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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 for anything. No one. It’s meaningless. So why bother? If you were to ask anyone on the street they would probably agree with me. So I'm OK with my homies' supportET
March 15, 2020
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ET: Ok I get it. See I admit when I made a mistake. Why I did (a-b)^7 is beyond me. I don't know either. It happens. It was just a mistake. To be honest, I couldn't figure out how you got the rest of it right and mucked up the signs!! That's why I suggested you have another look. No one would get that much right and mess up the signs if they didn't know what they were doing. Again, I have explained ALL of that to you on my blog. I am not going over it again. It’s already been more than once. But people haven't seen those explanations here, probably worth repeating so they know you can handle those cases. it's your call. I never said they were. I said they are both representations of the SAME wave. I agree with that characterisation. I don't remember the argument that well but what you're saying now I agree with. Again, as I have told you, the CONTEXT was one person presenting papers on the absorption frequency of CO2 and the other was presenting papers on its wavelength. I was saying that it doesn’t matter because we are talking about the same thing. Yup, fine with me. If someone else remembers things differently then I leave it to them to bring that. But I'm good. I haven’t shown it to any mathematician. Why not? No matter how much I argue with you you are clearly firm in your conviction. I would think you would give it a go and see if anyone agrees with you. You know my opinion but . . .JVL
March 15, 2020
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LoL! @ Jimmie- No one uses the concept for anything. No one. It's meaningless. So why bother? The only people I see arguing it are blog people.ET
March 15, 2020
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”I haven’t shown it to any mathematician” That tells the whole story.Jim Thibodeau
March 15, 2020
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Ok I get it. See I admit when I made a mistake. Why I did (a-b)^7 is beyond me.
Use your “concept” on the set of positive primes. What is the “relative cardinality” of the positive prime numbers? Here’s another one: what’s the “relative cardinality” of the set of the powers of 3? How about this: what’s the relative cardinality of the perfect squares?
Again, I have explained ALL of that to you on my blog. I am not going over it again. It's already been more than once.
BUT wavelength and frequency are NOT the same thing,
I never said they were. I said they are both representations of the SAME wave. Again, as I have told you, the CONTEXT was one person presenting papers on the absorption frequency of CO2 and the other was presenting papers on its wavelength. I was saying that it doesn't matter because we are talking about the same thing.
I am allowed to disagree with you.
True, it's the reason I am questioning. You can disagree that the Sun is a star, for all I care.
But your method is disputed by every mathematician on the planet yet you keep using it.
I haven't shown it to any mathematician.ET
March 15, 2020
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ET: You are a LIAR. Nope. No, I didn’t. Yeah, you did. Check the signs. I have explained that. Are you a retard? I'm just trying to understand what you think exists and what you don't think exists. No one uses Cantor’s concept for anything. Mine works for all sets. YOU are too stupid to figure it out. Use your "concept" on the set of positive primes. What is the "relative cardinality" of the positive prime numbers? Here's another one: what's the "relative cardinality" of the set of the powers of 3? How about this: what's the relative cardinality of the perfect squares? I know. Wavelength and frequency are interchangeable when discussing the emissions of CO2- you can talk about the frequency or the wavelength and you are discussing the SAME thing. BUT wavelength and frequency are NOT the same thing, we agree on that. For a fixed speed the wavelength will determine/dictate the frequency, yes? The emissions of CO2 . . . what frequency and wavelengths are you talking about? Visible light? Assuming that's the issue then, I agree: you can refer to the "waves" in question either by their frequency ranges or their wavelength ranges because one determines the other. BUT they are NOT the same thing. Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance. I am allowed to disagree with you. All Jerad can do is continue to ignore reality and prattle on like a fool. And to top it off he is using the thing I am disputing to settle the dispute. But your method is disputed by every mathematician on the planet yet you keep using it. How is that fair? How pathetic can you be, Jerad? I'm not sure, I've never tried to figure that out. I'm not sure how to measure . . . pathetic-ness. And I'm not sure what scale to use. Interesting question.JVL
March 15, 2020
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All Jerad can do is continue to ignore reality and prattle on like a fool. And to top it off he is using the thing I am disputing to settle the dispute. How pathetic can you be, Jerad?ET
March 15, 2020
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JVL:
I dispute your method and provide examples where it doesn’t work and you continue to use it.
You are a LIAR.
Close, you screwed up some of the coefficients.
No, I didn't.
So you worked with infinite series yet you’re not sure infinite sets exist?
I have explained that. Are you a retard?
My refusal to agree with you is because your system a) is not used, b) doesn’t work for a lot of sets and c) doesn’t give the same result as a system which IS used and DOES work for a lot of sets.
No one uses Cantor's concept for anything. Mine works for all sets. YOU are too stupid to figure it out.
IF you have a fixed speed then a given wavelength will give a specific frequency and vice versa.
I know. Wavelength and frequency are interchangeable when discussing the emissions of CO2- you can talk about the frequency or the wavelength and you are discussing the SAME thing. Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance.ET
March 15, 2020
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ET: I dispute your method and Jerad continues to ay it’s true. I provide examples that contradict Jerad’s method and Jerad ignores them like the ignorant coward that he is. I dispute your method and provide examples where it doesn't work and you continue to use it. That's a double standard. Now Jerad wants to try to change the discussion. That says it all. Jerad has proven ignorant of science. Jerad has proven to be ignorant of biology. And now Jerad has been proven to be the coward of mathematics. I just thought it would be interesting, you don't have to play if you don't want to. a^7 – 7a^6xb+ 21a^5 x b^2 – 35a^4 x b^3 + 35a^3 x b^4 – 21a^2 x b^5 + 7ab^6 – b^7 Close, you screwed up some of the coefficients. Have another go. a=2; r= 2/3;(absolute) r< 1 S=a/(1-r); 2/(1-2/3) = 6 Yes, it converges to 6 Very good. So you do agree that infinite sets exist and can be worked with. That's good. How about this one: ! + (2^2)/2! + (3^3)/3! + (4^4)/4! + . . . Does it converge and if yes to what? Yes, to all. What no one has ever done, you little wanker, is use the concept being debated for anything. Ooo, very impressive. So you worked with infinite series yet you're not sure infinite sets exist? Again, truth is not determined by the number of real world applications. Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance. My refusal to agree with you is because your system a) is not used, b) doesn't work for a lot of sets and c) doesn't give the same result as a system which IS used and DOES work for a lot of sets. And I understand that you are desperate to avoid those. But then again you clearly do NOT understand infinity. I'll keep telling you why I disagree with you and your "method" if you like. I just thought you might be getting a bit bored. Even Hazel and Jerad understood what I was saying. So clearly you are the loser, Acartia. IF you have a fixed speed then a given wavelength will give a specific frequency and vice versa. Like two sets matched one-for-one isn't it? Yes, it's exactly like that. So, if the wave speed was, say, 1000 ft/sec then a frequency of 200 cycles per second would match up with a wavelength of 5 feet. So the wavelength and the frequency are not the same thing, but FOR A GIVEN SPEED one dictates the other. In fact, for a given speed you can match up, one-for-one elements from the frequency set with elements of the wavelength set. Which means both those sets have the same size! Get in!!JVL
March 15, 2020
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Jim Thibodeau seems reluctant to be truthful. I wonder why...ET
March 15, 2020
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Correction to 313- there are 2 7'sET
March 15, 2020
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Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance. And I understand that you are desperate to avoid those. But then again you clearly do NOT understand infinity.ET
March 15, 2020
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Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance. And I understand that you are desperate to avoid those. But then again you clearly do NOT understand infinity.ET
March 15, 2020
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Do you know how to design a complex electrical circuit using differential equations? Have you used complex variables to analyse fluid flow? Do you understand how prime numbers are used in cryptography? Have you found the volume of a solid of revolution using calculus? Have you found the eigenvalues of a muti-dimensional vector space? Have you found a Taylor series for a periodic function? Have you done triple integrals over volumes defined by surface functions? Have you actually done any higher level mathematics? You have to learn a lot of abstract principles before you get to the applications.
Yes, to all. What no one has ever done, you little wanker, is use the concept being debated for anything.ET
March 15, 2020
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JVL:
Does the infinite series 2 + 4/3 + 8/9 + 16/27 + 32/81 . . . converge? If yes then to what?
a=2; r= 2/3;(absolute) r< 1 S=a/(1-r); 2/(1-2/3) = 6 Yes, it converges to 6ET
March 15, 2020
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Acartia Eddie lies again:
He demonstrated his fundamental ignorance of math during his multi-year defence of his claim that Frequency = Wavelength.
Your quote mine proves that you are a clueless coward and a liar. Mt=y defense was only muliti-year because YOU ate too stupid to understand anything. Even Hazel and Jerad understood what I was saying. So clearly you are the loser, Acartia.ET
March 15, 2020
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What is the coefficient of the term a^3b^6 in the binomial expansion of (a + b)^7 ?
The binomial expansion of (a+b)^7 has several coefficients. There will be a 1 (twice), a 21, a -21, a 35, a -35, and a 7: a^7 - 7a^6xb+ 21a^5 x b^2 - 35a^4 x b^3 + 35a^3 x b^4 - 21a^2 x b^5 + 7ab^6 - b^7ET
March 15, 2020
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Now Jerad wants to try to change the discussion. That says it all. Jerad has proven ignorant of science. Jerad has proven to be ignorant of biology. And now Jerad has been proven to be the coward of mathematics.ET
March 15, 2020
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I dispute your method and Jerad continues to ay it's true. I provide examples that contradict Jerad's method and Jerad ignores them like the ignorant coward that he is.ET
March 15, 2020
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@308 Jeez that’s an easy one.Jim Thibodeau
March 15, 2020
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Here's another good, basic question: Does the infinite series 2 + 4/3 + 8/9 + 16/27 + 32/81 . . . converge? If yes then to what? I loved infinite sequences and series. Really fun stuff. And heavily used in Talyor series and therefore a lot of analytic tools and situations.JVL
March 15, 2020
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Here's a easy question for ET, please can no one else give the answer? Let's see if he (?) can get it. What is the coefficient of the term a^3b^6 in the binomial expansion of (a + b)^7 ?JVL
March 15, 2020
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Jim T: Mostly Abstract Algebra. Never liked that much. Grew to like Linear Algebra though after finding an excellent textbook. Didn't spend nearly enough time on discrete topics; number theory is sublime.JVL
March 15, 2020
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Fun questions! “Do you know how to design a complex electrical circuit using differential equations?” Let’s see...the capacitor is like a mass, and the inductor is like a spring...or the other way around... :-D “Have you used complex variables to analyse fluid flow?” No. ”Do you understand how prime numbers are used in cryptography?” Primes are the things you multiply together to get the keys if I recall correctly. “Have you found the volume of a solid of revolution using calculus?” That was Calc 2. “Have you found the eigenvalues of a muti-dimensional vector space?” Had to do that for advanced QM. “ Have you found a Taylor series for a periodic function?” Calc 2. “Have you done triple integrals over volumes defined by surface functions?” Calc 3. “Have you actually done any higher level mathematics?” Mostly Abstract Algebra.Jim Thibodeau
March 15, 2020
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ET: Learn how to read. You are NOT matching the elements. Of course I am! I showed you the scheme. "Matching" just means pairing up. And I can do it the way I am doing it, it's allowed. LIAR. All I have done is pointe out its faults. You said it was bogus, which is an opinion. You said your "set subtraction" contradicts it but no one else uses "set subtraction" when working with cardinalities. Your "set subtraction" can't handle lots and lots of situations. My approach is used in many, many textbooks and on many, many sites because it's allowed and it works, especially for this particular case. It is NOT use for anything. It is a useless concept. It's true regardless. It’s not that I don’t like it. It’s BOGUS, you ignorant loser. I don't remember ever reading a mathematical definition of bogus. Maybe I missed something. Both set subtraction and my counter example contradict Cantor. That you refuse to understand is a reflection on YOUR willful ignorance. I understand that you are desperate to avoid admitting you're wrong. I understand what hundreds of mathematicians have done working with such things. I understand why matching elements of sets one-for-one works to compare their cardinalities. And that all you can do is repeat what I am disputing proves that you are a willfully ignorant coward. You lost the dispute. I've told you why over and over and over again. Plus you cannot find anyone who says otherwise. There is no dispute, just you trying to score a point. Good luck with that. Let me know whenever you are able to think for yourself and can formulate an argument without using the disputed nonsense. I dispute your method and you continue to insist it's true. So you have a double standard. Nicely done. Do they allow that in debates? That only pertains to the math people can and have used. No one uses Cantor’s concept of all countably infinite sets have the same cardinality. It is useless without an application. And to top it off it is contradicted by at least two different models. Of course it's true!! Your fixation on applied mathematics is why you don't get proofs and abstract work. Do you know how to design a complex electrical circuit using differential equations? Have you used complex variables to analyse fluid flow? Do you understand how prime numbers are used in cryptography? Have you found the volume of a solid of revolution using calculus? Have you found the eigenvalues of a muti-dimensional vector space? Have you found a Taylor series for a periodic function? Have you done triple integrals over volumes defined by surface functions? Have you actually done any higher level mathematics? You have to learn a lot of abstract principles before you get to the applications. You show me a math concept that has survived the centuries that is contradicted by two different models and I will listen to you None of the ones that have survived the centuries are contradicted. Some models have been refined (like physics moving from Newton to Einstein) but the math is all still true.JVL
March 15, 2020
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ET seems reluctant to debate Sewell. Wonder why....Jim Thibodeau
March 15, 2020
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JT
Ed, you have to admit, ET’s just as good at biology as he is at math.
He demonstrated his fundamental ignorance of math during his multi-year defence of his claim that Frequency = Wavelength.Ed George
March 15, 2020
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What's to discuss? I made my points. Perhaps at least Dr. Sewell would address them properly. I know that you cowards can't. And again, it is all moot as the concept under dispute is useless and because of that, meaningless. But you are too dim to understand even that.ET
March 15, 2020
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@JVL Sewell posts here sometimes, doesn’t he? Somebody should make a post where he and ET discuss this set theory business.Jim Thibodeau
March 15, 2020
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JVL:
Not in mathematics. what was true 2000 years ago is still true, what was true 1000 years ago is still true, what was true in the 19th century is still true.
That only pertains to the math people can and have used. No one uses Cantor's concept of all countably infinite sets have the same cardinality. It is useless without an application. And to top it off it is contradicted by at least two different models. You show me a math concept that has survived the centuries that is contradicted by two different models and I will listen to youET
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