Preservationism: a short history

Preservationist consequence relations dispense with the usual assumption that the semantic and syntactic properties preserved by consequence must be truth and consistency. Instead, this family of consequence relations draws on other semantic and syntactic features of premise sets, conclusion sets and even of consequence relations themselves. Preserving those features across extensions of sets of sentences, or a range of cases, provides new accounts of consequence. In general, an interesting preservable property of premise sets will be preserved under some but not all extensions of the premise set. This chapter gives an account of the familiar classical consequence relation, emphasizing its preservational character. The main early motivation for preservationism emerges from this account: the need for a consequence relation that deals more constructively with inconsistent premises. The chapter discusses the history of preservationism in rough chronological order, the main preservationist systems, and what is known (and not yet known) about them.

[1]  G. Ryle,et al.  Contemporary aspects of philosophy , 1976 .

[2]  A. Tarski,et al.  Boolean Algebras with Operators. Part I , 1951 .

[3]  P. K. Schotch,et al.  Epistemic logic, skepticism, and non-normal modal logic , 1981 .

[4]  D. Serenac,et al.  The Preservation of Relevance , 2003 .

[5]  Ray E. Jennings,et al.  Some remarks on (weakly) weak modal logics , 1981, Notre Dame J. Formal Log..

[6]  Philippe Besnard,et al.  Paraconsistent Reasoning as an Analytic Tool , 2001, Log. J. IGPL.

[7]  Ray E. Jennings,et al.  The n-adic first-order undefinability of the Geach formula , 1981, Notre Dame J. Formal Log..

[8]  Gerald J. Massey.  Negation, material equivalence, and conditioned nonconjunction: completeness and duality , 1977, Notre Dame J. Formal Log..

[9]  Peter K. Schotch,et al.  Logic and Aggregation , 1999, J. Philos. Log..

[10]  Gerald J. Massey.  Semantic Holism is seriously false , 1990, Stud Logica.

[11]  Bryson Brown,et al.  Old Quantum Theory: A Paraconsistent Approach , 1992, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[12]  R. E. Jennings.  VIII.—PREFERENCE AND CHOICE AS LOGICAL CORRELATES , 1967 .

[13]  Raymond E. Jennings,et al.  Paradox-tolerant logic , 1983 .

[14]  Bryson Brown.  Rational Inconsistency and Reasoning , 1992 .

[15]  Bryson Brown.  Adjunction and Aggregation , 1999 .

[16]  Peter Apostoli,et al.  A Solution to the Completeness Problem for Weakly Aggregative Modal Logic , 1995, J. Symb. Log..

[17]  Graham Priest,et al.  Paraconsistent Logic: Essays on the Inconsistent , 1990 .

[18]  Peter K. Schotch,et al.  Remarks on the Modal Logic of Henry Bradford Smith , 2000, J. Philos. Log..

[19]  Bryson Brown.  Yes, Virginia, there Really are Paraconsistent Logics , 1999, J. Philos. Log..

[20]  Bryson Brown,et al.  How to be realistic about inconsistency in science , 1990 .

[21]  Graham Priest,et al.  Chunk and Permeate, a Paraconsistent Inference Strategy. Part I: The Infinitesimal Calculus , 2004, J. Philos. Log..

[22]  Dale Jacquette.  A companion to philosophical logic , 2002 .

[23]  Ray E. Jennings,et al.  Universal First-Order Definability in Modal Logic , 1980, Math. Log. Q..

[24]  P. K. Schotch,et al.  Modal logic and the theory of modal aggregation , 1980 .

[25]  Ray E. Jennings.  A utilitarian semantics for deontic logic , 1974, J. Philos. Log..

[26]  Ray E. Jennings,et al.  Inference and necessity , 1980, Journal of Philosophical Logic.

[27]  Peter Schotch.  Hyperdeontic Logic: An Overview , 1996 .

[28]  J. Beall,et al.  The Law of Non-Contradiction , 2004 .

[29]  Philippe Besnard,et al.  Modal (Logic) Paraconsistency , 2003, ECSQARU.

[30]  R. E. Jennings,et al.  The Genealogy of Disjunction , 1994 .

[31]  Gerald J. Massey.  The Theory of Truth Tabular Connectives, both Truth Functional and Modal , 1966, J. Symb. Log..

[32]  J. Meheus.  Inconsistency in science , 2002 .

[33]  R. E. Jennings.  A note on the axiomatisation of brouwersche modal logic , 1981, J. Philos. Log..

[34]  R. E. Jennings.  Can there be a natural deontic logic? , 2004, Synthese.

[35]  P. K. Schotch,et al.  The preservation of coherence , 1984 .

[36]  Bryson Brown.  Paraconsistent Classical Logic , 2002 .

[37]  Peter K. Schotch.  Skepticism and Epistemic Logic , 2000, Stud Logica.

[38]  David Kenneth Johnston.  A generalized relational semantics for modal logic , 1978 .

[39]  P. Schotch,et al.  Engaged philosophy : essays in honour of David Braybrooke , 2006 .