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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
Subtraction is the basic arithmetic operation used to determine if one thing is larger than the other. It doesn't get any more foundational than that. So yes, I am going to question anyone who goes against what subtraction uncovers. And the "answer" I am getting is subtraction doesn't work with sets of infinite elements- cuz it don't, so there. Seriously. And because I have called out that explanation as total nonsense, I am the one getting something handed to him. How does that work?ET
March 14, 2020
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The comment @ 244, "Ed George" says:
I know absolutely nothing
And I agreeET
March 14, 2020
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The last 22 comments further supports my comment at 244.Ed George
March 14, 2020
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There is only ONE infinity. It can be populated with differing densities of elements.
So, what’s the cardinality of the rational numbers? Of the real numbers? Of the transcendental numbers?
Each one has infinite elements. However, each has different densities of elements. But again, that is well over your limited thinking ability.ET
March 14, 2020
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Jerad, look, you are an imbecile. You can't even follow the discussion. Set subtraction uncovers unmatched elements.
Doubling down on a bogus system doesn’t give you the win.
And yet that is all you have ever done. Nice own goal. Set subtraction proves my point.ET
March 14, 2020
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JVL:
I’m saying that all three sets have the same cardinality.
And yet set subtraction proves that they don't.
That’s what your system of “relative cardinality” says!!
Only if you are an idiot. And here you are. My system is reflected by the one used to determine bijective functions. So clearly you are an ass.ET
March 14, 2020
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ET: Everyone agrees that the positive integers are comprised of the combination of the positive even integers and the positive odd integers yes. You have to be a complete dolt to deny it. I'm not denying that, you really are not paying attention. I'm saying that all three sets have the same cardinality. Only if you are an idiot. Are you an idiot, Jerad? You definitely make a strong case for it. That's what your system of "relative cardinality" says!! You should pay attention to what you've said. Can you find an unmatched element of either set in my matching? Yes or no?JVL
March 14, 2020
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ET: There is only ONE infinity. It can be populated with differing densities of elements. So, what's the cardinality of the rational numbers? Of the real numbers? Of the transcendental numbers? Yes, I do. And that is why you are a wanker for saying what you did. What, for asking you to find an unmatched element under my scheme? Pardon me!! Set subtraction proves that the set of positive integers contains more elements than the set of positive even integers. That means it proves that your matching scheme is the wrong tool for the job. And set subtraction proves your scheme doesn’t work. Find an unmatched element in my scheme. You can't. That means your idea of how it all works is wrong. Doubling down on a bogus system doesn't give you the win. Not being able to support your idea (that the the set of positive integers is bigger than the set of positive even integers) by finding an unmatched element means you've lost. Congratulations for going down with the sinking ship though. I'm not sure why you would do that but you clearly are committed.JVL
March 14, 2020
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JVL:
In your system the cardinality of the integers is equal to the sum of the cardinality of the evens and the cardinality of the odds.
Yes
So that means 1 x infinity = 2 x infinity.
Only if you are an idiot. Are you an idiot, Jerad? You definitely make a strong case for it.ET
March 14, 2020
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Everyone agrees that the positive integers are comprised of the combination of the positive even integers and the positive odd integers yes. You have to be a complete dolt to deny it.ET
March 14, 2020
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JVL: You agree that the positive integers are comprised of the combination of the positive even integers and the positive odd integers yes? So you are adding infinities . . . LoL! Adding the ELEMENTS, not infinities. It's as if you are proud to prove that you are an ass.ET
March 14, 2020
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Guess what I found when I did an online search for “set arithmetic”? Absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it. And only a desperate loser would think that means we have to throw out set theory. Enter Jerad...ET
March 14, 2020
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ET: Yes, Jimmy, your desperation knows no bounds. I never said anything about adding infinities, loser. You agree that the positive integers are comprised of the combination of the positive even integers and the positive odd integers yes? So you are adding infinities . . . In your system the cardinality of the integers is equal to the sum of the cardinality of the evens and the cardinality of the odds. So that means 1 x infinity = 2 x infinity. Does that mean that 1 = 2? (by the way, Cantor figured out how to handle this . . . just sayin')JVL
March 14, 2020
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JVL:
Do you have any idea how large all of set theory is?
Yes, I do. And that is why you are a wanker for saying what you did. Set subtraction proves that the set of positive integers contains more elements than the set of positive even integers. That means it proves that your matching scheme is the wrong tool for the job. And set subtraction proves your scheme doesn't work.ET
March 14, 2020
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JVL:
I have chosen not mention the fact that there are different sizes of infinity.
There is only ONE infinity. It can be populated with differing densities of elements.ET
March 14, 2020
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Yes, Jimmy, your desperation knows no bounds. I never said anything about adding infinities, loser.ET
March 14, 2020
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1*Infinity = 2*Infinity Don't get me started . . . I have chosen not mention the fact that there are different sizes of infinity. We'll save that for another life time it appears.JVL
March 14, 2020
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ET math {1+2+3....} = {1+3+5...} + {2+4+6...} Infinity = Infinity + Infinity 1*Infinity = 2*Infinity Cross out like terms, 1 = 2 Wow!!! ET you’re going to win The Fields Medal!!!!Jim Thibodeau
March 14, 2020
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ET: So there isn’t any “4” in the set of positive evens? No “8”- no “12”? Really? There isn’t any “2” in the set of positive integers? No “4”- no “6”? Really? Oh dear, ET is really not paying attention. I was just addressing his(?) claim that the odd-positive integers were unmatched in my scheme so I just repeated that part of the scheme. I thought he was paying attention. I'll re-iterate the whole scheme, again. J = the set of positive integers. E = the set of positive even integers. Here's the scheme: "1" in J is matched with "2" in E "2" in J is matched with "4" in E "3" in J is matched with "6" in E "4" in J is matched with "8" in E "5" in J is matched with "10" in E "6" in J is matched with "12" in E "7" in J is matched with "14" in E "8" in J is matched with "16" in E "9" in J is matched with "18" in E "10" in J is matched with "20" in E and so on! So, each and every positive integers is matched with one and only one element in the positive even integers. AND each and every positive even integers is matched with one and only one element in the positive integers. Is there anything unmatched? I can't see one. How could that happen if one set was bigger than the other? Gosh, I don't think it could happen. I guess the sets are the same size! Why would I use your scheme? It is obviously the wrong tool for the job. ???? It does what I want. It's a one-for-one matching between all the elements of the positive integers and all the elements of the positive even integers. And it's not disallowed so . . . yup, I'm good with it. And all Jerad can do is whine about set theory like a loser. How desperate do you have to be to think that the topic under discussion is all of set theory? Do you have any idea how large all of set theory is? The stuff we're talking about is in the first part of chapter one of any standard textbook. And much of the rest follows. But you know that because you've studied set theory haven't you? What was the textbook again? I can't remember what you said. Oh, that's right, you didn't say! So, once again, can you find an unmatched element in my matching between the positive integers and the positive even integers? Yes or no? I've stated it over and over and over again. And you've made up issues like "contrived vs derived" and "standard matching" none of which have turned out to be real issues. All you have to do now is answer yes or no. Under my scheme are there any unmatched elements of either set? Yes or no?JVL
March 14, 2020
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So, you still haven’t found any unmatched elements of the positive integers using my scheme.
Why would I use your scheme? It is obviously the wrong tool for the job. :razz:ET
March 14, 2020
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Jerad can't even follow his own blatherings:
“1” in J is matched with “2” in E “3” in J is matched with “6” in E “5” in J is matched with “10” in E “7” in J is matched with “14” in E and so on.
So there isn't any "4" in the set of positive evens? No "8"- no "12"? Really? There isn't any "2" in the set of positive integers? No "4"- no "6"? Really? Thank you for proving that you are a loser, Jerad.ET
March 14, 2020
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Guess what I found when I did an online search for “set arithmetic”? Absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it. And all Jerad can do is whine about set theory like a loser. How desperate do you have to be to think that the topic under discussion is all of set theory?ET
March 14, 2020
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Acartia Eddie:
I know absolutely nothing
This is true. But you didn't have to say it as your posts prove it.ET
March 14, 2020
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Jimbo:
ET, when every single mathematician in the world disagrees with you about very basic math concepts,
Set subtraction is a basic math concept, you ignorant tool.ET
March 14, 2020
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JVL:
Oh dear, guess we’d better throw out all those textbook and papers based on set theory.
Spoken like a totally ignorant ass. Nicely done, loser. J-E=D, The entire set of positive odd integers is left unmatched. You lose, again. Set subtraction refutes you, Jerad.ET
March 14, 2020
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I know absolutely nothing about set theory but I do know when someone is getting his ass handed to him. And I also know when someone is too narcissistic to acknowledge that they may be wrong. This thread would make a perfect case study of both.Ed George
March 14, 2020
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ET, when every single mathematician in the world disagrees with you about very basic math concepts, you might want to consider the possibility that....Jim Thibodeau
March 14, 2020
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ET: Guess what I found when I did an online search for “set arithmetic”? Absolutely no one uses the concept that all countably infinite sets have the same cardinality. It’s as useless as the people saying it. ???? Oh dear, guess we'd better throw out all those textbook and papers based on set theory. What a shame. J-E=D, The entire set of positive odd integers is left unmatched. You lose, again. Ah, no. I just told you: "1" in J is matched with "2" in E "3" in J is matched with "6" in E "5" in J is matched with "10" in E "7" in J is matched with "14" in E and so on. Do try an pay attention or you'll have to sit in the naughty corner. So, you still haven't found any unmatched elements of the positive integers using my scheme. Maybe there aren't any . . . you did admit it was one-to-one . . . and it is onto as well . .. gosh, I guess the sets are the same size! Hooray!!JVL
March 14, 2020
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Already have. Your willful ignorance is your problem. Not mine. Stay focused on this discussion.
Really?
Really, really. Grow up or stuff it, Jerad.ET
March 14, 2020
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J = the set of positive integers, E = the set of positive even integers.
D = the positive set of odd integers. J-E=D, The entire set of positive odd integers is left unmatched. You lose, again.ET
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