Relevant deduction

This paper presents an outline of a new theory of relevant deduction which arose from the purpose of solving paradoxes in various fields of analytic philosophy. In distinction to relevance logics, this approach does not replace classical logic by a new one, but distinguishes between relevance and validity. It is argued that irrelevant arguments are, although formally valid, nonsensical and even harmful in practical applications. The basic idea is this: a valid deduction is relevant iff no subformula of the conclusion is replaceable on some of its occurrences by any other formula salva validitate of the deduction. The paper first motivates the approach by showing that four paradoxes seemingly very distant from each other have a common source. Then the exact definition of relevant deduction is given and its logical properties are investigated. An extension to relevance of premises is discussed. Finally the paper presents an overview of its applications in philosophy of science, ethics, cognitive psychology and artificial intelligence.This paper is based on the first part of my habilitation Schurz (1989). For various helps and comments I am indebted to Paul Weingartner. Andrzej Wrónski, Georg Kreisel, David Miller, Kit Fine, Terence Parsons and Peter Woodruff.     

Verisimilitude and Belief Revision. With a Focus on the Relevant Element Account

The expansion or revision of false theories by true evidence does not always increase their verisimilitude. After a comparison of different notions of verisimilitude the relation between verisimilitude and belief expansion or revision is investigated within the framework of the relevant element account. We are able to find certain interesting conditions under which both the expansion and the revision of theories by true evidence is guaranteed to increase their verisimilitude.     

Completeness and Correspondence in Chellas–Segerberg Semantics

We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas–Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) non-trivial frame conditions in CS semantics which correspond to the 30 principles.     

Optimality justifications: new foundations for foundation-oriented epistemology

In this paper a new conception of foundation-oriented epistemology is developed. The major challenge for foundation-oriented justifications consists in the problem of stopping the justificational regress without taking recourse to dogmatic assumptions or circular reasoning. Two alternative accounts that attempt to circumvent this problem, coherentism and externalism, are critically discussed and rejected as unsatisfactory. It is argued that optimality arguments are a new type of foundation-oriented justification that can stop the justificational regress. This is demonstrated on the basis of a novel result in the area of induction: the optimality of meta-induction. In the final section the method of optimality justification is generalized to deductive and abductive inferences.     

Probability,Approximate Truth,and Truthlikeness: More Ways out of the Preface Paradox

The so-called Preface Paradox seems to show that one can rationally believe two logically incompatible propositions. We address this puzzle, relying on the notions of truthlikeness and approximate truth as studied within the post-Popperian research programme on verisimilitude. In particular, we show that adequately combining probability, approximate truth, and truthlikeness leads to an explanation of how rational belief is possible in the face of the Preface Paradox. We argue that our account is superior to other solutions of the paradox, including a recent one advanced by Hannes Leitgeb (Analysis 74.1).