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For alternation in the status of A to be a cause of the alteration in the status of B, we naively demand that the former alteration exists before the later, and so the later [i.e.; the alteration in the status of B] must have a start in time.

That said then the cause-effect relationship implies a temporal difference.

This entails that no alternation K in the status of A can be the cause of alteration K in the status of A, because simply this would entail that alteration K existed before itself, which is clearly paradoxical.

From now on, we'd use "status" to mean "alteration in status" for brevity.

Also to clarify, when we say a status has a start, it means that this status begins at some moment of time, like for example A being the status of some ball moving from one point to the other thereby colliding with another ball that would cause it to move from the position of collision to another position, resulting in status B (i.e. status B is the movement of the other ball between those positions), now here both status A and status B would be called as "starting statuses" because they had a start in time. On the other hand a status that doesn't have a start, is an infinite status that exists and yet not having a start for its existence, i.e. it extends infinitely into the past.

From this we stipulate premise 1:

  1. if A cause B, then B starts and A exists before the start of B.

Also we naively demand:

  1. No status can start without being caused.

The reason is because we need a theory that is explanatory, i.e. can account for at least the starting of statuses. It would be nicer if we had a theory that can account for the 'existence' of any entity, but that would be too ambitious. For the current treatment, we'd content ourselves with a theory that can account for having starts of statuses.

If we hold that:

  1. Every status is ought to have a start.

Then we get an infinite conditional regress of statuses, of the following structure:

n+1 cannot start, unless n starts

n cannot start, unless n-1 starts,

.

.

.

where n is an integer (can be negative of course).

However this conditional series doesn't have an end, so we don't have an inference rule from which we can infer that any status in that series did start!

But we KNOW that there is a status that did start! This is observed!

So 3 cannot account for this observation!

What is wanted for a theory that can account for our observations of starting statuses, is a finitely long series of statuses the starting member of which doesn't beg a cause for it, i.e. an un-caused prime mover! But that can only be if that prime mover does not itself have a start!

So

  1. There exists an infinite [doesn't have a start] un-caused status that is a prime start of alterations.

The only alternative to that is a finite regress of finite statuses that ends by a first status that starts and such that we cannot speak sensibly of any occurrence before it, since 'before it' is not a sensible sentence.

The problem is that this would violate rule 1 and its underpinnings. So this would allow for a status to cause the starting of a status without being before it. This would be shown to hamper our accountability of starting of statuses, as follows:

If the first status that had a start didn't have a cause for its starting, then why did it start? This would be difficult to account for!

If we say that it itself is the cause of its starting, then there is the problem of circularity that would haunt that possibility, if A starts A then it starts A which starts A, etc.. This entails that A itself is the self starting of itself, but A being that status is not the same as A being the cause of the start of another status B, one cannot have A being both the status of self starting and the status of starting another status B, since this is paradoxical. To clarify, what I mean here is that if A starts itself, then it can be identified with the logical statement "A starts A and whatever A starts then it is A", by then it would be paradoxical to add the assumption that "A starts B, and B=/=A". However, this can be resolved by stipulating that A can be taken to be what fulfills the following statement "B=/=A and A starts A and whatever A starts then it is A or it is B", Of course this would solve the above-mentioned paradox, we can call that divergent self starting, but by then we'd have the problem of accounting for why A should be a divergent self start and not simply the simple status of self starting? And obviously there is no obvious reason why it should be that way?

Now to compare this with 4, here with 4 we have a finite regress of causation, and the first member of it doesn't beg a cause for it, because it doesn't itself have a start, i.e. we have:

n+1 cannot start, unless n starts

.

.

.

2 cannot start, unless 1 cause 2 to start

1 caused 2 to start

1 doesn't have a start.

Here we won't have problems of divergent self starting or of not having a causation for some status that have a start, or having an infinite regress that begs a start that is not there. So in some sense 4 has less conundrums than the others. So no formal paradoxes, and nothing that begs accounting for as far as causation of starting statuses is concerned.

The real problem of 4 is that we didn't observe a status that is infinite in that sense, and also the nature of such an infinite status itself is very vague, we are speaking of a status that had always been there in the past, never started at some moment of time, this is very difficult to grasp, one cannot be sure that such entities would exist in the real world. So although formally speaking it is the best solution, yet from reality point of view it is very doubtful and vague in itself. So one may be prone to accept the model of finite regress with a divergent self starting start, since the first status at least shares finite-hood with ordinarily observed objects. However, it needs to be understood that this objection only pertains to inability of understanding the nature of infinitude of such status and not to its explanatory value regarding causation of "started statuses", so it is about a step a head question.

As far as explaining causation of started statuses, the model in which there is an infinite prime mover model [i.e. statement 4], is the best model.

To summarize:

  1. Whatever begins, must have a cause
  2. Whatever is caused, must have a beginning
  3. A cause precedes the caused

It is a theorem of those premises (+logical axioms), that:

Theorem: There is something that doesn't have a beginning.

Proof: For a proof by negation, let's assume the opposite, i.e.:

ASSUMPTION: "Everything has a beginning"

then we get:

There is an infinite regress of causes begging a starting cause that is not there.

So we cannot infer the existence of anything?

So the above assumption must be rejected!

Question: in which respect this argument is different from the argument of prime mover of Aristotle?

  • It is unclear from the text if you are trying to make a version of the prime cause argument or an objection to it. "One cannot have A being both the status of self starting and the status of starting another status B, since this is paradoxical" is obscure. Self-causing has been discussed for centuries, there is nothing "paradoxical" about it. One may find it quaint, but quaint is not an obstacle to something being the case. – Conifold Apr 4 at 20:34
  • @Conifold, how can self causation be non-self causation? if A is "A causing A", then A cannot be "A causing B", where B is distinct from A. – Zuhair Apr 4 at 21:16
  • Why not? A lamp illuminates itself along with other stuff around it. There is nothing logically problematic with A causes A, and A causes B both being true. If you want to postulate it impossible the issue is with your postulate, not with some paradox. If one accepts the standard interpretation of quantum mechanics the outcomes of double slit experiments are self-caused, which does not prevent them from causing a number of other things down the road, e.g. triggering a detonator and killing the Schrodinger's cat. – Conifold Apr 4 at 23:09
  • @Conifold, the situation I'm describing is similar to saying that status A would satisfy the statement (for ALL x (A causes x if and only if x=A)), and then stipulating that (exists B (B =/= A and A causes B)), logically the second statement provides a counter-example to the first, it is paradoxical to stipulate both. That's what I mean by saying that A would be the self production of A [it means the first statement above]. – Zuhair Apr 4 at 23:34
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    @HWalters Consider the integers ..., -3, -2, -1, 0, 1, 2, 3, ... Each integer has an immediate predecessor to its left. Yet there is no first integer. What say you? And who says time couldn't be just like that? – user4894 Apr 5 at 17:11
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I find the question rather difficult to disentangle but seem to agree with its conclusion, and this seems to agree with Aristotle's conclusion.

This may be another example of an issue being made more and more complex in an effort to overcome what is in fact a simple problem to state.

if a thing exists it must have a status and it must be subject to constant change and motion. This status must be caused or uncaused. If it is caused then it is part of a casual chain that must be finite or infinite. A finite chain requires a Prime Mover, an idea that does not make sense (How can a non-mover cause motion?) while an infinite chain also does not makes sense. Thus existence, motion and change are all paradoxical concepts for Realism. (As Nagarjuna, Zeno, Bradley and others have argued).

A solution would require something like Buddhism, which speaks of a 'causeless cause'. Likewise, Lao Tsu does not suggest that the beginning is caused in the sense of being the result of some action or movement for this would be a paradoxical idea, but that the space-time world manifests 'Tao being what it is'.

This is not an easy quick-fix since the idea is still difficult, but once we reify objects, thus also motion, change and 'status', then Aristotle's argument follows, so it seems we either need a Prime Mover or Lao Tsu's idea.

I'd say your argument mirrors that of Aristotle's, reaching the same conclusion as him and as most people who study this issue.

The simplest way to summarise the situation is to say 'All positive metaphysical positions are logically indefensible'. This disposes of the question of whether time, space, objects, change and motion do or do not have a beginning. Both ideas fail under analysis. The only solution I know of is to say that these phenomena are not real in the way we usually imagine.

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    I've summarized my argument, so that it can be easily disentangled. – Zuhair Apr 6 at 9:21

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