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Why the universe cannot logically be infinite in time backwards

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File:Wooden hourglass 3.jpg
passage of time, imaged/S. Sepp

Further to “No Big Bang: Universe Always Was” just posted by Donald McLaughlin, Ashby Camp gave Uncommon Descent permission to post these notes from a class he taught at the 2018 Harding University Bible Lectureship titled “Answering the New Atheism.” Worth pondering:


1.The second premise of the Kalam cosmological argument is: The universe began to exist. It is more reasonable to believe this is true than to deny it because, Scripture aside, there are strong philosophical and scientific reasons for believing it.

a. The philosophical argument for the universe having a beginning is that past time cannot be infinite because an infinite amount of time cannot already have been exhausted so as to arrive at the present. Infinite time is limitless, inexhaustible, and thus cannot have been exhausted.

(1) Put differently, one could never traverse an infinite sequence of time units, an infinite number of seconds, minutes, hours, etc., to arrive at now. There always would be more time units to traverse before now. If one begins counting down from minus infinity, one cannot count to the present. An infinite amount of time can never pass because it is limitless; it can only be in process, never complete. To quote the New Dictionary of Christian Apologetics, (p. 700), “One can neither count from one to infinity nor count down from infinity to one. There is always an infinite distance to travel, so one never arrives.”

(2) Sean McDowell and Jonathan Morrow make the point this way in Is God Just a Human Invention? (Grand Rapids: Kregel Publications, 2010), 75-76:

Imagine you went for a walk in the park and stumbled across someone proclaiming aloud, “… five, four, three, two, one—there, I finally finished! I just counted down from infinity!” What would be your initial thought? Would you wonder how long the person had been counting? Probably not. More likely, you would be in utter disbelief. Why? Because you know that such a task cannot be done. Just as it’s impossible to count up to infinity from the present moment, it’s equally impossible to count down from … infinity to the present moment. Counting to infinity is impossible because there is always (at least) one more number to count. In fact, every time you count a number, you still have infinite more to go, and thus get no closer to your goal. Similarly, counting down from infinity to the present moment is equally impossible. Such a task can’t even get started! Any point you pick in the past to begin, no matter how remote, would always require (at least) one more number to count before you could start there. Any beginning point would require an infinite number of previous points. Here’s the bottom line: we could never get to the present moment if we had to cross an actual infinite number of moments in the past. Yet, since the present moment is real, it must have been preceded by a finite past that includes a beginning or first event. Therefore, the universe had a beginning.

(3) The impossibility of infinite past time, of having already traversed an infinite timespan, does not mean that future time will not go on forever. Future time is potentially not actually infinite. In other words, it is infinity in progress, something that will move toward infinity but never arrive; you’ll never get to the end of it. So it poses no problem like the claim of having already traversed an infinite timespan.

(4) The impossibility of traversing an infinite timespan, an infinite sequence of time units, need not mean that God has not always existed. There are ways of dealing with God’s relationship to time so that he does not exist (or has not always existed) in a sequence of individuated moments, a sequence of time units. His eternality is not one of infinite time but one of either timelessness or a different kind of time that has no measure or metric. For example, William Lane Craig’s view is that “God is timeless without creation and temporal since creation.” Philosophers Alan Padgett and Richard Swinburne refer to time before creation as “metrically amorphous time,” meaning it differs from our “measured time” (see, e.g., Eternity in Christian Thought).

(5) This philosophical claim that the universe cannot always have existed makes sense to me and to many philosophers, but there are others who are not persuaded.

(a) Some, for example, point to the fact a finite timespan, say one minute, can be subdivided infinitely into units of decreasing length, and yet one can still traverse that timespan. The claim is that in going from 0 to 1 minute one traverses an infinite number of time units to arrive at 1 minute, so it is not true that one cannot traverse an infinite number of time units to arrive at the present. But there is a problem with that claim. The subdivisions of a finite timespan are only potentially infinite in number. It is true that one could keep subdividing forever, but each further subdivision results in a finite number of subdivisions the sum of which is the finite timespan being subdivided. The number of subdivisions can grow toward an infinite number but can never actually reach an infinite number. Whereas, when speaking of an infinite timespan one is speaking of an actually infinite set of time units, the sum of which is an infinite length of time.

(b) Though this philosophical claim that the universe necessarily began to exist continues to be debated, it dovetails nicely with the scientific acceptance of the universe having a beginning. That is the subject to which I now turn.

  

Readers?

Comments
No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept. And all Jerad can do in the face of that is to attack me. I am OK with that.ET
March 10, 2020
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JVL:
I’m just saying that, based on what you’ve said on this forum, that you do not understand axiomatic set theory.
And I can say the same about you. You clearly don't understand infinity.
Then why are you spending so much time arguing about it?
You are the loser who brought it up. You are the loser who won't let it go. You are the loser who avoids reality. The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. If you can't understand that then no one can help you.ET
March 10, 2020
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ET, 86: Yes I have and yes I do. So shut up and stop being such a cowardly loser. Okay, then tell me: do you think the Axiom of Choice is true or false? And all Jerad can do in the face of that is to attack me. What a coward. I'm not attacking you. Look, if I came onto a forum and claimed that I knew how to handle semi-automatic weapons but it was clear to you that I didn't you would say so. Of course you would. I'm just saying that, based on what you've said on this forum, that you do not understand axiomatic set theory. It's not a value judgement. The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. Yes, this is true. But both sets are still the same size. You don’t know how it’s used. You are clearly just a blind parrot who is unable to think for himself. Things that are proven in mathematics are true. Always. But it is all moot, anyway. There can never be a set with infinite elements. Then why are you spending so much time arguing about it? And, again, all you have to do to prove me wrong is to find an unmatched element of the positive integers with the positive even integers under my scheme. That's it. You think the set of positive integers is larger than the set of positive even integers so, under my scheme, there should be an unmatched element of the set of positive integers. All you have to do is to find one, just one, unmatched element. You can bury my arguments with just that one thing. That is how you falsify my (and Cantor's) ideas. Can you do that?JVL
March 10, 2020
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You haven’t studied axiomatic set theory so you don’t know how it’s used.
Yes I have and yes I do. So shut up and stop being such a cowardly loser. No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept. And all Jerad can do in the face of that is to attack me. What a coward. The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. Another fact that Jerad avoids.
You haven’t studied axiomatic set theory so you don’t know how it’s used.
You don't know how it's used. You are clearly just a blind parrot who is unable to think for himself. But it is all moot, anyway. There can never be a set with infinite elements.ET
March 10, 2020
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ET, 83: Oh my. Your inability to follow along is priceless. I don't mind being in line with actual axiomatic set theory. No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept. You haven't studied axiomatic set theory so you don't know how it's used. And it's usefulness has nothing to do with its truth. It is true. And there are. The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. Fine, name a positive integer that is not matched with a positive even integer in my scheme. And that you can’t understand derived vs contrived doesn’t mean anything. Because it's not a mathematical issue. You just made it up. There are no references in any mathematical publication to such a thing. And look, Jerad, just because I disagree with an insignificant part of set theory doesn’t mean I don’t understand set theory. It is exactly because I understand it that I say what I do. And all you can do is parrot the 19th century. Clearly you don't or you wouldn't be saying the things you are saying. In mathematics it doesn't matter when a result was proven; once it's proven it's proven. it's still true. Euclid's Elements are still true and they are a lot older than Cantor's work. No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept. You haven't studied axiomatic set theory so you don't know how it's used. And, again, if you think the set of positive integers is larger than the set of positive even integers then, under my scheme explained above, you should be able to specify a positive integer not matched with a positive even integer. Find one and you win.JVL
March 10, 2020
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Game. Set. Match. No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept. JVL:
No one uses it because it doesn’t work.
ET
March 10, 2020
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JVL:
Since you can’t count to infinity you can’t look at your counters at infinity.
Oh my. Your inability to follow along is priceless. No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept.
No one uses it because it doesn’t work.
Thank you.
Anyway, IF the set of positive integers is larger than the set of positive even integers then there should be an element of the set of positive integers that is not matched to an element of the positive even integers.
And there are. The set of positive integers has every element contained in the set of all positive even integers PLUS it contains all of the odd integers as well. And that you can't understand derived vs contrived doesn't mean anything. And look, Jerad, just because I disagree with an insignificant part of set theory doesn't mean I don't understand set theory. It is exactly because I understand it that I say what I do. And all you can do is parrot the 19th century.ET
March 10, 2020
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ET, 81: What is clear is that Jerad is a coward who cannot support the trope he spews. Check any textbook on axiomatic set theory. Check Wikipedia. Lots of places will uphold what I am saying. No shit. But thanks for proving that you can’t even grasp the basic terminology. Since you can't count to infinity you can't look at your counters at infinity. Set subtraction is OK to use on infinite sets. No one says you can’t. No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept. No one uses it because it doesn't work. There is already a matching concept that is used, Jerad. It matches the elements that are the SAME in both sets. It is used to determine if one set is a proper subset of another. And it is used with infinite sets for that same purpose. I agree that the set of positive even integers is a subset of the set of positive integers; that's not in contention. In fact there is a theorem which says that a countably infinite set will have a countably infinite subset. No problem with that. BUT they are still the same size. Math can get a bit weird. Anyway, IF the set of positive integers is larger than the set of positive even integers then there should be an element of the set of positive integers that is not matched to an element of the positive even integers. Using my matching scheme above can you find an element of set J that is unmatched with an element of set E. If you can't find one then the sets are the same size. Simple. And, again, there is no "contrived vs derived" criteria so don't play that card. I've found a matching that I claim proves the two sets have the same number of elements. If you think they don't then you can easily prove me wrong by finding an element of either set that does not have a "partner" in the other set. That's it. That's all you have to do to prove my matching is bogus.JVL
March 10, 2020
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What is clear is that Jerad is a coward who cannot support the trope he spews.
You cannot count for or into infinity. You’ll never get there.
No shit. But thanks for proving that you can't even grasp the basic terminology. Set subtraction is OK to use on infinite sets. No one says you can't. No one uses the concept that all countably infinite sets have the same cardinality. NO ONE. It is a totally useless concept. There is already a matching concept that is used, Jerad. It matches the elements that are the SAME in both sets. It is used to determine if one set is a proper subset of another. And it is used with infinite sets for that same purpose.ET
March 10, 2020
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ET: I understand your cowardly false accusations, Jerad. It's clear you don't understand axiomatic set theory. That's not a value judgement; I have lots of friends who don't understand it either. Jerad cannot find any reference that says set subtraction cannot be used on infinite sets. That means what he says about it is BS. Nobody spend hours and hours generating lists of things you shouldn't do. What they do do is show you how to deal with things correctly. As I said, read any axiomatic Set Theory textbook. And: you haven't been able to find any textbook that uses "set subtraction" for infinite sets. Gee, if nobody uses it . . . Jerad can’t even read for comprehension! Why would anyone believe what you say, JVL? Because what I'm saying is backed up by any textbook on axiomatic set theory. When do they have the same number of elements? Please show your work or shut up. Two sets have the same number of elements (or are the same size) when they can be put into one-for-one correspondence with each other so that every element of each set is matched with one and only one element of the other set. That works for finite as well as infinite sets. I'll show you for the two sets in question: set J = the positive integers, set E = the positive even integers. Match "1" from J (its first element when listed in ascending numerical order) with "2" from E (its first element) Match "2" from J with "4" from E Match "3" from J with "6" from E and so on. If you pick any element of either set I can tell you what its matched with in the other set. Nothing is left out. Each element of J has one and only one match in E. Each element in E has one and only one match in J. No element of either set is left out. That can only happen if the sets have the same number of elements. QED Exactly why an infinite set is total BS. Then why are you arguing about them? It was first proposed by Galileo. Was it? Anyway, Cantor did the real rigorous work in the late 1800s. You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B? At any given point one counter will be double the other. But points are finite. You cannot count up to infinity so no matter when you compare the counters (when being a particular finite time) one will be double the other. But the sets still have the same number of elements as illustrated above. Notice the LAST sentence: Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B? You cannot count for or into infinity. You'll never get there. Your ignorance is not an argument, Jerad. At least I understand axiomatic set theory which is back up by every textbook on the subject. And we are still stuck on the main point- that being no one uses the concept that all countably infinite sets for anything. It is meaningless to the real world. And Jerad cannot find anything that refutes that claim. So he is forced to attack me from across the sea. I call that cowardice. Whether you think it's useful or not it's still true. I think it's very useful in mathematics. You've not studied that kind of mathematics so you don't see the use.JVL
March 10, 2020
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Ooops- And we are still stuck on the main point- that being no one uses the concept that all countably infinite sets have the same cardinality for anything.ET
March 10, 2020
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And we are still stuck on the main point- that being no one uses the concept that all countably infinite sets for anything. It is meaningless to the real world. And Jerad cannot find anything that refutes that claim. So he is forced to attack me from across the sea. I call that cowardice.ET
March 10, 2020
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You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B? Notice the LAST sentence: Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B? Your ignorance is not an argument, Jerad.ET
March 10, 2020
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I understand your cowardly false accusations, Jerad. Jerad cannot find any reference that says set subtraction cannot be used on infinite sets. That means what he says about it is BS.
Any point in time will be finite that’s why what you’re saying doesn’t work for infinity
Jerad can't even read for comprehension! Why would anyone believe what you say, JVL?
But the two sets have the same number of elements which is not dependent on the way you count them.
When do they have the same number of elements? Please show your work or shut up.
You cannot collect items forever.
Exactly why an infinite set is total BS.
It was very controversial at the time.
It was first proposed by Galileo.ET
March 10, 2020
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ET: And that proves that you are clueless with respect to what we are discussing. So perhaps you should just stop with your bluffing equivocation already. It's not my fault you don't understand axiomatic Set Theory.JVL
March 10, 2020
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ET: 71: Wow, moar stupidity and still the refusal to answer my questions. I did actually. Set subtraction works for all sets. There isn’t anything in any math textbook that says otherwise. Find one that uses it on infinite sets. Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. Find anyone or any textbook that uses your approach. They don't exist. Because your method doesn't work. Which is why you will never find any mathematics supporting your view. Jerad has NOT presented anything that says anything contrary to what I have said about infinity. I guess you don't understand the math resources I linked to. You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B? Any point in time will be finite that's why what you're saying doesn't work for infinity. It only works for particular finite points in the future. At any point in the future one counter will be twice the other. But the two sets have the same number of elements which is not dependent on the way you count them. My example typifies collecting items for a set. Jerad cannot deal with reality and it shows. Sure, collecting items for a finite set. But not for an infinite set. You cannot collect items forever. But Cantor figured out a way to work with sets that never end. It was very controversial at the time. But eventually mathematicians realised he was right.JVL
March 10, 2020
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JVL:
I’ve linked to articles that discuss the foundational nature of set theory
And that proves that you are clueless with respect to what we are discussing. So perhaps you should just stop with your bluffing equivocation already.ET
March 10, 2020
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You have two counters, both starting at zero. One, counter A, counts every second and the other, counter B, counts every other second. Is there any point in time, after one second, that the two counters will have the same count? Or will counter A always and forever, ie for/ into infinity, have a higher count than counter B? My example typifies collecting items for a set. Jerad cannot deal with reality and it shows.ET
March 10, 2020
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Wow, moar stupidity and still the refusal to answer my questions. Set subtraction works for all sets. There isn't anything in any math textbook that says otherwise. Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. Jerad has NOT presented anything that says anything contrary to what I have said about infinity.ET
March 10, 2020
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ET, 68: Jerad, you are a liar. No one showed me anything pertaining to people using the concept of all countably infinite sets have the same cardinality. Clearly you haven't studied axiomatic set theory. Or understood the material I have linked to. You are a coward for refusing to answer my questions. I have. I showed you links to proofs that the cardinality of the positive even integers is the same as the cardinality of the positive integers. I've linked to articles that discuss the foundational nature of set theory (including the trivial result mentioned). I've agreed that if you count the way you want to and stop at any time then one counter will be twice the other. But that's a finite example, you stopped someplace, and you can't count to infinity. Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. Moar cowardly nonsense doesn’t refute what I said. You can choose to ignore what's in every single textbook on advanced Set Theory if you wish. You can ignore the material I've provided links to. You can ignore lots of other resources that a simple internet search will bring up. It's your choice. Everything Jerad has said about that has been a lie, Nope. Check out any textbook on Set Theory. You don't even have to buy one; just go to your local university library and go to the math section and find one. That’s pure stupidity. That's the way it works. Derived is always the best route. It doesn't matter how you find a one-for-one matching. If you can find one then the two sets have the same cardinality. There is no "derived vs contrived" condition or preference. Look in any Set Theory text book. Cardinality refers to the number of elements in a set. Some define it as the number of distinct elements within a set. So if set A = {all positive integers}, set B = {all positive even integers} and set C = {all positive odd integers}, then A-B=C proves that set A has more distinct elements than sets B and C. Yes for finite sets but not for infinite sets. Opinions don’t count. And opinion is all that you have. I've got well known and well established mathematics on my side. Set subtraction works with all sets. Not with the cardinality of infinite sets. Jerad wants references but he will NEVER provide a reference that says set subtraction cannot be used on infinite sets. He will NEVER provide a reference that shows people using the concept of all countably infinite sets having the same cardinality. And he will never support his claim that infinite sets do not work as I have said. That''s 'cause no one uses set subtraction with infinite sets! Go check out any textbook on Set Theory. And I have provided references for the other things mentioned. If you didn't understand them that's not my fault. And to top it all off Jerad refuses to answer my questions. All of that proves that Jerad doesn’t know what he is talking about. I've answered, you just don't like the answers. What I am saying is easily found in any Set Theory textbook and on many, many online resources. No one uses set subtraction for infinite sets because it doesn't work. The cardinality of an infinite set is not a number which is why you don't get relative cardinalities. You can easily find material that supports what I am saying. You cannot find any reputable mathematical resource that back up what you are saying.JVL
March 10, 2020
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Jerad wants references but he will NEVER provide a reference that says set subtraction cannot be used on infinite sets. He will NEVER provide a reference that shows people using the concept of all countably infinite sets having the same cardinality. And he will never support his claim that infinite sets do not work as I have said. And to top it all off Jerad refuses to answer my questions. All of that proves that Jerad doesn't know what he is talking about.ET
March 10, 2020
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Jerad, you are a liar. No one showed me anything pertaining to people using the concept of all countably infinite sets have the same cardinality. You are a coward for refusing to answer my questions. Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. Moar cowardly nonsense doesn’t refute what I said. Everything Jerad has said about that has been a lie,
Nope, set subtraction doesn’t work with infinite sets.
That's pure stupidity.
Show a reference that upholds your claim that “derived” is inferior to “contrived”.
Derived is always the best route. Cardinality refers to the number of elements in a set. Some define it as the number of distinct elements within a set. So if set A = {all positive integers}, set B = {all positive even integers} and set C = {all positive odd integers}, then A-B=C proves that set A has more distinct elements than sets B and C.
Not with infinite sets.
Opinions don't count. And opinion is all that you have. Set subtraction works with all sets.ET
March 10, 2020
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ET, 62: Look, Jerad, you should have learned how to count by the first grade. I'm very good at counting. But you can't count to infinity. It’s been years and you have been unable to produce anything. You are just unaware. You you are clearly just a bluffing coward. It's not my fault you don't understand what's been shown to you. Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. Moar cowardly nonsense doesn’t refute what I said. What I've said is correct and can easily be verified by anyone checking. And it absolutely refutes what you're saying. The true thing is that set subtraction can prove if one countably infinite set has more elements than another countably infinite set. Nope, set subtraction doesn't work with infinite sets. If you have the positive integers, a countably infinite set, and you take away the positive even integers, another countably infinite set, you get a third countably infinite set, the positive odd numbers. All three sets continue without end. You cannot say one set has more elements than another. You can take all three sets and match them up so that no element of any set is left out of being matched which means they all have the same number of elements. It's easy really. And derived vs contrived does matter. Natural vs made-up matters. Consistency is they key with respect to mathematics. But Jerad prefers the 19th century. Show a reference that upholds your claim that "derived" is inferior to "contrived". Or even show a reference that defines "contrived" in a mathematical context. Show a reference that supports your idea of relative cardinality between countably infinite sets. If you're right you should be able to find sources that support your ideas. I'll wait. I prefer being right, no matter when the mathematics was proven. Cardinality refers to the number of elements in a set. Some define it as the number of distinct elements within a set. So if set A = {all positive integers}, set B = {all positive even integers} and set C = {all positive odd integers}, then A-B=C proves that set A has more distinct elements than sets B and C. Not with infinite sets. If you take the positive integers, a countably infinite set, and add the element "0" you still have a countably infinite set. You think that you would have increased the cardinality. By how much? By one? What's infinity plus one? It's still infinity. "Set subtraction" does not work with infinite sets. To use the other example: the positive integers take away the positive even integers does not have half the elements as before. Infinity divided by two is still infinity. Infinity + 1 = infinity infinity x 2 = infinity infinity ÷ 2 = infinity infinity + infinity = infinity the square root of infinity = infinityJVL
March 9, 2020
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What does an appeal to an infinite regress of contingent causes really prove? The answer: Nothing, because you can never prove that such a series exists and even if we assume that it exists, it explains nothing. The following is an argument I’ve developed for the existence of a transcendent, self-existent mind (God) which I think is a logical defeater for the idea that an infinite regress of “natural” causes is a good explanation for our existence.
(1) Everything that begins to exist is contingent. (2) Anything that is contingent has an explanation for its existence. (It must be caused by something else.) (3) If the universe is contingent it has an explanation for its existence. (4) If the universe began to exist it must be contingent. (5) However, it is logically possible that something exists which is not contingent. (6) If such a being exists it exists necessarily. In other words, it is eternal or self-existent. (7) A necessary or self-existent being is not explained by anything else. Conclusion #1: Therefore, only a necessarily existing being could be the ultimate explanation for everything else. Conclusion #2: Therefore an infinite regress of contingent causes can never reach an ultimate explanation.
Some implications: A necessary or self-existing being must have causal power. If it is the cause of the universe it must have sufficient power to cause the universe. It must have volitional intentionality. In other words, it does not need to create anything, it freely decides or chooses to create. It must be transcendent due to the fact that it is not contingent. Therefore, it must have mind and intelligence as well as personal self-consciousness. This idea fits very nicely with a basic classical conception of God. In other words, if something is contingent then it cannot be necessary. If a necessary being exists it cannot be contingent. If it is even logically possible for the universe to be contingent how can we claim that it is necessary? In other words, if it is logically possible for the universe to be contingent then it cannot be logically necessary for it to be ontologically necessary. If a transcendent necessary being exists then it is logically necessary that it is ontologically necessary.john_a_designer
March 9, 2020
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Cardinality refers to the number of elements in a set. Some define it as the number of distinct elements within a set. So if set A = {all positive integers}, set B = {all positive even integers} and set C = {all positive odd integers}, then A-B=C proves that set A has more distinct elements than sets B and C. Basic. Set. Mathematics. All naturally derived.ET
March 9, 2020
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"Ed George":
Maybe nested hierarchies, or frequency = wavelength?
You don't understand either of those concepts. :razz:ET
March 9, 2020
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@JVL there is a lot of entertainment in Alternative Math. ;-DJim Thibodeau
March 9, 2020
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JVL:
Then how is it I can match the set of positive integers one-for-one with the set of positive even integers?
Look, Jerad, you should have learned how to count by the first grade.
You’re not a mathematicians so you are unaware of its use.
It's been years and you have been unable to produce anything. You are just unaware. You you are clearly just a bluffing coward. Infinite sets work exactly as I have said. And Jerad cannot demonstrate otherwise. Moar cowardly nonsense doesn't refute what I said. The true thing is that set subtraction can prove if one countably infinite set has more elements than another countably infinite set. And derived vs contrived does matter. Natural vs made-up matters. Consistency is they key with respect to mathematics. But Jerad prefers the 19th century.ET
March 9, 2020
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Can we change this discussion to something else? Maybe nested hierarchies, or frequency = wavelength?Ed George
March 9, 2020
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JVL
Something we can definitely agree on!! Who thought taking it away was a good idea?
Perhaps it was an attempt to get rid of the recurring problem of the comments list n to being updated.Ed George
March 9, 2020
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