## Saturday, December 10, 2011

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Imagine a chair in empty space, not “falling” but remaining in place. Now imagine we wonder why this should be (for surely, we think, the chair should be moving, floating, falling). Obviously, this chair’s sitting atop one other chair would not explain the phenomenon. Would the chair’s sitting atop a stack stretching infinitely beneath it provide an explanation? Surely not. If we think that it would, let’s imagine what would happen if we pushed down on the top chair. Would the stack not budge at all, not sink--even though there is nothing stable beneath the stack to resist the downward pressure? Would the stack move downward but eventually (after an infinite amount of time?) rebound--even (again) with nothing stable beneath the stack to repulse the downward motion? It seems to me that the stack most certainly would sink--in fact, that it would be “sinking” or “falling” even before we applied pressure to the top chair. Unless, that is, there were something stable somehow, somewhere beneath the stack. Does this little thought experiment demonstrate anything at all about the explanatory power of infinite series in general?

Thank you Bill. Appreciate the help.

For now let me ask you about your belief in the possibility of an infinite regress of contingent beings. You agree we can’t reify the whole regress and attribute necessity to it. So the whole regress is as contingent as any member. Now, to say that’s ‘possible’ is to say a world of absolute contingency (void of all necessity whatsoever) is possible. That’s possible?

Tom

Hi Bill,

You are right that an infinite regress of contingent beings is no explanation of why there is contingency at all.

The primary question to be considered is not, "Why does this or that contingent being exist?", but, "Why does anything contingent at all exist?", this or that contingent being simply being a particular to which the general question applies.

No genuine explanation of the contingent being of anything contingent can itself be contingent; that is because the explanandum (viz., contingent existence) will be in the explanans.

Now, to address Tom's question: No, no possible world can contain only contingent beings. Contingent being requires a ground, and this ground must be necessary. But if it is necessary, then there is no possible world with out it.

Bill perhaps meant that an infinite regress of contingent beings is possible in the sense that there is no contradiction in an infinity of contingent beings existing, although, of course, if such a chain of beings did exist, they would require a necessary ground. There may be a possible world in which an infinity of contingent beings exist; but of course, in such a world, a necessary ground of their existence would also exist.

Thanks to all. Yes, concentrate on the question of why there should be anything at all. That’s what needs explaining. I put that to Jeff in those terms. He seems to feel that an infinite regress of contingent entities/causes enjoys the same exemption from the need to explain why it should exist at all as any necessary being enjoys. The latter is self-explanatory, and so is the infinite regress in his view. It’s infinite! I pressed for an explanation of why the regress should exist at all since all things on that account are contingent. I may be at a deadlock with him.

I’ve got Hartshorne stuck in my head on this. Hartshorne argued that (ultimately) logical and metaphysical possibility are one and the same; they’d certainly be the same for an omniscient being, so that nothing which is ‘metaphysically impossible’ (say, an infinite regress of only contingent beings) can be ‘meaningfully conceivable’. So if one wishes to posit such a regress, I like to insist (with Hartshorne) that one be consistent and recognize that to posit such a regress is to posit the impossibility of a necessary being, for a necessary being could not fail to exist contingently. But to grant the possibility of a necessary being constrains one to grant the actuality of such a being. But that gets us off onto Hartshorne’s Modal Argument.

Tom

It is important to distinguish the following:

A. If the totality of contingent beings has an explanation, then it cannot be in terms of a contingent being; it must be in terms of a necessary being.

B. The totality of contingent beings has an explanation.

C. It is possible that all beings are contingent beings.

We all agree that (A) is true. And we all agree that a sum of contingent beings is itself contingent. But obviously (A) does not entail (B). So what reason do you gentlemen have for thinking that (B) is true? Equivalently, what reason do you have for thinking that the existence of contingent beongs is not a brute fact?

As for (C), what is the argument for its being false? Steven says that contingent beings need a ground. But why? Why can't they just exist as a matter of brute fact?

I said: >>But it is not clear that an infinite regress of contingent beings is impossible. Why should it be impossible? There are benign infinite regresses.<<

You all seem to have misunderstood it. So let me explain.

First, there is nothing problematic about an infinite series as such. Second, there is -- I will assume for present purposes -- nothing wrong with an actually infinite series as such. Consider the actually infinite regression of negative natural numbers: . . . -n . . . -3, -2, -1. (There is of course the issue of a potential vs actual infinite whihc I have discussed in separate posts. We can't go into that now.)

Now consider a universe U1 which has an infinite past and which consists of an actually infinite series of contingent beings one after another, coming into being and passing away, but without being causally connected. That's conceivable. An omnipotent god could have created such a world. So why should an infinite regress of contingent beings be impossible?

Now suppose that each being in the series causes the next one in the series. This too is conceivable. God could have created such a universe, all it U2.

U3 is like U2 except that there is no God. U3 is also conceivable. The existence of U3, of course, would have to be a brute fact.

What we cannot allow is the idea that the existence of the entire series is explained by the fact that each member of the series is caused by the one before it.

It is important to realize that not every infinite regress is a vicious infinite regress. Many are, if not exactly virtuous, at least benign.

Tom,

Just saw your latest comment. Will respond later in the day. Now I need to go for a 10 K run. You see, I favor a 'peripatetic approach.'

>>He seems to feel that an infinite regress of contingent entities/causes enjoys the same exemption from the need to explain why it should exist at all as any necessary being enjoys. The latter is self-explanatory, and so is the infinite regress in his view. It’s infinite!<<

The mistake your friend is making is obvious. He is confusing the temporal and the modal. Perhaps he doesn't understand quite what is meant by 'necessary being.' Try the Leibnizian imagery of possible worlds. This may help. (Or it may only confuse him further.) A necessary being is one that exists in all broadly-logically possible worlds. Challenge him to show that a universe that consists of an actually infinite regress of causes exists in all BL-possible worlds. He won't be able to do it.

I would say your friend just doesn't get it, and that you are better off not discussing the question with him any further.

A very interesting and more plausible variant of the argument we have been examining is scrutinized in my journal article, "Could the Universe Cause itself to Exist?" PHILOSOPHY 75 (2000)604-612.

Mark,

I would take your thought experiment as supporting the point I was making, namely, that if contingent beings have an explanation, then that explanation cannot be given terms of an actually infinite temporal regress of causes. The whole infinite collection as it were 'hangs in the air.'

Bill,

I agree that my thought experiment supports your point. I posted it only because I have found that it helps some (those who don't quite follow the logic--perhaps like Jeff) to see the problem with the explanatory power of an infinite series.

Thanks, Mark. Merry Christmas!

If we grant that an infinite regress of contingent beings (i.e. a world void of all necessity) is possible, then positing its possibility is to posit the impossibility of a necessary being (since the only way a necessary being can be conceived of as not existing is necessarily). But if we cannot succeed at arguing the impossibility or inconceivability of a necessary being, then we ought to concede its actuality, in which case an infinite regress of contingent beings is what's impossible. So, given "the infinite regress of only contingent beings" and "a necessary God," one of these is impossible and one is necessary. This particular kind of regress looks VERY suspicious to say the least.

I believe if scientists understood that a necessary supportive cause is a necessary cause, there wouldn’t be much contention over whether the universe has a necessary cause or not. From the little I know, there’s really no cosmological theories without either laws of physics or a zero-point field (quantum vacuum) serving as a necessary supporting cause of the universe’s existence. So other than terminology, I’m not sure there’s much to dispute.

Nearest I can gather, the bulk of the dispute regarding causality seems to center around the notion of time as a measurement of change, and hence at the early stage of the universe there’s really no time since there’s nothing discrete to measure change with. But I don’t think the metaphysician is necessarily constrained by that notion of time in regard to determining causality. We do experience time as a sort of qualia of duration or being, from which we can imagine our way back to the early universe and when the physicists’ time plunges down the rabbit hole at the singularity (because there’s nothing to measure) we can imagine duration without change continuing in a straight line. In a sense thinking, “there is something, there is something, there is something, there is nothing, there is nothing, there is nothing, etc.” Or, vice-versa, “there is nothing, there is nothing, bang!, there is something ex nihilo!”

Tom,

You are just not thinking hard enough or carefully enough.

>>If we grant that an infinite regress of contingent beings (i.e. a world void of all necessity) is possible, then positing its possibility is to posit the impossibility of a necessary being (since the only way a necessary being can be conceived of as not existing is necessarily).<<

First of all, you cannot identify an infinite regress of contingent beings with a world devoid of all necessity. I gave an example above. There could be a universe containing (i) an actually infinite temporal series of contingent beings that are causally disconnected, and (ii) one or more necessary beings. So what you are saying is plainly false.

Apparently, you failed to heed the distinction I made above between an infinite regress of contingent beings and an infinite regress of contingent beings in which the existence of each member of the series is explained by a causal relation to an earlier member of the series.

Your conditional statement is just plain false. From 'There is an infinite regress of contingent beings' it does not follow that there is no necessary being.

Let me clarify (what Jeff's alternative to positing a necessary being). The regress I have in mind is an infinite regress of only contingent beings, each one causally brought to be by the previous. You're right...there could be an infinite regress of contingent (and causally related) beings AND a necessary being as well. That's not what Jeff's offering for consideration. He was offering a particular kind of regress, one populated exclusively with causally related contingent beings, as an explanation of our contingent universe. So in the regress under consideration, there is no necessary being at all. But I see your point. You've said such a regress could just be a brute fact. But you agree that it doesn't explain why there should be anything at all.

Thank you for letting me think out loud here.

Tom,

As for your dispute with Jeff, you are quite right. The universe of contingent beings cannot be self-explanatory. Therefore, it either has an explanation in terms of a transcendent being, which must be a necessary being, or it has no explanation at all and exists as a matter of brute fact.

Since we are both theists, we both reject the brute fact alternative.

A question you need to ask yourself is how you exclude the brute fact alternative. But this goes beyond the present discussion.

Shouldn't it be the case, Bill, IF brute facts are conceivably meaningful, that one can only justifiably posit such a fact in the absence of all possible explanations? If X is a brute fact, then by definition it defies explanation. So it seems one can only rattionally posit such facts after demonstrating the impossibility of its explanation; one would have to demonstrate that all candidates for explanation fail. Only THEN (at the very least) would one be justified in appealing to brute fact. Yes? No?

Tom,

First of all, to maintain that there are brute facts is not to maintain that every fact is a brute fact. Despite your formulation, I think you appreciate this point.

You seem to be saying that one cannot justifiably call a fact F brute unless one can demonstrate the impossibility of its having an explanation. But a partisan of brute facts will just turn it around: He will challenge you to demonstrate that every fact must have an explanation.

He will say that you are assuming what he denies, explanatory rationalism. I'll put up a post on that.

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