The following argument is inspired by one that Rob Koons gives here:
- 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.
- Completely unexplained contingent states of affairs have no objective probability.
- 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.
- 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.
- I know I have two hands.
- So, the Principle of Sufficient Reason is true.
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”):
ReplyDelete1cp: 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).
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?
ReplyDeleteNicholas:
ReplyDeleteI 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.
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.
ReplyDeleteHow so? Remember that "not objectively likely" does not imply "unlikely".
ReplyDeleteI'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.
ReplyDeleteThrow 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.
ReplyDeleteI see, point taken.
ReplyDeleteI'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.
That's another problem for the PSR skeptic. However, we could at least give a range of probabilities in the sum case: [a,1], where a is the probability of it happening with an explanation.
DeletePerhaps P1 is false here, since one could grant a kalam principle, such that all things which begin to exist have a cause, and so, our sense data, beginning to exist, therefore has a cause?
ReplyDeleteOne could do that, but I don't think there is good reason to accept that all things which begin to exist have a cause that isn't also a good reason to accept a "bigger" PSR.
ReplyDeleteFurthermore, imagine a classical system consisting of a brain in a vat. Now extrapolate the system backwards for all time using classical physics. The result: a system that has existed for all time and results in a brain in a vat. Now we really do need the PSR to rule this out.
Well, perhaps some sort of ex nihilo nihil fit defense would work, and that seems to not motivate the PSR. Or maybe we take some sort of thomistic argument that all reductions from potency to act require an actualiser, which again seems defensible without committing yourself to the PSR.
DeleteAs for the classical system consisting of a brain in a vat, nonetheless, if the brain began, or its sensory data, it would have a cause. Although I suppose you would argue that the cause is not going to produce truth tracking sensory data, but how does the PSR rule that out?
Once you have the PSR, you have at least a chance that probabilities can be assigned. But if you don't have the PSR, you can't say that the probability of such a classical system is high or that it is low or anything else. As a result, you can no longer engage in Bayesian reasoning.
ReplyDeleteThat is a great argument, I liked it when you presented it in various papers, but, - and I might be missing the point of the argument, so forgive me, - might we not say that brute facts do have objective features about them that subjective probabilities can follow, for example maybe the fact they are not in our background information, or among other theoretical virtues? Furthermore, if one accepts intuition as an authority over our probabilities (at least a priori probabilities) could we not therefore assign comparative probabilities based on that? Lastly, if something within the vicinity of the principle of indifference is true, could we not assign a symmetrical probability (if we manage to specify the partition)?
DeleteNote: I don't think these objections are good such that they avoid the argumentative use of the PSR, for example the objection from theoretical virtues I presented would probably tilt our probabilities in favour of any particular thing or object of inquiry having an explanation, but they might challenge the conclusiveness or strength of this specific argument for the PSR