The Logical form of Existence-Assertions

Abstract

The enigma of singular existence-denials does not even begin to bother us until we treat assertions of existence as simple subject—predicate statements. (See claim 2 of my initial layout of the puzzle in the Introduction). The most popular way of dissolving the problem, therefore, is to appeal to the worn-out slogan: “Existence is not a predicate.” In this chapter I shall try to expose several ambiguities in this slogan, and then rebut the standard arguments given for the underlying view that “... exists” is not a first-level predicate of objects. It is becoming increasingly clear to logicians these days that there are no insuperable logical obstacles to treating ... exists“ as a first-level predicate.² How its attachment to a singular term results in a well-formed sentence encoding information that could possibly turn out to be false is, of course, a deep mystery which I shall try to unravel briefly at the end of this chapter and then gradually in greater detail through the rest of the book.

Question: Does the proposition “Man Exists” have a predicate or not?

Answer: This is a problem on which both the ancients and the moderns disagree: some say that this sentence has no predicate, and some say that it has a predicate. To my mind, both these judgements are in a way correct, each in its own way.

al-Fāazābī (c. 873–950 A.D.)¹