## Wednesday, March 19, 2014

### Scepticism and the Principle of Sufficient Reason

The following argument is inspired by one that Rob Koons gives here:

1. If the Principle of Sufficient Reason is not true, then it is possible for there to be only one finite conscious being, a completely unexplained brain in a vat with perceptual states just like mine.
2. Completely unexplained contingent states of affairs have no objective probability.
3. So, if the Principle of Sufficient Reason is not true, it is not objectively unlikely that the only finite conscious being is a brain in a vat with perceptual states like mine.
4. If it is not objectively unlikely that the only finite conscious being is a brain in a vat with perceptual states like mine, then I do not know that I have two hands.
5. I know I have two hands.
6. So, the Principle of Sufficient Reason is true.

Nicholas said...

I suspect that I may be missing something here, but premise 1 seems false. Here’s why. Consider the contrapositive of 1 (which I’ll call “1cp”):

1cp: If it is not possible for there to be only one finite conscious being, a completely unexplained brain in a vat with perceptual states just like mine, then the Principle of Sufficient Reason is true.

But the following conjunction seems consistent: (i) it is not possible for there to be only one finite conscious being, a completely unexplained brain in a vat with perceptual states just like mine and (ii) it is possible for there to be one finite conscious being, a completely unexplained brain in a vat with perceptual states just like mine.

So assume the conjunction of (i) and (ii) is true. From it, given (i) and 1cp, we learn that PSR is true. But the following conditional (C) also seems true: if (ii), then PSR is false. From (ii) and C, we learn that PSR is false, and so we have a contradiction.

Obviously, you could deny that (i) and (ii) are consistent. Or you could deny C. But if you deny C, I’m not sure what work PSR is designed to do (and perhaps this is where I’m missing something).

We could run a similar argument by considering the contrapositive of 3 (doing so would show that “possibly BIV” and “PSR is true” are compatible, but that seems wrong to me).

Mikhail Lastrilla said...

Doesn't (1) and (2) also show that, if the PSR is not true, then it is not objectively likely that the only finite conscious being is a brain in a vat with perceptual states like mine?

Alexander R Pruss said...

Nicholas:

I am not saying that it is inconsistent to deny (1). All I am saying is that it is a true material conditional.

Sure, you could have narrowly logically consistent theories on which the PSR is false and yet the brain in a vat scenario is impossible. But such theories seem ad hoc and unlikely to be true.

Mikhail:

Yes.

Mikhail Lastrilla said...

If so, then an argument parallel to yours can be given, which shows that, if the PSR is false, I know I have two hands, and so the PSR's falsity does not lead to skepticism.

Alexander R Pruss said...

How so? Remember that "not objectively likely" does not imply "unlikely".

Mikhail Lastrilla said...

I'm afraid I don't see the distinction. "It is not objectively likely that my computer will explode right now" seems synonymous to "It is unlikely that my computer will explode right now". But I may be missing something here.

Alexander R Pruss said...

Throw a dart at a target in a way that is uniformly distributed over the target. Let S be a maximally nonmeasurable subset of the target (i.e., a subset such that its only measurable subsets have measure zero, and the only measurable subsets of its complement also have measure zero). Then it's not likely you will hit S, but it's also not unlikely. There just are no probabilities here. And that's how it is for unexplained events.

Mikhail Lastrilla said...

I see, point taken.

I'm now wondering why we should accept (2). Presumably, the objective probability of a state of affairs happening is the sum of the objective probability of that state of affairs happening with an explanation plus the objective probability of that state of affairs happening without an explanation. But if the latter has no value, then the summand has no value either - a conclusion the PSR skeptic will want to reject.