Abstract

FUNCTIONS, EXISTENCE AND RELATIONS IN THE RUSSELL-MEINONG DISPUTE, THE BRADLEY PARADOX AND THE REALISM-NOMINALISM CONTROVERSY Herbert HOCHBERG The University of Texas, Austin 1. Negation, Existence and RusseLL's Point Let us take Russell's contradiction to be the two-fold claim that if it is true that the round square is both round and square then it is true, first, that the round, non-round square is both round and not round, and, second, that the existent golden mountain both exists and does not exist. Both cases appear contradictory. The first argument is countered by distinguishing between not being <pe -,<px) and being non-<p (non-<px) and holding that while '-,<px iffnon-<px' may hold for all existents, it does not hold for non-existents or "incomplete" objects. Thus, since (1X)( <px & non-<px) does not exist, it can be both <p and non-<p without acknowledging the contradiction that it both is and is not the case that it is <po This can be taken to accept: (<p )(x)(x exists iff (-,<px iff non-<px)), where 'x' ranges over existents and non-existents. This blocks the first but not the second case, since by the Meinongian Sosein Principle (MSP), that for any <p, (1X)(<pX & ... )