MIPC as the Formalisation of an Intuitionist Concept of Modality

1. In the course of a recent paper on modal' extensions of the intuitionist propositional calculus, [1], I made some suggestions as to the relationships between the system MIPC, the intuitionist predicate calculus, and the question of producing a genuine intuitionist concept of modality.1 This paper may be regarded as a clarification of those rather inaccurate ideas in the light of Kripke's outstanding analysis of the intuitionist predicate calculus, [2]. (I use Kripke's notation and terminology here without explanation this work is intended to be read in conjunction with [2].) In particular, I shall adapt his interpretation of his modelling to give an account of MIPC in terms of differing mathematical intuitions. MIPC is the extension of the intuitionist propositional calculus with the rules: