Entailment : semantic and syntactic approaches
This thesis gives an account of the nature of entailment through consideration of the role which semantics and syntax have to play in logical theory. This is done in two parts. The first part deals with a class of non-formal logical relations arising from the use of determinate predicates. The second deals with the core of relevance logic and with natural deduction systems of logic and their semantic counterparts. In this part, a philosophical analysis of the concept of normalisability is given, and the significance of transitivity for logic is discussed. The failure of the Lewis proof of B from A & -A is analysed, this analysis giving rise to the notion of suasive power as the key to our understanding of entailment. It is concluded that entailment is to be understood through proper appreciation of its role in clarifying commitments inherent in sets of statements and in particular in revealing contradictions where these occur. For a full account of entailment, both semantically based and syntactically based concepts are necessary.