One of Aristotle's premises for proving that God exists is that there cannot be an infinite chain of causes and effects, hence there must be one cause which had no previous cause (i.e. God).

Does anyone know the logic behind this? Why can't there be an infinite chain of causes/effects?

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    There are more than 15 questions about varitions on this theme "the cause of the universe" in this site. I cannot believe in a new answer now. – Annotations Mar 24 '13 at 14:09
  • could not find anything that addressed this particular point. – user813801 Mar 24 '13 at 20:32
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    I am rather tired of this as well; we should wiki a single super-question with the above questions in the body, so we can refer people to that. The bottom line for all the questions is that we almost certainly will never be able to prove an infinite anything because the idea itself is unbounded, and that even if you were to prove through some linguistic trickery that there must have been a First Cause, it only presupposes "a thing which causes which is itself uncaused", certainly not a God nor even something that need be sentient. – stoicfury Mar 25 '13 at 3:48
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    While there are authors who do try to reason for a first cause (or otherwise) through various means, it seems to me that the choice of a particular author in presupposing either is essentially arbitrary, and seems to always be driven by an agenda. Is it any wonder why so many (if not every single one I've ever read) religious philosophers posit that there "must be" a first cause (namely God)? To find the answer to the question is a fool's errand, and even if an answer was found, it's unclear what value it would have, if any at all. – stoicfury Mar 25 '13 at 4:05
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    re: @stoicfury's first comment above, I now have attempted to write the definitive question/answer on this subject. – Niel de Beaudrap Mar 25 '13 at 15:33

I can only speculate that it is because we typically view causation as a finite process (in which case there must be a first one)--but this begs the question--or that when doing induction we normally use the natural numbers not the integers:

Prove P for case 0
Prove that P(n) => P(n+1)
Therefore P is true for all natural numbers

instead of

Prove P for case m
Prove that P(n) => P(n+1)
Prove that P(n) => P(n-1)
Therefore P is true for all integers

which is equally valid. (You can also get it with P(n) <=> P(n+1).)

It's also slightly distasteful to be left without an ultimate reason because it's reasons all the way down.

Disquieting though it may be, it's not logically invalid.

  • not sure what these equations mean. can you explain? – user813801 Mar 24 '13 at 20:34
  • @user813801 - P(.) is some predicate parameterized by a number. P(n) => P(n+1) means that if the nth predicate is true, the n+1st is also true. – Rex Kerr Mar 24 '13 at 20:48
  • So infinite regress is possible? – Minimus Heximus Jun 24 '15 at 1:54
  • @MinimusHeximus - It's logically consistent, and has not been demonstrated conclusively to be impossible. – Rex Kerr Jun 24 '15 at 2:36
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    @MinimusHeximus - Not all models support it (finite ones don't, for instance). So far, to my knowledge, no one has proven (or even has really strong evidence) that our reality is a model that does not support it. There are hints that time began with the Big Bang, which would make infinite regress tricky, but it's more of a statement that things are so different that we don't know what physical laws are than a certainty that time (in the sense of progression of events) had a beginning. – Rex Kerr Jun 24 '15 at 8:11

There cant be an infinite chain of causation because there cant be an infinite anything. Here i quote wikipedia "An actual infinity is something which is completed and definite and consists of infinitely many elements. According to Aristotle, the idea is paradoxical, both in theory and in nature."

If there were such an infinite chain, you couldnt ever utter them all, or write them down, or find them, or even define them, these properties, if you think about it, is quite similar to non-existence. If you could write them down (as in Rex's example), then you could view that description as a single cause.

A realizeable endless chain of causation is, "A is caused by B, B is caused by C, C is caused by A", these clearly needs more then one temporary direction, unlike our universe. This chain is remniscent of Hofstader "strange loops", explored in his book GEB.

  • "If you could write them down [...] then you could view that description as a single cause": but that does not negate the fact that this 'single' cause is infinitely divisible, by construction. Indeed, if you believe that time is continuous, then infinite causal chains are everywhere; and there is as yet no proof (nor is it clear that there could be without other assumptions) that time is discrete. – Niel de Beaudrap Mar 25 '13 at 1:01
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    Note that "According to Aristotle, [actual infinities are] paradoxical, both in theory and in nature" is a little dogmatic, and also discards out of hand a significant amount of thinking with regards to physics and mathematics. – Niel de Beaudrap Mar 25 '13 at 1:26
  • @deBeaudrap: I think he might be more subtle than you're assuming. Given ZFC, you have an actual transfinite hierarchy; but you can go beyond it by adding a large infinite cardinal. Compare this to his argument that you can't have an actual infinity, because if you had it, you can always go beyond it. Perhaps, I'm being anachronistic though. – Mozibur Ullah Mar 25 '13 at 4:20
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    @MoziburUllah: "actual" infinity does not mean "absolute" infinity — at least not in the modern nomenclature. Besides: if there could be an ultimate cause preceded by nothing, why can one not posit an ultimate cardinality superseded by nothing, that is containing all elements of the "universe", so that nothing may be added to it? Such infinite cardinalities exist in NBG set theory, for example (proper classes). – Niel de Beaudrap Mar 25 '13 at 4:25
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    @deBaudrap: Is NBG is roughly ZFC+Proper Classes? Presumably with careful thought one can introduce large cardinal axioms here too. I agree actual is not absolute in modern nomenclature, but isn't the question is what did Aristotle mean by actual? Presumably if Aristotle denies actual infinities, then he's also denying ultimate causes too. – Mozibur Ullah Mar 25 '13 at 4:50

I think we have good reason for believing that there can be 'an infinite chain of cause and effects' because we have a lot of evidence of effects which have causes, and close to no evidence of effects without causes.

Except for maybe some quantum mechanic observations which we have not yet found the cause of, but since effects happen according to some probability pattern it sounds reasonable to say that one day we will find what creates the pattern, i.e. the causes, and it sounds very likely that this is just at the edge of what we know at the moment.

This does not guarantee that there is 'an infinite chain of cause and effects' but it surely give us more reasons for believing that there CAN be 'an infinite chain of cause and effects', than for believing that there CANNOT be.

The quantum mechanic evidence are the only evidence I know which could give us some small reasons to believe that there might not be 'an infinite chain of cause and effects', but I cannot find any reasons for believing there CAN'T possibly be 'an infinite chain of cause and effects'.

I especially don't understand why difficulty in defining/describing what infinity is would give us reason to believe that it cannot exist. To me that sounds similar to saying that art does not exist because it is difficult to define accurately.

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