Theory of Automorphisms

Abstract

We shall introduce two new elements into our model: the ‘existence’-function I which assigns to every world w in W the set of all individuals that exist in w, and the set A of automorphisms. We shall write ‘Iw’ sinstead of ‘I(w)’ and we shall often use the symbol ‘I’ in order to refer to the set of all individuals which exist in one world or another. Thus, ‘I’ shall frequently represent the union of all values of the existence-function. If a is an individual, then by Wa we shall understand the set of all worlds in which a exists, i.e., {w∈W: a∈I_w}. Letters a, b, c, d,… shall stand for individuals (=members of I), and we shall refer to the members of A as p, p', p",….

Below, we shall mark with an asterisk all important principles and definitions which we have appropriated from Fine’s paper (cf. footnote 1 above).