Sunday, September 05, 2004

More Modality

I'm enjoying this little to-and-fro with Bill Vallicella, the Maverick Philosopher. His responses force me to clarify and explain ideas that I might otherwise have taken for granted. I had hoped that my previous post on Logic & Possibility had clarified matters, but the misunderstandings in Bill's latest response demonstrate that I still have not explained myself clearly enough. So let me try to remedy that with this post.

Overview:
Bill argues that the laws of logic cannot be mere empirical generalisations, because if they were, then they would be logically contingent. But in fact they are logically necessary (by definition, there is no logically possible world containing a true contradiction). Hence, he concludes, the laws of logic are not empirical generalisations.

In response, I suggested that by defining empirical generalisations as logically contingent, BV was begging the question. Instead, I argue, we should say that empirical generalisations are metaphysically contingent - that is, contingent in the broadest sense - contingent, 'period'.

Some Corrections:
I am afraid that RC is not engaging the precise question that I raised in my original post, namely, could LNC be an empirical generalization, as John Stuart Mill thought? [...] Mill questions the necessity of logical laws, period, not their metaphysical necessity as opposed to some other sort of necessity.

It should be clear from the above overview that I am indeed engaging his precise question. As Bill says, the empiricist "questions the necessity of logical laws, period". Bill has assumed that plain necessity ("period") means logical necessity. This is the crux of our disagreement - this is where I see him as begging the question. I say that "necessity, period" means metaphysical necessity.

Part of the problem here is that RC does not tell us exactly what he means by 'metaphysical necessity.' This is not a term I used in my original post; yet he brings it in to criticize my post.

As previously mentioned, I use 'metaphysical necessity' to mean "necessity in the broadest sense", i.e. "necessity, period". To say something is metaphysically possible is to say reality could have been like that. I think this is fairly standard usage, but do correct me if I'm wrong. Now, Bill may not have used the term in his original post, but I say he should have. Because as was noted above, an empirical generalisation is contingent (i.e. not necessary), period. And that means "not metaphysically necessary".

As I said before: "Logic, [the empiricist] suggests, is generalised from our experience of reality, but that reality could have been different, and so our logical systems could have been different". Each of the ways reality could be different, represents a different possibility ('period'). It may or may not be the case that being possible (period) implies being logically possible. That all depends on whether a true contradiction could exist - which is, I think, an open question. (See 'more detail' below.) [Update: I change my mind here.]

RC is saying that 'The laws of logic are logically necessary' is an "empty tautology." This is simply false. The refutation of psychologism cannot be this easy! A statement of the form Every F is a G cannot possibly be a tautology. The easiest way to see this is to consider the negation of 'Every law of logic is logically necessary,' namely, 'Some laws of logic are not logically necessary.' Is this latter statement a contradiction? No, since it is not contradictory in virtue of its logical form.

Perhaps I should have said 'analytic'. I mean that it is an empty truth in the same sense that "all bachelors are unmarried" is empty - it is true by definition; true in virtue of how we use the words, rather than in virtue of facts about the world; stipulatively true. I will say more on this below. Also let me repeat my point that the mere logical necessity of logical laws does not refute psychologism. What must be established is their necessity, period (i.e. metaphysical necessity).

RC also confuses logically true with stipulatively true. What we stipulate to be true cannot fail to be true for the simple reason that we so stipulate it. Thus I might stipulate that a fred is anything both fat and red.

Again, BV has missed my point. I am not saying that LNC is stipulatively true. Rather, I am saying the claim that "LNC is logically necessary" is stipulatively true. The necessity of LNC is stipulated. (It may not be actually true at all.) See my "more detail" section, below.

That's not the question I posed. RC is further confusing the issue by bringing in the question of alternative logics. I didn't mention that. My argument assumes classical logic, with its LNC, and then asks whether its laws could be laws of psychology as Mill and others have maintained.

Within paraconsistent logics, it is possible to violate LNC. That is, there are (according to such alternative logics) possible worlds where LNC is false - the laws of classical logic become merely contingent. It is no wonder BV didn't mention that, for it is devastating to his argument.

The basic problem with RC's attempted critique is that it foists upon my argument extraneous distinctions and questions.

On the contrary, I would submit that the distinctions I've raised are highly relevant ones, and their omission by BV was a serious oversight.

More Detail:
Since my previous posts have been so thoroughly misunderstood, I think I had better go back and clarify the general understanding of modality that I'm working with, as outlined in my original modality post. I don't think the following is crucial to my rebuttal of BV's "reductio" (all that that requires is the recognition that empirical generalisations are claims of metaphysical, rather than logical, contingency), but it may help in understanding where I'm coming from. Here was my conclusion:
Modal notions seem to arise from a certain sort of counter-factual thinking. We establish some particular limitations, and then we consider what states of affairs are allowed within our chosen framework. But divorced of any such framework, modal notions strike me as meaningless. If you take away the limitations, then we're stuck with the empty truism: "anything is possible".

According to my theory, there are an infinite number of (arbitrary) modal frameworks (or 'systems', I use the words interchangably). One way to understand them, is to say that you stipulate various limitations on what is 'allowed' within the system, and then consider all and only those 'worlds'* that comply with the limitations. The usual definitions of possibility and necessity then apply (e.g. X is F-possible if there exists some world within framework F where X is true.)

* = (I can't say "possible worlds" yet, because their possibility is determined by the chosen limitations. So take these base 'worlds' as a broader and more basic concept, that may include what are normally understood as "impossible worlds" also.)

Now, it should be clear that all the limitations of a framework are "necessary" when considered within that system (i.e. they are all F-necessary). They could not possibly be broken, for they define what is allowed within the system. (E.g. as Bill said, "LNC is the criterion of logical possibility".)

For example, consider the framework of "classical plogic", which is limited by the laws of classical logic, plus the "Law of Non-Flying" (LNF) which asserts that pigs don't fly. LNF is a necessary truth within this system. For any world where pigs do fly breaks the limitations, and so is excluded from consideration. LNF will hold in every possible world within the framework. So it is "plogically necessary". Of course, that doesn't tell us very much; it's a pretty empty sort of 'necessity'.

Classical logic is a similar system. In fact, it's exactly like classical plogic but without the silly pig law. Now, clearly all the logical laws, such as LNC, are going to be "logically necessary", in just the same way that LNF is "plogically necessary". Pretty empty stuff still, I say.

(Note that even false claims can be necessary within a system. Take a framework including the law that pigs DO fly. Of course this system excludes the actual world. But the law is still necessarily true within its own framework, for it is true of all the possible worlds that are included in the - somewhat limited - system.)

Now, let's suppose an empiricist comes along and makes the shocking claim that LNF is merely an empirical generalisation, rather than a necessary truth. Suppose I then respond by pointing out that there is no plogically possible world where pigs do fly, hence the law cannot be a mere generalisation!

That's clearly an inadequate response. After all, what if there are (metaphysically) possible worlds that are plogically impossible? This is a serious objection, and I cannot avoid it by complaining about "extraneous distinctions", or asserting that "my argument assumes classical plogic".

Anyway, enough with the analogy, I'm sure you get the idea now. What this argument all hinges on is the claim that there is no (metaphysically) possible world where LNC is broken. The empiricist says that for all we know there is such a possible world. The Maverick Philosopher simply assumes that there isn't, and from there constructs a reductio to "refute" the empiricist.

Now, I don't know whether the laws of classical logic are metaphysically necessary or not. Perhaps Bill is right that they are. But he can't just assume it, as he did in his reductio. There's reason for doubt (including some apparent cases of actual contradictions!), as I spent much of my original modality post arguing. Again, from our epistemic position, I'm not sure how we can rule out anything as impossible in the broadest sense.

I thank Bill for taking the time to discuss these issues with me, thereby forcing me to clarify my thoughts. I hope that I have explained my position more clearly this time around.

Post-script: Just a quick thought... does being an empirical generalisation actually entail anything about its modal status? Isn't the former just a matter of the idea's genesis? It seems that we could learn a necessary truth (though we would not know it was necessary) via the method of empirical generalisation - which suggests that they mustn't be mutually exclusive after all. But I will assume the empiricist's claim is stronger than that: let him say that the laws of logic are "merely" empirical generalisations (understood as implying the further claim that they are metaphysically contingent). Then my defence above becomes relevant.

P.P.S. I think it might be standard practice for philosophers to take logical impossibility as being genuinely (metaphysically) impossible. If the Maverick Philosopher is deeply embedded in that tradition then that might explain his difficulty in understanding my objection. Basically, I'm asking for a justification of this (perhaps common?) assumption. If there is one, then that's well and good, I would benefit greatly from learning it.

Given my theory of modality described above, 'metaphysical possibility' is difficult to pin down. (Well, I think it always is, but my theory highlights this fact!) If simply understood as possibility with no limitations, it would exclude nothing and thus be a pretty useless concept. (That was one of the major points of my first post on this topic.) I guess what we really want to do is limit it according to the ultimate metaphysical principles that govern reality. Whatever they are.

The difficulties there make me skeptical about whether modality actually corresponds to anything real - or at least whether we can know anything about this real modality. Instead, I suggest, it's a useful mode of counter-factual thinking that we can engage in. This justifies philosophers' preoccupation with logical possibility, since I would agree that, generally, classical logic is the most useful framework for philosophers to work within. There's nothing absolute about it though - for example, I imagine that what I call 'natural possibility' could be more useful for many scientific matters. Perhaps alternative logics might have their uses for philosophers and metaphysicians too?

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