The Real Logic of Individuals

Hartley Slater (the University of Western Australia)

Timothy Williamson has recently been concerned with an argument that seemingly proves that he exists.  It goes as follows (see Williamson 2002): (1) Necessarily, if I do not exist then the proposition that I do not exist is true.
 (2) Necessarily, if the proposition that I do not exist is true then the proposition that I do
not exist exists.
 (3) Necessarily, if the proposition that I do not exist exists then I exist.
 (4) Necessarily, if I do not exist then I exist. So (5) I necessarily exist.  Williamson is unconvinced by this argument, saying, amongst other things, that parallel arguments would have to be equally sound, such as those that replace ‘necessarily’ with ‘at all times’, and ‘I’ with ‘this body’.  But the further conclusions then obtained, namely that he exists at all times, and that his body necessarily exists, he finds totally implausible.  He has gone on to write a book Modal Logic as Metaphysics, which debates in great detail whether the existence of individuals is necessary or contingent.  I show in this paper that the conclusion of Williamson’s argument is true, and in a way that shows the further conclusions that might be drawn in parallel arguments are also true.  I will not debate, like Williamson, the individual worth of his premises, but arrive at his conclusion(s) another way.  The central distinction that needs to be made is between logical existence and other forms of ‘existence’, such as ‘being alive’, ‘being present’, and ‘being actual’. But the required distinction is not readily made using just the Predicate Calculus, as Williamson does for his non-modal base. Instead what is wanted is its conservative extension, Hilbert’s Epsilon Calculus.  The matter has further consequences concerning the notion of Truth.