Paraconsistent logic

Under paraconsistent logics and Parainkonsistenten logic is understood calculi in which the logical principle ex contradictione sequitur quodlibet ( lat. For "a contradiction follows Any") does not apply, ie where it is not possible for two contradictory statements or from an opposition derive any statement. ${\ displaystyle A, \ neg A}$ ${\ displaystyle A \ wedge \ neg A}$

Different systems of paraconsistent logics

There are four directions:

the Australian ( Graham Priest , Richard Sylvan , et al.)
the South American / Brazilian, for which the work of Newton da Costa is central,
the Belgian ( inter alia Diderik Batens ) and
the Polish (influenced by Stanisław Jaśkowski ).

In the Australian school (see Priest, Tanaka) dialeth (e) ism occupies a central position. As Dialeth (e) ism of the opinion referred to it true are contradictions. The other representatives of paraconsistent logics do not share this point of view.

Be differentiated

non-adjunctive systems,
non- truth-functional systems,
multi-valued paraconsistent logics and
Relevance logics .

Non-adjunctive systems are calculi developed by Stanisław Jaśkowski ( Lemberg-Warsaw School ) as a partial calculus of the systems of natural reasoning , in which the following rule for the introduction of the conjunction is missing: ${\ displaystyle \ {\ frac {a \ quad b} {a \ wedge b}}.}$

In particular, it follows from the two mutually contradicting statements and not the contradiction in one statement. This discursive (discussion) logic means in one interpretation of Jaśkowski that participants in the conversation can calmly have contradicting opinions, because that does not lead to a conversation partner contradicting himself. ${\ displaystyle \! \ a}$ ${\ displaystyle \! \ \ neg a}$ ${\ displaystyle a \ wedge \ neg a}$

literature

Jean-Yves Béziau : What is Paraconsistent Logic? In: Diderik Batens et al. (Ed.): Frontiers of Paraconsistent Logic (Studies in logic and reputation; Vol. 8). Research Studies Press, Baldock 2000, ISBN 0-86380-253-2 , pp. 95-111.
Manuel Bremer: An Introduction to Paraconsistent Logics. Peter Lang Verlag, Frankfurt / M. 2005, ISBN 3-631-53413-2 .
Newton da Costa, Otávio Bueno, Steven French: The Logic of Pragmatic Truth. In: Journal of Philosophical Logic , Vol. 27 (1998), ISSN 0022-3611 , pp. 603-620.
Newton da Costa, Steven French: Partial Truth and Partial Structures. A Unitary Account of Models in Scientific and Natural Reasoning. University of São Paulo and University of Leeds, 2001.
Adolf Fuhrmann: paraconsistent / paraconsistency. In: Jürgen Mittelstraß et al. (Ed.): Encyclopedia Philosophy and Philosophy of Science, Vol. 3 . Metzler, Stuttgart 1995, ISBN 3-476-01352-9 , pp. 47-48.
Irene Mikenberg, Newton da Costa, Rolando Chuaqui: Pragmatic Truth and Approximation to Truth. In: Journal of Symbolic Logic. Vol. 51 (1986), No. 1, ISSN 0022-4812 , pp. 201-221.
Jerzy Perzanowski: Fifty Years of Parainconsistent Logics . In: Logic and Logical Philosophy. Vol. 7 (1999), ISSN 1425-3305 , pp. 21-24. (PDF file; 652 kB)
Graham Priest: Paraconsistent Logic. In: Dov Gabbay , Franz Guenthner (Ed.): Handbook of Philosophical Logic, Vol. 6 . 2nd Edition. Kluwer, Dordrecht 2002, ISBN 1-4020-0583-0 , pp. 287-393.
Graham Priest, Richard Routley, Jean Norman (Eds.): Paraconsistent Logic. Essays on the inconsistent . Edition Philosophia, Munich 2002, ISBN 3-88405-058-3 , pp. 437-470.
Graham Priest, Koji Tanaka: Paraconsistent Logic . In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy . 2nd ed. The Metaphysics Research Lab, Stanford, Calif. 2011 ISSN 1095-5054 .
Hans Rott: Paraconsistent logic in In: Jürgen Mittelstraß: Encyclopedia philosophy and philosophy of science . Second edition. Volume 5, Metzler 2013, ISBN 978-3-476-02104-5 , pp. 75-77.
John Woods: Paradox and Paraconsistency. Conflict Resolution in the Abstract Sciences. CUP, Cambridge 2003, ISBN 0-521-81094-9 .

Individual evidence

↑ Until 1983 known under the name Richard Routley (1935–1996).

Web links

Graham Priest and Koji Tanaka: Paraconsistent Logic. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy . (1996 / Update 2013)
Zach Weber: Paraconsistent Logic. In: Internet Encyclopedia of Philosophy .
Graham Priest and Francesco Berto: Dialetheism. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .

[1] Until 1983 known under the name Richard Routley (1935–1996).