Foundations of Logical Consequence Workshop I: Proof-Theoretic vs Model-Theoretic Semantics
12 - 13 January 2009, St Andrews
Project website: http://www.st-andrews.ac.uk/~arche/events/event?id=190
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 aim of the Workshop was to explore these two approaches, clarify their statement and evaluate their relative success in providing a foundation for the notion of logical consequence.
e-Records of three of the talks are available from the links below. (Peter Milne's session will be available shortly.)
Sessions
| Speaker | Title |
|---|---|
| JC Beall, University of Connecticut | Remarks on validity and truth-preservation in some non-classical truth theories |
| Patrick Allo, Brussels Free University | A Logic of Ambiguous Connectives: Discrimination vs Disagreement |
| Stephen Read, Arché | General-elimination harmony and the meaning of the logical constants |
| Marcus Rossberg, University of Connecticut | On Validity |
| Peter Milne, University of Stirling | Prospects for a Modest Inferentialism  |
| Crispin Wright, Arché and NYU | Inferentialism and Harmony |
| Ole Hjortland | The Semantic Role of Proof-Conditions |
| Graham Priest, University of Melbourne and Arché | Is the ternary relation depraved? |