85:4 October 2002
Consequences

Advisory Editor: Greg Restall, Macquarie

The concept of deductive consequence has enjoyed a central role in philosophy since Aristotle. It received its first formal treatment in the work of Bolzano, but it was Tarski’s model-theoretic analysis which has done most to shape our contemporary understanding of the concept and of its role in determining the bounds of logic. Tarski’s analysis yielded great insight into the semantics of the propositional connectives and quantification, and it has led many to conclude that logical consequence is to be identified with validity in classical predicate logic. This consensus is at best an apparent one, however, and quite recently many criticisms of Tarski’s analysis of logical consequence have come to prominence.

Defenders of constructive, relevant and paraconsistent accounts of logic agree with Tarski that there is a distinction between the particles of a language which are logical constants and those which are not. But they disagree with Tarski and classical logic on the behaviour of those logical constants. Other critics disagree with Tarski on the boundary between the logical and the non-logical. Thus they argue in favor of conceiving identity, second-order quantification and modal operators as logical constants. Still other critics question the very distinction between the logical and the non-logical parts of a language, or they call into question the assumption that logical consequence must deal merely with linguistic representation. Thus some have sought recently to analyse consequence relations of other types, for example, between visual representations.

This issue of The Monist will examine these different analyses of logical consequence, concentrating on those which extend or diverge from classical predicate logic, such as those involving constructive or relevant reasoning, second-order quantification, and reasoning involving diagrammatic or other forms of representation. In what senses are these divergent systems ‘logic’? What can they teach us about the notion of consequence? In what ways are they useful in philosophy and in allied disciplines?

Table of Contents:

Sebastian Bauer and Heinrich Wansing 

Consequence, Counterparts and Substitution

Peter Milne 

Harmony, Purity, Simplicity, and a ‘Seemingly Magical Fact’

Aleksy Molczanow 

Quantification and Inference

Gila Sher 

Logical Consequence: An Epistemic Outline

Mark Siebel 

Bolzano’s Concept of Consequence