Is Aristotle coherent? Aristotle's position in Int. 9 has been taken to be incoherent. For Aristotle accepts Excluded Middle (which involves endorsing every instance of ‘α ∨ ¬α’) but denies Bivalence (which involves denying that at every time every assertion is either true or false). It is hard to see how this could be coherent – but the following formal semantic theory shows that it is.

Expanded semantic theory Appendix 5 contained a formal presentation of a semantic theory for a fragment of natural language that includes some present-tense predicative assertions. Here, in appendix 6, this semantic theory is expanded. The expanded semantic theory covers a slightly larger fragment of natural language, a fragment including not only some present-tense predicative assertions, but also some past- and future-tense predicative assertions, some ‘tomorrow’-assertions (i.e. predicative assertions that begin with an utterance of the phrase ‘tomorrow it will be the case that’), and some negative and disjunctive assertions.

Expansion of the alphabet The alphabet of the semantic theory presented in appendix 5, described in [54] and [55], must be expanded.