The Laws of Logic: Contingent or Necessary?

One of the debates in philosophical logic is whether the laws of logic hold contingently or necessarily. One of the possible motivations for thinking that they hold contingently is that they bear some sort of analogue to physical laws. Whereas physical laws express regularities in nature, logical laws might express regularities in human language, or our cognitive structure. So, just as the regularities we see in nature are generalized into universal laws by induction, so regularities in human reasoning are generalized into universal laws.

To me, though, this is a false picture. There are several irremediable issues, as I see it, with the contingent view of logical laws. I think that the necessity view of logical laws, properly expressed, more fully captures their nature. But, before addressing what my own view is, I want to take a look at what the specific issues are in regard to the contingent view (hereafter simply CV).

The first issue is that CV seems to be self-refuting in a way. The reason is that, whenever you try to establish a proposition, you assume that various logical laws hold necessarily. Consider the following argument:

(1) If Reason X, then CV.
(2) Reason X.
(3) Therefore, CV.

Most arguments seeking to establish the truth of CV would take that form or something like it (where "Reason X" might be the contingency of our conceptual scheme, quantum weirdness, or whatever). But, if CV is true, then any such argument (which will assume such laws as implication, non-contradiction, transitivity, and the like) will hold contingently. That is, it will be a contingent truth that the laws of logic hold contingently, which seems counter-intuitive if not outright self-refuting. Further, if the laws of logic are contingent contingently, then they could have been necessary de dicto, but aren't. Which leads to the further, extremely counter-intuitive conclusion that the S5 axiom of modal logic is false (that is, If possibly necessarily P, then necessarily P). So we're already in a muck of circularity, contradiction, and outright confusion.

The next issue with CV is with the inability to concieve of, or describe, a world in which our logical laws did not hold. Try and concieve of a world in which something both can be an A, and not an A, in the same way at the same time. It seems literally impossible. But I don't think the impossibility arises from our lack of ability to picture it (due to our limited experience or whatever), but it rather arises from the fact that such a statement is literally meaningless. The statement "Something is both an A and not an A" doesn't describe any state of affairs, and thus is about nothing. But if we can't even speak meaningfully about such a possible world, why should we take the thesis of CV seriously?

This leads us to my view. I think the correct view of the laws of logic is that (a) they are necessary, and (b) analytically necessary. What exactly I mean by analytically necessary I'll address in a moment, but I first want to look at the aforementioned apparent analogue between physical and logical laws.

I think the analogue is false for the following reason: When we observe regularities in nature, and proceed to generalize them into laws, we do so because of inductive evidence along with the assumption of the uniformity of nature. But, there's nothing inherent in the evidence itself that suggests the regularity just is or implies the physical law (as Hume pointed out, correctly, in his discussion of constant conjunction). This differs from logical laws in that it doesn't seem they are generalizations of observation, but rather generalizations of meaning. To see this, consider the following comparison between the law of gravity and the law of transitivity:

When we continually observe that things fall, objects are attracted to eachother, and the like, we take the inductive leap and say "This is a physical law, the law of gravity". But (again, as Hume pointed out) there's nothing inherent in the meaning of X number of objects falling and/or being attracted to one another that necessarily implies such a law. The law is just a deductively unwarranted assumption, which functions more pragmatically than evidentially. So, again, there's nothing inherent in the meaning of our observations that just means "the law of gravitation".

But what about in the case of a logical law like that of transitivity (A->B, B->C, :. A->C)? In this case, it can be seen that part of what we mean by the conjunction of "A->B" and "B->C" just is "A->C". And this is what I meant by all logical laws being analytically true. For any given logical law, upon reflection we can see that it holds in virtue of its meaning, not in virtue of its use or anything else. Another way to put this would be to say that all logical laws are merely tautologies. To take another example, consider the law of non-contradiction. When we assert "A", part of what we mean by "A" is just "~~A". And thus we express such a tautology as the "law" "A cannot be both A and not A".

It can be seen that my view differs from a more Platonic view where the laws of logic are necessary de re (in virtue of abstractly existing objects and the relations they bear to one another). But rather, all logical laws are true de dicto. And hence, if my view is true, there are no possible worlds in which, say, modus ponens could be invalid without the meaning of modus ponens also changing. Suffice it to say, the contingent view is false, and the necessity view far more plausible.