Chappell on the A Priori

The a priori seems to be on the rise of late, especially with defenders like Richard Chappell championing the cause. According to Chappell an ideallly rational being would have access to all the metaphysical possibilites. Given that we can ideally (or coherently)  conceive something we can infer that the thing in question is metaphysically possible. This is, of course, the basis for the zombie argument against materialism. Since we can coherently concieve of a zombie world (a world where there are beings like us in every physical way except that they lack conscious experience) that shows that consciousness cannot be a physical property.

The standard (Kripkean) objection to this line of argument is to try to distinguish between metaphysical and epistemic possibility. Some things that are epistemically possible (i.e. seem coherently conceivable) turn out to be impossible (a classic example is to point out that before you learn that the square root of 1,987,690.000 is 1409.855 (rounded up to the nearest thousandth) it is concievable that it be other than 1409.855 but once we find out what it is it is impossible for it to be otherwise. According to the materialist one of these things is the zombie world. While it seems that we can coherently concieve of such a world, we are actually missing some contradiction, or physical difference between our world and the zombie world and so it is not actually (ideally/coherently) concievable. 

Chappell objects to this line of argument for (at least) two reasons. The first has to do with the theoretical extravagance of the materialist’s claim that the identity between (say) H2O and water is necessary. It posits an unexplained strong necessity, wheras the modal rationalist (the one who thinks that it is a metaphysical possibility that water could be other than H2O, not just an epistemic possibility) doesn’t have to posit something like this. All that she needs to posit is a single uniform space of possibilities that we describe in various ways. The materialist has to posit a space of epistemically possible worlds and a seperate space of metaphysically possible worlds. Parsimony and simplicity seem to favore that modal rationalist here.

The second is an attack on the claim that calling something a rigid designator settles the dispute. As Chappell says,

Perhaps our term ‘consciousness’ is, like ‘water’, a rigid designator. But who cares about the words? Twin Earth still contains watery stuff, even if we refuse to call it ‘water’, and the Zombie World still lacks phenomenal stuff (qualia), even if we stipulate that our term ‘consciousness’ refers to some neurophysical property (and so is guaranteed to exist in this physically identical world).

Yes it will, IF we have settled the issue in favor of Chapell’s view and we then think that we are genuinely concieving of a real metaphysical possibility. If there is a question as to whether these kinds of possibility are distinct then Chapell has done nothing more than beg the question.

This is evidenced when he says,

Kripke himself noticed something along these lines. While we can imagine a world where watery stuff isn’t truly water, it’s incoherent to imagine a world where “painy” stuff isn’t truly pain. To feel painful is to be painful.

Pointing out that Kripke begs the same queston as you are beging is not a way to absolve yourself of beging the question. There is a legitimate case to made that being in pain and feeling pain are in fact two seperate things. The evidence for this comes, not from a priori reflection on the nature of pain, but from evidence from cognitive science.

 But suppose that you are not moved by this evidence and you still maintain that a priori analysis reveals that the zombie world is metaphysically (not just epistemically) possible. Is this a coherent position? One objection that immediately pops up is that on this view it seems that we can concieve of various possible worlds that result in contradiction. So, I seem to be able to concieve that God necessarily exists and that God necessarily doesn’t exist (or that numbers do and don’t necessarily exist). Since the claim that conceiveability entails possibility entails that God (or numbers) both necessarily exists and doesn’t exist only one of those possibilities can be a real metaphysical possibility; the other must be an epistemic possibility.

Chappell is of course aware of this objection and tries to deal with it in the post linked to above. Here is what he says,

I agree with Chalmers that the most attractive response for the modal rationalist here is to hold on to their strong position, and instead deny the… conceivability intuitions found, for example,…above. It isn’t at all clear that a necessary being, or a shrunken modal space, is coherently conceivable in the appropriate sense. The modal rationalist will want to hold that their position is not just true, but a priori. They would then expect opposing views to be refutable a priori, and hence not feature in any a priori coherent scenario. Of course, it would beg the question to merely assert: “the thesis is true and hence has no successful counterexamples”. But that is not what’s going on here. Rather, I hope to show that the modal rationalist can explicate their commitments in a way which makes clear exactly why, on their view, the meta-modal cases in question are not taken to be genuinely conceivable. If successful, this should suffice to undermine the charge of internal inconsistency or self-refutation.

The problem with this line of argument is that it commits the very ‘fallacy’ that Chappell accuses the Kripkeans of making. The strategy that he is here proposing is that of trying to show that there is some possible state of affairs that seems conceivable but which, on reflection, is not in fact metaphysically possible (i.e. that there are possibilities that (seem)concievable but are not metaphysically possible). But if there are possibilities that (seem) concievable but not metaphysically possible then we need an independent argument that the zombie world is not one of these worlds. No such argument has been given. Rather what Chappell does is to assume that it is in fact coherently concievable; but this cannot be assumed if there are any possibilities which (seem) concievable and are not metaphysically possible. Chappell’s own view commits him to there being such possibilites, so by his own view the modal argument against materialism is suspect.

There Might Not Be Any Numbers

I was re-reading an old post where I expressed doubt that there are any necessary existents at all, not even numbers, and I saw Richard Chapell’s comment,

I’d expect the ontological status of numbers to be non-contingent — after all, what in the world could they be contingent on? Abstract objects seem to be the kind of things that exist necessarily, if they exist at all.

I guess I was being dense that month 🙂 because I didn’t see what the objection was supposed to be. But now I do. If numbers are the kinds of things that are not necessary then they must depend on something to exist. But what could numbers depend on? Since there is no plausable candidate we should conclude that if numbers exist they would do so necessarily. Here is what I should have said.

Whether a given possible world has non-physical elements is surely a contingent fact about that possible world. The worlds which do have non-physical elements will most likely have numbers and those that don’t won’t. If this were the case then the existence of numbers is contingent on which possible world best describes the actual world (or if one doesn’t like this way of characterizing the actual world as a possible world we can say it depends on what is actually the case). In some worlds, the existence of numbers may be contingent on whether they were created by some non-physical being. In short there are a couple of different ways in which the existence of numbers could turn out to be contingent.  

Why does 1+1=2?

If someone demanded proof that 1+1=2 is true what would you do? Would you get an object and place it next to another object and then count them? One might argue that that doesn’t prove that 1+1=2 because 1+1=2 is a necessary truth and you cannot get necessity from experience (as per the history of philosophy). If one thought that all knowledge comes from experience one might then, like Quine, think that it is possible that we could have experience that dis-confirmed mathematics. For instance David Rosenthal has argued that if we ever had irrefutable counting evidence (i.e. widespread, re-created and independently confirmed) that 1+1=2 were false then we would have to admit that it was false and so mathematic is contingent on experience. Yikes!

Or would you appeal to the Peano axioms, which include the claim that 0 is a number and that it has a successor denoted by S(0) and then define addition as

(for all a) a+0=a

(for all a and b) a+S(b)=S(a+b)

So then it is easy to show that 1+1=2 as follows

1+1=a+S(0)=S(0+1)=S(1)=2

But then one might worry about the successor relation. It might seem as though we have simply assumed addition in the definition of the successor relation (i.e. it tacitly assumes that S(a)=(a+1)).

Of course we can show that S(a)=(a+1) by the definition of addition above. So, let S(0)=1 then a+1=a+S(0) by the definition of addition we get a+S(0)=S(a+0) and since a+0=a we get S(a) so (a+1)=S(a). But then we seem to have assumed addition by stipulating that S(0)=1 (as we actually did in the initial proof of 1+1=2…worse and worse!)

Is the claim that when you have nothing and add a thing you then get only the one thing (i.e. S(0)=1) supposed to be a truth that we just apprehend with pure reason? A self-evident truth that is ‘clear and distinct’? Or something that experience has trained us to believe? Is there any non-question begging reason to prefer either of these?

Truth and Necessity

I have been reading Jason Stanely’s paper on names and rigid designation from the Oxford Companion to the Philosophy of Language in the course of doing some research for my frigidity v. rigidity axe-grinding. It is an interesting and informative, though technical, introduction to issues about rigidity and I will come back to its relation to frigidity in a later post… but one thing caught my attention early on. He says, 

consider Kripke’s class of strongly rigid designators (Kripke, 1980, p. 48). This class contains the rigid designators of necessary existents. That is, this class contains all and only those designators d of an object x which exists in all possible worlds, which designate the same thing in all possible worlds (viz. x). For example, the descriptive phrase “the result of adding two and three” is a strongly rigid designator, since its actual denotation, namely the number five, exists in all possible worlds, and the phrase denotes that number with respect to all possible worlds.

Is it really the case that ‘the number five exists in all possible worlds’? Isn’t there a possible world where fictionalism about math is true? In that world 2+2=4 is not true because ‘2’ stands for an existing object, viz. The Number Two, it is true because ‘in the story we tell about mathematics’ ‘2’ stands for The Number Two in just the same way that ‘Santa wears a red suit’ is true, not because ‘Santa’ picks out some guy who wears a red suit but because ‘in the story about Santa’ ‘Santa’ picks out a guywho wears a red suit. Maybe fictionalism about math isn’t actual, but surely it’s possible, isn’t it? 

We can give the same kind of argument for any proposed ‘strongly rigid’ designator. Take God for instance. It take it that Atheism is a legitimate possibility for the actual world. That is, it migt actually turn out to be the case that there is no God. Of course it might also turn out to be the case that there isn’t one. Each of these seems to me to be a metaphysical possibility, not merely an epistemic possibility. If so then there is a possible world where God does not exist (it may or may not be the actual world). Isn’t this some reason to prefer, when faced with the possiblility of a proof of necessary existence, to take my view (fix it) rather than Williamson’s (accept it)? That is, isn’t there an issue here about whether there are any ‘strongly rigid’ designators?