Foundations of Logical Consequence

Two approaches have dominated discussion of logical consequence in recent years, the model-theoretic and the inferentialist. The model-theoretic analysis identifies logical consequence with truth-preservation in models: every model of the premises must also be a model of the conclusion. Such models can, in Etchemendy’s terminology, be either interpretational (varying the interpretation of the vocabulary) or representational (varying the “facts”). In contrast, the inferentialist analysis of consequence concentrates on the notion of proof or derivation, consisting in the application of a set of rules of inference. Rather than judge the rules as correct if they are truth-preserving over models, the inferentialist approach takes the rules as autonomous, constitutive of the meaning of at least the logical terms they contain. For example, the reason Modus Ponens (to infer B from A and ‘if A then B’) is a correct form of inference is not because it preserves truth; on the contrary, ‘if’ gains its meaning from being that expression which permits inferences of this form. The order of explanation is reversed.
The early stages of the project will consider and contrast these two approaches and seek clarity over their statement. But what is most important about the debate over the correctness of these two analyses of the concept of logical consequence is how successful each of them is at explicating and critically assessing our inferential practice. The concept may be a theoretical one, but it is one with important practical implications, for inferential behaviour is universal and an essential component of any rational practice. Those practices throw up theoretical questions. For example, can logical theory be revisionary of our actual practice? Should logic be topic-neutral, or can there be a variety of logics, each equally legitimate but suitable for different purposes or different areas? Is all valid inference formal, preserved through uniform substitution for non-logical terms or concepts, or are there material inferences, valid partly in virtue of the non-logical words used? Is there a clear criterion by which to distinguish logical terms and concepts from non-logical and descriptive terms? Can a systematic logic be developed for semantically context-sensitive expressions, like demonstratives and tenses? What is the connection between logical consequence and correct inference? How is tacit knowledge of logical principles possible, given that most actual inferential practice is carried on without reference to its theoretical underpinnings?
The driving concern of the project on the foundations of logical consequence will be to evaluate how successful each of the two approaches, model-theoretic and inferentialist, are in response to these and other questions.