An Intuitionistic Examination of Read's Harmony Requirement

Abstract

Stephen Read has done significant work towards clarifying the concepts of harmony, consistency, and conservative extensions as introduced by Prior, Belnap, and Dummett. Read argues that the conservative extension requirement is too stringent. Nonetheless, he develops a formal system in which the negation, though classical, is a conservative extension of the positive fragment, by strengthening the theory of the conditional and allowing multiple conclusions. In this thesis, I will closely examine this system to determine how he achieves this. Read concludes that this result indicates that the true debate between the classicist and the intuitionist is over bivalence. My project is to critically investigate Read’s work on intuitionistic terms, noting the non-intuitionistic moves made to reach this result. If Read’s conclusion is correct, and bivalence is the true source of disagreement between the classicist and intuitionist, then it follows that any disagreement along the way should stem from bivalence. Ultimately I conclude that Read correctly identifies the source of disagreement. With this in mind, I return to Dummett’s philosophy and attempt to show why this conclusion is perfectly in line with the intuitionist’s stance.