[Introductory note from Jason Pratt: the previous entry in this series of posts can be found here. The first entry can be found here.]
[Note: the previous entry ended with the questions, "So why can there not be grounds stretching on forever with no end, no Final Fact? Why can there not be an infinite regression?"]
For what it is worth, I don't think it is possible to prove that an infinite regress does not exist--nor that it does exist. So I will presume each of these two mutually exclusive options; and then check to see if either or both of the options crash.
Let me presume, for purposes of argument, that an infinite regress is real. What advantages does a proposed system of thought have, when based on this presumption?
None! If an infinite regress is true, then we have no means of reaching valid conclusions.
This is because we habitually presume, when we offer explanations or arguments, that somewhere 'behind' or 'under' the explanation (metaphorically speaking) is an actual reality that just is. This reality provides us the standard by which to explain other things; it cannot be explained the same way, in terms of something more fundamental than itself.
Now I grant that we humans are very good at turning our analytical 'spotlights' onto our presumed grounds and discovering that those grounds can, after all, be explained in terms of something else. But then the 'something else' becomes in effect the ultimate ground. Perhaps it, too, can be explained in terms of 'another something else'. That would be fine: as long as the next 'something else' doesn't turn out to be one of the earlier 'somethings', because then we have a circular argument and all the conclusions reached along that train of thought collapse!
We can keep doing this for as long as it is non-contradictory, and non-circular, to do so. But every time we do this, we must presume that we have reached a stopping point. We may eventually discover that we really had not reached the last stopping point; but that is very different from proposing that there is no stopping point!
We (usually) explain the existence of 'something' in regard to a more foundational 'something else'. But an infinite regress means that there can never be 'something else' which stands as a proper explainer to the 'something'.
Put another way: if there could be such a thing as a bottomless pit, you would never be able to answer the question "How deep is it?" Replying "It is infinitely deep" would be one way of saying the deepness is real but cannot be quantified: and "How deep?" asks for quantification. Yet in the case of an ultimately infinite metacosmic regress, this would apply to every question, and not merely in regard to quantification.
The infinite regressor may not be bothered by this. "Why, I can answer all sorts of questions!" he may snort. "I can add 2 + 2 and get 4 just like anyone else!" Yes; but you do this by presuming there is an unalterable characteristic of reality which cannot be 'explained away' or 'explained in terms of something else', which the math expression (and, for that matter, the logical 'law of noncontradiction') reflects.
"No, I pretend for purposes of convenience that there is a stopping point." Yes--because you know perfectly well that the statement will be reduced to absurdity if there is no stopping point! Yet, by saying there is (in fact) no stopping point, you concurrently assert that the proposition 2 + 2 = 4 is in fact (all possible appearances to the contrary) an ultimately unreliable statement! Furthermore, any arguments and conclusions you may draw with an infinite regress as your ultimate presumption, are rendered equally nonsensical.
"Christianity and similar theisms are false", you may say, "because in fact there is an infinite regress." [Footnote: This attempt could, of course, be made against atheism by counter-atheists, too; perhaps by a certain class of positive pantheists. But in my experience it’s more likely to be applied the other way around.] But this statement has been rendered as moot as the statement 2 + 2 = 4. The only 'explanatory power' an infinite regressor has, is borrowed by him from the position of his direct opponents: the people (atheists, theists, etc.) who do propose an IF of some kind. A position that must borrow all of its strength (even if only for purposes of convenience) from a presumption that its opposition must be correct, can only be an untenable position.
In other words, infinite regression has an ultimate and inescapable problem, which I think sinks it as a viable alternative to an Independent Fact: no one can possibly believe in an infinite regression.
'What!? Are you telling me I do not really believe my own position?'
Do you propose that there really is an infinite regress?
'Yes, of course!'
Then you have proposed that there is, in fact, an unalterable, final characteristic of reality: there is an infinite regress.
So you are proposing that it is impossible to explain an infinite regress in terms of "something else" which is itself not an infinite regress.
'Naturally; otherwise I would be saying there is ultimately no infinite regress!'
But an infinite regression requires precisely that everything can be explained in terms of "something else" forever! You must make a tacit exception against the infinite regress itself, to even seriously propose it is true; thus immediately contradicting your own position!
Even if I tried to accept a so-called 'infinite regress', I would necessarily be putting it into some type of ultimate framework which cannot itself be explained in terms of something else--and this immediately undercuts the whole point to proposing an infinite regress.
I therefore conclude, that although I may assert I believed an 'infinite regress' to be true, I would have to be mistaken; I would actually be proposing an Independent Fact in order to try to propose an infinite regress, and I would have been misled in my labeling by not considering one of the chief properties of an infinite regression: it must be what it is, and so not be fully explainable (in principle, even if not in practice) in terms of something which is not an infinite regress. But then I would no longer be proposing an infinite regression philosophy.
I find myself and everyone else (including the infinite regressors!) already presuming that an IF of some sort must in principle exist; so either an IF exists or we might as well treat reality as if it did. To do otherwise leads us precisely nowhere, even if it was possible to consistently (or even coherently) presume otherwise (which I think is impossible).
So an Independent (or Interdependent) Fact should be formally presumed to exist. For all practical purposes I should even believe it must exist; and all metaphysics and philosophy should center either on discovering what we can about it, or else on working out what must be true given presumptions about it (including the necessary presumption we all evidently make--whether we express it or not--that it in fact exists).
But the infinite regressor has one more bolt in his crossbow: the IF must be something that we cannot say is 'caused' by something else, or 'derives from' something else, or is a 'piece of' something else that 'includes' it. It is what it is (or even "I AM THAT I AM!") and absolutely no further reductive explanation is possible.
But some people find this intolerable, especially among opponents to supernatural theism. "To explain the origin of Nature," an atheist may say, "by invoking a supernatural Designer, is to explain precisely nothing, for it leaves unexplained the origin of the Designer." This is a common and not altogether unreasonable type of complaint. But if we really accepted the use of this principle, then to explain the origin of the DNA-replication process (for instance) by invoking a blindly automatic Nature would also be to explain precisely nothing!--for it would also leave unexplained the origin of the Nature.
"Aha!" says the infinite regressor. "Now you see why I propose an infinite regress!" But there is no escape by that route; I can ask the exact same question about the infinite regress: how did it "come to be"?
So whatever philosophy we propose (and apparently whyever we propose one), we seem, at first glance, to be either explicitly or implicitly requiring the existence of an ultimate Fact that does not have to be caused.
"Hah!" barks the infinite regressor (and perhaps some of my earlier targets in this book). "That which is uncaused, does not exist! Here is a contradiction! Eat your own sword!"
I agree; so I should modify the statement to remove the contradictory proposal:
Whatever philosophy we propose (and whyever we propose one), we will explicitly or tacitly be requiring the existence of an ultimate Fact that sustains its own existence.
It is not, strictly speaking, uncaused: I agree, that would be a contradiction. It causes itself; as the Final Fact it must do so eternally. [See first comment below for a footnote here.]
I am intentionally contrasting this with the proposition that it merely exists without cause. In fact, this will be very important to part of my forthcoming positive argument. However, for the moment, let us stay with the conclusion that we must necessarily presume a self-causing IF to exist. To presume otherwise leads us to nonsense. I think that the notion of a self-causing Independent Fact is, at least, self-consistently coherent.
So I find, whatever I do, that I am necessarily presuming an IF exists. I would feel nervous about this, except (as I've already noted) I think virtually every philosopher does this already, whether they spell out the implications or not. [See second comment below for a footnote here.]
For most people, this shouldn't require anything like a jolting revelation. If I go to an atheistic naturalist and ask her, "Does Nature really exist and is it dependent on anything but itself for its existence?" she would probably answer Yes to the first part, and certainly answer No to the second. [See third comment below for a footnote here.] If I go to a certain type of pantheist (one who is not a 'negative' pantheist in the sense that everything must be illusion, although he might perhaps say that most things are illusion) and ask him whether the Absolute exists and if it depends on anything else, he will also say Yes and No respectively. If I go to a Muslim and ask him if Allah exists and if anything created Allah, he will also say Yes and No to those questions.
All of these people (I would fall into the same basic class as the Muslim) are affirming the existence of what I am calling 'the IF'. [See fourth comment below for a footnote here.] They will be assigning different properties to the IF; but they are still talking about an IF.
This raises my second topic for this chapter: could all three of these people (the naturalistic atheist, the positive pantheist and the Muslim theist) be correct, and if so to what extent?
[Next time: in question of infinite possibilities]
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[Introductory note from Jason Pratt: the previous entry in this series of posts can be found here. The first entry can be found here.]