On the density of truth in Dummett's logic
Zofia Kostrzycka, Marek Zaionc · Jagiellonian University Repository (Jagiellonian University) · 2003
For the given logical calculus we investigate the size of the fraction of true formulas of a certain length n against the number of all formulas of this length.We are especially interested in asymptotic behaviour of this fraction when n tends to infinity.If the limit of the fraction exists it represents a number which we call the density of truth for the investigated logic.In this paper we apply this approach to the Dummett intermediate linear logic (see [2]).This paper shows the exact density of this logic and demonstrates that it covers a substantial part of classical propositional calculus.In fact, despite strictly mathematical means used to solve all discussed problems, this paper may have a philosophical impact on understanding to what extent the phenomenon of truth is sporadic or frequent in random mathematics sentences.