Abstract

In this paper I present the strategy behind the proof-theoretic justification of logical inference. I then discuss how this strategy leads to the famous requirement that the inference rules for the logical constants should be in harmony. I argue that the proof-theoretic justification of the logical constants can be used to justify classical logic. To substantiate this I present a new normalisation theorem for first order classical logic involving Sheffer Stroke. The proof of this theorem can be modified to yield a normalisation result for classical logic with conjunction, negation and the universal quantifier