III—The Logical Status of ‘Exists’

Abstract

M [ any philosophers have denied that 'exists' is, in Frege's sense, a first-order predicate. What a first-order predicate is is defined in terms of sentences and singular terms (which are also called in Fregean parlance 'proper names'), as follows: a first-order predicate (Frege 1893, p.43) is what you are left with if you remove from a sentence one or more occurrences of a proper name.1 Thus to deny that the grammatical subject of an existential statement can be a proper name, as Russell (Whitehead and Russell 1962, p.66) and Strawson (1959, p.227) have done, is equivalent to denying that 'exists' is a first-level predicate. In recent decades the idea that 'exists' is a first-order predicate after all has been returning to respectability, but I would guess that many people still cling to the Fregean view. So when I say that the purpose of this article is to demonstrate the incoherence of regarding 'exists' as anything other than first-order, I hope that this thesis will not be dismissed as trite. It is not exactly painless either: I will argue that acceptance of the first-order status of 'exists' requires giving up either one or the other of two well-established philosophical tenets. To make it clearer what position I am attacking, I would like to point out that I do not consider that denying that 'exists' is a firstlevel predicate commits you to the view that it is second-level (though that view may have had its representatives) or that it fits into