A Truth-functional Non-modal Interpretation of Ockham's Theory of Consequences

Abstract

Philotheus Boehner, in his paper of 1951 demonstrated that Ockham knew of material implication, and his book of 1952 translated many of Ockham's rules for simply valid consequences as tautologies (hence theorems) of PC (propositional calculus). E. A. Moody, in his book of 1953, gave a conflicting interpretation, identifying Ockham's simply valid consequences with Lewis and Langford's CSI (calculus of strict implication) and Ockham's consequences valid ut nunc with PC. It is demonstrated here that Moody was wrong and Boehner right. It is also shown that PC with propositional constants provides a framework for a truth-functional interpretation of Ockham's consequences without modal adverbs '□' and '◊' ('necessarily' and 'possibly' where '□' = df '~◊~').