Quine writes:

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? (Plantinga, Nature of Necessity, Ch. 1, 2)

This is a case of confusion of necessity of the consequent with necessity of the consequence. In order to conclude that

(30) Zwier is necessarily bipedal,

we need

(31) Cyclists are necessarily bipedal

and

(32) Zwier is a cyclist.

But (31) can be read de dicto as □(x is a cyclist → x is bipedal), in which case it’s true, yet (30) does not follow;

or de re as (x is a cyclist → □(x is bipedal)), from which (30) would follow but which is unfortunately false.

In other words, we have the following 4 true statements:

(1) □(x is a mathematician → x is rational)
(2) ~□(x is a mathematician → x is bipedal)
(3) □(x is a cyclist → x is bipedal)
(4) ~□(x is a cyclist → x is rational).

Suppose in the actual world x is both a mathematician and a cyclist. Then he is both rational and bipedial. Suppose in some world W our x is a cyclist and is irrational. Then in that world he is not a mathematician. And so on. Whence the bewilderment?


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