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July 2014
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infinite regress, epistemology

What exactly is wrong with an infinite regress? As far as I'm aware, an infinite regress could potentially be a real problem for foundationalists (because justification must stop somewhere). If so, what about apparently "harmless" instances of infinite regress? For example, I'm reminded of Stephen Schiffer on mutual knowledge*. "Sally and Harry are enjoying a candlelit dinner. They're seated opposite each other, and on the table between them is a large and conspicuous candle; they sit watching the reflection of the candle (and themselves) in each other's eyes. Sally knows there's a candle on the table; she also knows that Harry knows that too. Furthermore, she knows that Harry knows that she knows that he knows that. And she knows that Harry knows that she knows that he knows that she knows that he knows it. And so on. It seems that there is an infinite number of things which Sally knows. And, of course, Harry on his side of the table knows just as much. And so on." Do examples like this really have any consequences for epistemology?

Comments

Well, if you're not a foundationalist, then you've got to be a coherentist, right? And the idea of a "regress" is incoherent under a coherence analysis (pun fully intended) because there's no such thing as a basing relation for coherence theories.

So an "infinite epistemic regress" is only a problem to the foundationalist, because her theory cannot handle a basing relation that continues indefinitely.

On the other hand, I'm not sure how much of a problem Schiffer's example actually poses for a foundationalist. The foundationalist is not concerned with how many things Sally knows, as long as he can trace all of them back to some atomistic facts. She can know infinitely many things on the basis of infinitely many facts.

She could know infinitely many things on the basis of infinitely many facts, but when you lock those things and those facts together (i.e., that Sally knows that a because Sally knows that b because Sally knows c... in which a is the farthest along in a chain of "Sally knows that Harry knows that Sally knows that..."), don't you end up with an infinite epistemic regress, anyway?

No, they're not separate claims.

If Sally knows (a) on the basis of her also knowing (b), then the basing relation is just (a) → (b).

If sally only knows (b) because of (z), then she doesn't know (a) on the basis of (z). Basing relations aren't transitive (at least, I've never run across a foundationalist theory that says the relation is transitive). Anything you already know is the perfect basis for another level of knowledge... as long as you're moving horizontally.

Consider something like Carnap's system in the Aufbau. Everything Sally knows is still just a second-order knowledge claim, so there's no change between order forms when discussing what she knows.

Do examples like this really have any consequences for epistemology?

Indubitably - you might clarify the English word "know" some, investigate whether we can know things that never actually entered our consciousness, &c.

It's a mildly interesting fact that any statement implies an infinite number of very boring facts, but I don't see how this interacts with the problem of infinite regress. I don't see how it could interfere with the justification of our ordinary important beliefs.

The infinite regress problem is a problem for coherentism, not foundationalism. Foundationalism stops any infinite regress by having "basic beliefs" of some sort which are not justified in virtue of some other belief but are justified "directly" and which other justified beliefs are ultimately based upon. You can't make an infinite regress argument against a foundationalist, and the possibility of such an argument against a coherentist is one of the main ways to support foundationalism.

Your Harry/Sally example isn't really what people have in mind when they talk about an infinite regress. As long as you can provide the "basic belief" that grounds whatever iterated knowledge claim you make, it won't be an infinite regress, because it will stop at the basic belief. You could construct an infinite chain of iterated knowing-that claims, but it wouldn't be a regress because it would still stop at one of the foundational beliefs (presumably, that it appears as if there is a candle, or it appears as if Harry sees a candle).

I think it might be a problem for foundationalist accounts if you could discover an infinite regress that couldn't be justified in terms of a "basic belief."

But you're right about my example.

Oh, ok, I didn't read what you wrote closely enough. If you could discover an infinite regress that was not justified in terms of a "basic belief," then ya, you would have a problem, although a foundationalist could aways deny that the links in the infinite chain were justified to begin with. After all, a foundationalist thinks every justified belief can be traced back to a foundational or basic belief (or, to a foundational or basic experience, or whatever). Coming up with a regress that could not be justified in terms of something "basic" would then mean that you just don't have a case of justification to begin with, regardless of whether the regress was infinite or not.

Well regardless of your philosophical foundations, the example you present suffers a serious logical difficulty in any case. Harry and Sally will die before they can achieve a truely infinite regression of 'knowing what the other knows'. You can't have an truly infinite regress of that nature, because it's simply technically impossible.

I challenge anyone to demonstrate a real world example that wouldn't suffer this problem.

Imaginary infinite epistemiological regress, yes.
Actual infite epistemiological regress, no. Regardless of your philosophical basis.

As long as we're bringing up the technical limits of the human brain, it would take them well less time than death, since most humans only have some single-digit-order intentionality.

I challenge anyone to demonstrate a real world example that wouldn't suffer this problem.

Disproving Achilles and the Tortoise? Finding the present value of an income stream? Constructing aleph-null?

(The question marks indicate lack of confidence, not sarcasm.)

I can't speak for Aleph-Null, as I'm not that familiar with the concept. But let me address your other 2 examples.

Zeno's Paradox is only a paradox because although seemingly a rational description of a real world event (a race between Achilles and a Tortoise) it's conclusion conflicts with the reality.

Obviously the description of events in Zeno's paradox are incorrect or incomplete. Which brings us back to my statement - infinite regress is not possible in the real world (in this case, in the real world there is a minimum distance you can move over a minimum period of time: the Planck length/time, as described in quantum physics).

As for the present value of an income stream, the problem of infinite regress only arises when we try to calculate that value: which is exactly when we encounter the problem I've described - it is technically impossible to perform a infinitely regressing calculation in the real world. I'd say that this is because in the real world, that value does not actually exist, because the value is a measure of something in the real world, which is of course subject to quantum indeterminancy.

Using the explanation that I've just given, we can see that it's quite possible have logically consistent theories, philosophies and modes of logic, which require infinite regress to resolve, but we can also see that these seem to inescapably suffer from the fatal problem of being inconsistent with physical reality, because infinite regression is technically impossible in reality, for a variety of reasons.

That's a good point, actually. I know that Sally and Harry couldn't possibly actually take the implications of knowledge in this situation out to infinity (because eventually they'd die), but it at least has the implication of being an infinite regress (I think).

It's easy to imagine beliefs where the implications of such a belief can lead to a non-finite set of other beliefs, but this does not speak of justification for said beliefs- which is the issue at hand for standard analytic epistemology.

From my knowledge of 1+1=2, I can generate beliefs such as 1+1 does not equal n, where n can be any non-2 number. I don't bother generating such beliefs, because well... what's the point? But had I decided to generate these true beliefs, I would not run into a problem of justification, as these beliefs would be foundationally justified by my acceptance of 1+1=2.