Holy Cyclops

I was reading Alvin Plantinga’s The Nature of Necessity yesterday, and he quoted and analyzed, in great detail, a couple of passages, one from William Kneale and one from W.V.O. Quine, whose quotation and analysis reminded me once again that professional philosophers sometimes make silly mistakes.

The discussion was about essential and accidental (necessary and contingent) properties.  Kneale’s anti-essentialist argument was, in my reconstruction from memory, that one couldn’t say that the number twelve was essentially composite, because surely it is only a contingent fact that the number of apostles was twelve, so the number of apostles couldn’t be essentially composite; but since the number of apostles and the number twelve are the same number, twelve can’t be essentially composite.

I’ve rendered it in more detail than he did in the quoted passage.  But one can easily see the mistake:  An equivocation on the meaning of “The number of apostles.”  Does “the number of apostles” mean “the actual number of apostles (i.e., twelve),” or does “the number of apostles” mean “the possible number of apostles (i.e., twelve or eleven or thirteen or…)”?  “The number of apostles” and “twelve” denote the same number only if “the number of apostles” is intended as “the actual number of apostles (i.e., twelve)”; if one intends “the number of apostles” as “the possible number of apostles (i.e., twelve or eleven or thirteen or…),” then one can no longer equate twelve with the number of apostles.  One may either say

1. Twelve is a composite number.
2. The (actual) number of apostles is twelve.
3. Therefore, the (actual) number of apostles is composite.

or

1. Twelve is a composite number.
2. The (possible) number of apostles might be twelve but might be some other number, like eleven or thirteen.
3. Therefore, the (possible) number of apostles might be composite but might not be.

In the first case, “the (actual) number of apostles” is a Kripkean “rigid designator,” if I’m remembering his terminology correctly, always equalling twelve and therefore always composite, just like twelve—rendering the argument against essentialism toothless.  In the second case, “the (possible) number of apostles” is a non-rigid designator, not always composite but also not always equalling twelve—again rendering the argument against essentialism toothless.  Only if one could argue that the number twelve had the kind of fluidity of designation that “the (possible) number of apostles” has could one go on to argue that twelve is not necessarily composite—but, of course, that can’t be done.

Quine’s argument, again in my reconstruction of it, was that whether or not a property is thought to be necessary depends on how we describe the property-bearer—that properties of objects are not essentially necessary or non-necessary but are, rather, only necessary or non-necessary relative to our descriptions of those objects.  His example is as follows:  We might normally say that, in some sense, mathematicians are necessarily rational but are not necessarily bipedal, and that cyclists are not necessarily rational but are necessarily bipedal.  (Let’s set aside any question about either the rationality of all mathematicians or the bipedality of all cyclists.)  But suppose a mathematician is also a cyclist.  Then are we to say that he is both necessarily rational and not necessarily bipedal and also not necessarily rational but necessarily bipedal—a contradiction (a pair of them, really)?  Our assessment changes with our change in description:  We say that the mathematician-cyclist is both necessarily rational and necessarily bipedal.

I’m sure I’m not rendering his argument as persuasively as he did, but its main point is the contradiction given.  Two points can be made about this:  First, it may be that saying that mathematicians are not necessarily bipedal, and that cyclists are not necessarily rational, is saying something too strong.  We do not know of all mathematicians that they are not necessarily bipedal; perhaps some of them (like the mathematician-cyclist) are necessarily bipedal, while others aren’t.  (Similarly for cyclists and the non-necessity of their being rational.)  What we can justifiably say is that mathematicians are necessarily rational and possibly bipedal (and similarly that cyclists are possibly rational and necessarily bipedal).  But then the contradiction vanishes:  The mathematician-cyclist is necessarily rational and possibly bipedal, and he is possibly rational and necessarily bipedal, and that doesn’t contradict his being necessarily rational and necessarily bipedal.  Second—and, in my view, the more important point, and the one that qualifies Quine’s argument for inclusion in a post entitled “Silly Philosophical Mistakes”—is that while it is true that we make our descriptions on the basis of what we know, or on the basis of our present interests or purposes, rather than on the basis of what is true, and that for that reason our ascriptions of modal status with respect to different properties will seem to vary according to our present interests and purposes—in contradiction to the essentialist view that necessary properties, at least, are essential to entities—it is nevertheless also true, in opposition to Quine, that while what we know of an object may change (so that we realize, when we learn that a mathematician is a cyclist, that he is not only necessarily rational, as we had thought, but that he is also necessarily bipedal), and that while our choice of description may vary according to our interests or purposes (so that we may know very well that a mathematician is also a cyclist but may or may not choose to ignore it for the moment, resulting in our sometimes describing the mathematician-cyclist as necessarily rational and possibly bipedal and in our sometimes describing the mathematician-cyclist as both necessarily rational and necessarily bipedal), neither our knowledge change nor our choice of description implies that what is true of the object changes or is somehow malleable.  At best, Quine’s is an argument for description-relativism; it isn’t, as he appears to want it to be, an argument for fact-relativism (or for relativism of modal facts to description).  (Even if Quine thinks that we know the facts about objects, that simply means that a description of the object that expresses those facts must be complete in order to capture all of those facts—an incomplete description, chosen for our own reasons, might fail to capture all of those facts.)   

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