Tuesday, January 11, 2011

Seeking the nonexistent

Yesterday I discussed an apparent problem for the Brentano thesis (that every categorical sentence of the form ‘some A is a B’ is convertible with an existential sentence of the form 'an A-B exists'). The problem is sentences like

(1) Gerald is looking for a gold mine in Surrey

which can be true even though gold mines in Surrey don’t exist.

Such sentences are admittedly a problem, but they are not a problem for the Brentano thesis as such. For (1) above is equally consistent with the following sentence

(2) No gold mine is in Surrey

which is not existential, but categorical. Indeed, Brentano equivalence clearly holds for the conversion of ‘No gold mine is in Surrey’ and ‘no gold mine in Surrey exists’ or ‘a Surrey gold mine does not exist’. The problem is not for Brentano at all, but rather for Aristotle, and the principle of conversion of the particular proposition. According to Aristotle (and according to modern logic, as it happens) ‘Some A is B’ is convertible with ‘Some B is A’. But if ‘Gerald is looking for a gold mine in Surrey’ is true, then by conversion of the particular, the following sentence:

(3) some gold mine in Surrey, is looked for by Gerald,

ought to be true. But surely it isn’t, since it implies that some gold mine (namely the one sought by Gerald) is in Surrey, and we agreed that no gold mine is in Surrey. Is the principle of particular conversion invalid? Or is there something else going on? To me, this is the strongest evidence that there is a deeper logical structure to (1) than the surface grammar suggests. Consider:

(4) Some gold mine, thought by Gerald to be in Surrey, is looked for by him.

which I think is true. And that is roughly equivalent to

(5) Gerald thinks there is some gold mine in Surrey, and he is looking for it.


(6) Gerald is looking for a gold mine which he thinks is in Surrey

Thus the quantifier noun phrase ‘some gold mine’ has to be qualified by ‘is thought by’ or some other intentional construction, before the conversion is valid, and thus it is not an ordinary conversion. None of this (pace Vallicella and Lupu) has to do with metaphysics or weird objects or ‘the nonexistent’, except figuratively, but rather it has to do with a more complex logic that underlies our ordinary discourse, and which we need to make visible, if we can.

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