How finely are propositions individuated? This talk explores this question using a formal language with propositional quantifiers and plural propositional quantifiers. In such a setting, one can show along the lines of an argument by Russell and Myhill that propositions are not structured, by noting that a plural version of Cantor's theorem shows that there cannot be a distinct proposition for every plural parameter. The main alternative view on the individuation of propositions is Intensionalism, the view that necessarily equivalent propositions are identical. But what motivates this particular view, apart from familiarity? Here, it will be argued that Intensionalism is uniquely distinguished in terms of the theoretical virtues of simplicity and strength.
See the seminar webpage http://users.ox.ac.uk/~philmath/pomseminar.html for titles and abstracts of other speakers as available.
Philosophy of Mathematics Seminar Convenors: Daniel Isaacson and Volker Halbach