once there, another person can take up the same thoughts without becoming Aristotle.

    And so forth.

    KF

    KF

  21. 21
    bornagain77 says:

    Box at 10:

    Is to say that a thing exists, to say that it has autonomous existence? When we say that a red balloon “exists”, do we say that its existence does not depend on anything else than what the red balloon seems to be?

    Not to get into all the subtle details that you are getting into with kf past that comment at 10, but as to this ‘dependency’ comment itself I would like to add my unsolicited two cents:

    Perry Marshall, per Godel, states:

    Gödel’s Incompleteness Theorem says:
    “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.”
    https://www.perrymarshall.com/articles/religion/godels-incompleteness-theorem/

    Godel’s incompleteness proof has now been empirically verified in quantum mechanics. Namely any object in the universe, or any particle in the universe, or even the universe itself, i.e. any ‘THING’ that you can draw a circle around, cannot explain its own existence but is dependent on a ‘non-local’, beyond space and time, cause to explain its existence.

    Here are some of the experiments that have established that fact:

    Falsification of Local Realism without using Quantum Entanglement – Anton Zeilinger – video (16:30 minute mark)
    https://youtu.be/TrsnMNh9W9U?t=991

    Contextuality is ‘magic ingredient’ for quantum computing – June 11, 2012
    Excerpt: Contextuality was first recognized as a feature of quantum theory almost 50 years ago. The theory showed that it was impossible to explain measurements on quantum systems in the same way as classical systems.
    In the classical world, measurements simply reveal properties that the system had, such as colour, prior to the measurement. 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.
    Imagine turning over a playing card. It will be either a red suit or a black suit – a two-outcome measurement. Now imagine nine playing cards laid out in a grid with three rows and three columns. Quantum mechanics predicts something that seems contradictory – there must be an even number of red cards in every row and an odd number of red cards in every column. Try to draw a grid that obeys these rules and you will find it impossible. It’s because quantum measurements cannot be interpreted as merely revealing a pre-existing property in the same way that flipping a card reveals a red or black suit.
    Measurement outcomes depend on all the other measurements that are performed – the full context of the experiment.
    Contextuality means that quantum measurements can not be thought of as simply revealing some pre-existing properties of the system under study. That’s part of the weirdness of quantum mechanics.
    http://phys.org/news/2014-06-w.....antum.html

    Leggett’s Inequality, the mathematics behind it, and the Theistic implications of it, are discussed beginning at the 24:15 minute mark of the following video:

    Quantum Weirdness and God 8-9-2014 by Paul Giem – video
    https://www.youtube.com/watch?feature=player_detailpage&v=N7HHz14tS1c#t=1449

    Quantum physics says goodbye to reality – Apr 20, 2007
    Excerpt: They devised an experiment that violates a different inequality proposed by physicist Anthony Leggett in 2003 that relies only on realism, and relaxes the reliance on locality. To do this, rather than taking measurements along just one plane of polarization, the Austrian team took measurements in additional, perpendicular planes to check for elliptical polarization.
    They found that, just as in the realizations of Bell’s thought experiment, Leggett’s inequality is violated – thus stressing the quantum-mechanical assertion that reality does not exist when we’re not observing it. “Our study shows that ‘just’ giving up the concept of locality would not be enough to obtain a more complete description of quantum mechanics,” Aspelmeyer told Physics Web. “You would also have to give up certain intuitive features of realism.”
    http://physicsworld.com/cws/article/news/27640

    Experimental non-classicality of an indivisible quantum system – Zeilinger 2011
    Excerpt: Page 491: “This represents a violation of (Leggett’s) inequality (3) by more than 120 standard deviations, demonstrating that no joint probability distribution is capable of describing our results.” The violation also excludes any non-contextual hidden-variable model. The result does, however, agree well with quantum mechanical predictions, as we will show now.,,,
    https://vcq.quantum.at/fileadmin/Publications/Experimental%20non-classicality%20of%20an%20indivisible.pdf

    “hidden variables don’t exist. If you have proved them come back with PROOF and a Nobel Prize.
    John Bell theorized that maybe the particles can signal faster than the speed of light. This is what he advocated in his interview in “The Ghost in the Atom.” But the violation of Leggett’s inequality in 2007 takes away that possibility and rules out all non-local hidden variables. Observation instantly defines what properties a particle has and if you assume they had properties before we measured them, then you need evidence, because right now there is none which is why realism is dead, and materialism dies with it.
    How does the particle know what we are going to pick so it can conform to that?”
    per Jimfit – UD blogger

    Besides Leggett’s Inequality, Wheeler’s Delayed Choice was recently extended beyond merely photons to atoms and gave the same result as Leggett’s. Namely, ‘reality doesn’t exist without an observer’

    New Mind-blowing Experiment Confirms That Reality Doesn’t Exist If You Are Not Looking at It – June 3, 2015
    Excerpt: The results of the Australian scientists’ experiment, which were published in the journal Nature Physics, show that this choice is determined by the way the object is measured, which is in accordance with what quantum theory predicts.
    “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,” said lead researcher Dr. Andrew Truscott in a press release.,,,
    “The atoms did not travel from A to B. It was only when they were measured at the end of the journey that their wave-like or particle-like behavior was brought into existence,” he said.
    Thus, this experiment adds to the validity of the quantum theory and provides new evidence to the idea that reality doesn’t exist without an observer.
    http://themindunleashed.org/20.....at-it.html

    To say these recent findings in quantum mechanics undermine materialistic presuppositions would be a drastic understatement. Perhaps a more fitting description of what these finding do to materialistic presuppositions is illustrated in the following video:

    Atomic Bomb blast with shock and effects in HD
    https://www.youtube.com/watch?v=dflLFFZcZ0w

    🙂

    As to the question of what this non-local, beyond space and time, reality is that every “Thing” in the universe is ultimately dependent on, well Theism has been postulating God for centuries if not for millennium for the ultimate reason for why the universe and everything in it exists:

    Aquinas’ Third way – video
    http://www.youtube.com/watch?v=V030hvnX5a4

    Verse:

    Hebrews 1:3
    The Son is the radiance of God’s glory and the exact representation of his being, sustaining all things by his powerful word. After he had provided purification for sins, he sat down at the right hand of the Majesty in heaven.

  22. 22
    daveS says:

    Perry Marshall, per Godel, states:

    Wow, that page is the worst example of abuse of Gödel’s theorems I’ve ever seen.

    BA77, can you identify the problems with this statement:

    That high school geometry book is built on Euclid’s five postulates. Everyone knows the postulates are true, but in 2500 years nobody’s figured out a way to prove them.

  23. 23
    bornagain77 says:

    Well daveS, since you, as a dogmatic atheist, will try your damnedest to find any trivial mathematical loophole you can just so to avoid God as an explanation, why don’t you just go ahead and elucidate your gripe against Marshall’s site instead of playing stupid games? Whatever your gripe is against Marshall’s site, your gripe is irrelevant to the main point I was making in my post anyway.

    As to the main point of Godel which I focused on in my post, namely the incompleteness of material objects, Godel states:

    “In materialism all elements behave the same. It is mysterious to think of them as spread out and automatically united. For something to be a whole, it has to have an additional object, say, a soul or a mind. “Matter” refers to one way of perceiving things, and elementary particles are a lower form of mind. Mind is separate from matter.”
    Kurt Gödel – Hao Wang’s supplemental biography of Gödel, A Logical Journey, MIT Press, 1996. [9.4.12]
    http://kevincarmody.com/math/goedel.html

  24. 24
    daveS says:

    BA77,

    I have no problem with actual quotes from Gödel.

    But when you bring in this pseudo-mathematical nonsense as exemplified by Marshall, what are we skeptics supposed to do? Someone has to stand up for the truth.

  25. 25
    bornagain77 says:

    daveS, the quote I used from Marshall is succinct and true to the point that I made in my post.

    Many times I use quotes from atheists in the same fashion as I did from Marshall to make my points although I certainly do not agree with everything written on atheistic websites.

    Moreover, I consider you an enemy of truth.

    The fact that you are an enemy of truth is clearly seen in you trying to focus on minor flaws in a particular tree rather than focusing on the forest itself.

    For instance the main subject (i.e. the forest) of your gripe against Marshall, i.e. geometry itself, and our ability to understand geometry in the first place, is clear evidence for Theism, but you will never, ever, admit that geometry, and our ability to understand it, (i.e. to understand the forest), is evidence for Theism since you are not really concerned with truth at all but are only concerned with suppressing the truth so that you, for whatever severely misguided reason, never will have to accept God and so that you will feel pseudo-intellectually justified in your rejection of God.

    It is a stupid mind game that you are playing with yourself that will, IMHO, have horrific consequences for your eternal soul when you die and have to face God (regardless of your present denial of Him).

    “Geometry is unique and eternal, a reflection from the mind of God. That mankind shares in it is because man is an image of God.”
    – Johannes Kepler

    Romans 1:18-19
    For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men who suppress the truth in unrighteousness, because that which is known about God is evident within them; for God made it evident to them.

  26. 26
    Mung says:

    daveS: Someone has to stand up for the truth.

    Why?

  27. 27
    daveS says:

    BA77,

    I don’t expect all sources to be error-free, but I submit that Marshall’s page on Gödel’s work is so full of errors and misconceptions it should not be quoted.
    I just did some googling and found out Mr Marshall has a BS in Computer Science from the U of Michigan, which blew my mind.

  28. 28
    daveS says:

    Mung,

    I didn’t mean it literally. I cannot prove that it is necessary for someone to stand up for the truth.

  29. 29
    bornagain77 says:

    daveS,

    https://www.youtube.com/watch?v=_O-QqC9yM28

    Box, if you are interested, a bit more depth on Godel’s Incompleteness, and how it came about, is elucidated in the following documentary (especially the second part)

    Dangerous Knowledge – video
    https://www.youtube.com/channel/UCVg91fMhGp8gFIc_NFy3WwQ

  30. 30
    Box says:

    Bornagain77,

    The possibility to draw a circle around X without “touching” it, so to speak, — without leaving anything of X out — is exactly what I’m getting at.
    Gödel’s Incompleteness Theorem seems highly relevant, thank you for the links. I will be occupied the next two days, but will look at them as soon as I have time.

  31. 31
    Learned Hand says:

    News,

    All progressives aim at power, not fact. No fact can be allowed that limits their power.

    It is known. Also all progressives butter their bread with the blood of Christian babies. After all, nothing defines a progressive like their lust for slavery and the utter subjugation of all who oppose them. Definitely no one should think of them as human beings, pretty much like every other human being who’s ever lived–they’re cardboard cutouts to be reviled. Good reminder.

  32. 32
    Mung says:

    It’s their embracing of irrationality that is to be reviled.

  33. 33
    Learned Hand says:

    Oh, absolutely. It’s us who are rational and them who are irrational. Just ask anyone.

  34. 34
    Barry Arrington says:

    LH @ 33:

    When you say irrational things like “for all I know I might be Mount Everest,” why is Mung wrong to conclude that you are irrational? Indeed, how could he not conclude that?

  35. 35
    Box says:

    Bornagain77, I have sent you an email to your Yahoo account.

  36. 36
    bornagain77 says:

    Box: I sent one back. In case you did not get it, here are the links:

    Taking God Out of the Equation – Biblical Worldview – by Ron Tagliapietra – January 1, 2012
    Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties. 1. Validity … all conclusions are reached by valid reasoning. 2. Consistency … no conclusions contradict any other conclusions. 3. Completeness … all statements made in the system are either true or false. The details filled a book, but the basic concept was simple and elegant. He (Godel) summed it up this way: “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.” For this reason, his proof is also called the Incompleteness Theorem. Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation. Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3).
    http://www.answersingenesis.or...../equation#

    The God of the Mathematicians – Goldman
    Excerpt: As Gödel told Hao Wang, “Einstein’s religion [was] more abstract, like Spinoza and Indian philosophy. Spinoza’s god is less than a person; mine is more than a person; because God can play the role of a person.”
    – Kurt Gödel – (Gödel is considered one of the greatest logicians who ever existed)
    http://www.firstthings.com/art.....ematicians

  37. 37
    Box says:

    Thanks BA77!

  38. 38
    Learned Hand says:

    When you say irrational things like “for all I know I might be Mount Everest,” why is Mung wrong to conclude that you are irrational? Indeed, how could he not conclude that?

    He would have to show why my arguments are rationally wrong to be justified in reaching that conclusion. Perhaps he can, I don’t know; he, like you, hasn’t tried.

  39. 39
    Barry Arrington says:

    LH @ 38.

    Learned Hand asks yet again for me to give him an argument to convince him that he can be sure he is not Mount Everest. Thank you, LH, for demonstrating the lunacy to which materialism drives some people.

  40. 40
    StephenB says:

    Learned Hand

    He would have to show why my arguments are rationally wrong to be justified in reaching that conclusion.

    Even that statement is irrational. How can we show that your arguments are “rationally wrong” when you renounce the same rational standards that define what it means to be wrong? It is as if you had said, “prove to me that I am a bad writer, but be advised, I don’t believe in the rules of grammar.”

    Meanwhile, it requires no intellectual exertion whatsoever to claim that your adversary did not make his case, even if the opposite is true. It is the easiest thing in the word to just sit back and say, “you failed” or “not good enough” or “try again.” Anybody can do that and do it all day long.

    The fact is, though, we made our case not by our words, but by your words. When you said that you can’t be sure that you are not Mount Everest, we made our case. When you allowed that a slice of pizza could weigh more than the whole pie, we made our case. If you don’t believe me, ask a disinterested lurker.

  41. 41
    Mung says:

    Next time I order a pizza I am going to try that whole “no pizza should cost more than a slice of pizza” thing.

  42. 42
    Learned Hand says:

    Even that statement is irrational. How can we show that your arguments are “rationally wrong” when you renounce the same rational standards that define what it means to be wrong? It is as if you had said, “prove to me that I am a bad writer, but be advised, I don’t believe in the rules of grammar.”

    You cannot prove an axiom. That is why they are axioms, not things we can prove infallibly to be true.

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