“Essentialism and the Mathematical Cyclist” is the fourth section of Chapter II, “Modality De Re: Objections”, in Plantinga’s well-known The Nature of Necessity (Oxford University Press, 1974). I have picked it out for the particular light and clarity it throws on a popular criticism of essentialism given by W.V.O. Quine. So, the essay’s at least entertaining for the reason that it is basically Quine vs. Plantinga, with particular focus on Plantinga’s rebuttal. Who wins between the two? Prima facie, I’d like to say Quine, because I think he is the more able of the two philosophers—though, in this particular case, Plantinga appears to have the stronger argument (viz. appeal to the de re/de dicto distinction).
Famous Works Quoted/Cited/Mentioned/etc.: Word and Object, W.V.O. Quine; Ways of Paradox, W.V.O. Quine; From a Logical Point of View, W.V.O. Quine.

Allen, J.T. Copyright 2007

Essentialism and the Mathematical Cyclist

BY Alvin Plantinga

Let us therefore turn to a different but related complaint. Quine argues that talk of a difference between necessary and contingent attributes of an object is baffling:

            “Perhaps I can evoke the appropriate sense of bewilderment as follows. Mathematicians may conceivably be said to be necessarily rational and not necessarily two-legged; and cyclists necessarily two-legged and not necessarily rational. But what of an individual who counts among his eccentricities both mathematics and cycling? Is this concrete individual necessarily rational and contingently two-legged or vice versa? Just insofar as we are talking referentially of the object, with no special bias towards a background grouping of mathematicians as against cyclists or vice versa, there is no semblance of sense in rating some of his attributes as necessary and others as contingent. Some of his attributes count as important and others as unimportant, yes, some as enduring and others as fleeting; but none as necessary or contingent.”[1]

            Noting the existence of a philosophical tradition in which this distinction is made, Quine adds that one attributes it to Aristotle “subject to contradiction by scholars, such being the penalty for attributions to Aristotle”. None the less, he says, the distinction is “surely indefensible”.

            Now this passage reveals that Quine has little enthusiasm for the distinction between essential and accidental attributes; but how exactly are we to understand him? Perhaps as follows. The essentialist, Quine thinks, will presumably accept

            (25) Mathematicians are necessarily rational but not necessarily bipedal

and

            (26) Cyclists are necessarily bipedal but not necessarily rational.

But now suppose that

            (27) Paul K. Zwier is both a cyclist and a mathematician.

From these we may infer both

            (28) Zwier is necessarily rational but not necessarily bipedal

and

            (29) Zwier is necessarily bipedal but not necessarily rational

which appear to contradict each other twice over: (28) credits Zwier with the property of being necessarily rational while (29) denies him of that property; (29) alleges that he has the property of being essentially bipedal, an allegation disputed by (28).

            This argument is unsuccessful as a refutation of the essentialist, whatever its merits as an evocation of a sense of bewildernment. For consider the inference of (29) from (26) and (27). And presumably its first conjunct

            (30) Zwier is necessarily bipedal

is supposed to follow from the first conjuncts of (26) and (27), viz.

            (31) Cyclists are necessarily bipedal

and

            (32) Zwier is a cyclist.

But sensitive, as by now we are, to de re/de dicto ambiguity, we see that (31) can be read de dicto as

            (31a) Necessarily, all cyclists are bipedal

or de re as

            (31b) Every cyclist has the property of being necessarily bipedal.

And if (30) is to follow from (32) and (31), the latter must be seen as predicating of every cyclist the property (30) ascribes to Zwier; (31), that is, must be read as (31b). So taken, there is less than a ghost of a chance the essentialist will accept it. No doubt he will concede the necessary truth of

            (33) All (well-formed) cyclists are bipedal

and thus the truth of (31a); he will accept no obligation to infer that such well-formed cyclists as Zwier are essentially bipedal. And the same comments apply, mutatis mutandis, to the inference of the second conjunct of (29) from those of (26) and (27). Accordingly, (26) is true but of no use to the argument if we read it de dicto; read de re it will be repudiated by the essentialist.

            Taken as a refutation of the essentialist, therefore, this passage misses the mark; but perhaps we should emphasize its second half and take it instead as an expression of a sense of bewildered puzzlement as to what de re modality might conceivably be. Similar protestations may be found elsewhere in Quine’s works:

            “An object, of itself and by whatever name or none, must be seen as having some of its traits necessarily and others contingently, despite the fact that the latter traits follow just as analytically from some ways of specifying the object as the former do from other ways of specifying it.”

And

            “This means adapting an invidious attitude towards certain ways of specifying x… and favouring other ways… as somehow better revealing the ‘essense’ of the object.”

But “such a philosophy”, he says, “is an unreasonable by my lights as it is by Carnap’s or Lewis’s”.[2]

            Here Quine’s central complaint is this: a given object, according to the essentialist, has some of its properties essentially and others accidentally, despite the fact that the latter follow from certain ways of specifying the object just as the former do from others. So far, fair enough. Snubnosedness (we may suppose) is not one of Socrates’ essential attributes; none the less it follows (is the sense in question) from the description ‘the snubnosed teacher of Plato’. As we construe him, furthermore, the essentialist holds that among the essential attributes of an object are certain non-truistic properties—properties which, unlike the property of being red or not red, do not follow from every description; so it will indeed be true, as Quine suggests, that ways of uniquely specifying an object are not all on the same footing. Those from which each of its essential properties follows must be awarded the accolade as best revealing the essence of the object.

            But what, exactly, is “unreasonable” about this? And how, precisely, is it baffling? The real depth of Quine’s objection, as I understand it, is this: he holds that ‘A’s are necessarily B’s’ must, if it means anything at all, mean something like ‘necessarily, A’s are B’s’; for “necessity resides in the way we talk about things, not in the things we talk about” (Ways of Paradox, p. 174). And hence the bafflement in asking, of some specific individual who is both cyclist and mathematician, whether he is essentially rational and contingently 2-legged or vice versa. Perhaps the claim is, finally, that while we can make a certain rough sense of modality de dicto, we can understand modality de re only if we can explain it in terms of the former. I turn to such explanation in Chapter III [“Modality De Re: Explanation” pp. 27-43].

Notes:

[1] Word and Object (M.I.T. Press, 1960), p. 199.

[2] From a Logical Point of View (New York: Harper & Row, 1961), pp. 155-6.