Author
Abstract
Nowadays, we are confronted with important debates concerning “pluralism”, “monism”, “relativism”, and “absolutism” in logic on the one hand, and “combinations of logics”, and “translations of logics into each other”, on the other hand.
In a global reaction to the plurality of logics. Some important researches have been done in the framework of an extensive project called “universal logic” with two readings: 1) “universal logic as the general theory of logic(s)” or “universal logic as a general theory of logic(s)”; 2) “universal logic as the comprehensive logic”, or “super-logic”, or “mother logic”, a notion which encompasses all logics and generates them., The author gives a description as well as an explanation of the first reading, enumerating and evaluating the important constituents, fields, approaches, and methods of enquiry within the framework of “universal logic as the general theory of logic(s)”.
Keywords
- B 01 Beziau, J.-Y. (2001), “From Paraconsistent Logic to Universal Logic”,
SORITES, ISSN 1135-1349, Issue #12. May 2001. pp. 5-32, On-line
Version,{http://www.sorites.org/Issue_12/beziau.htm}, Accessed March 12,
2009
- B 06 B-eziau, J.-Y. (2006), “13 Questions about Universal Logic: 13 questions to
Jean-Yves B´eziau, by Linda Eastwood”, Bulletin of the Section of Logic,
Volume 35:2/3 (2006), pp. 133–150
- B 09 Beziau, J.-Y. “Is Logic Universal?”
{http://philo.at/pipermail/philweb/2009-March/003485.html}, accessed 15/10/2009.
- B 90 Béziau, J.-Y. (1990), “Logiques construites suivant les méthodes de da
Costa”, Logique et Analyse, 131-132, 259-272.
- B 93 Béziau, J.-Y. (1993), “La logique abstraite au sein de la mathématique
moderne”, Ruch Filosoficzny, 50 (1993), pp.289-293.
- B 94a Béziau, J.-Y. (1994), “De la logique formelle à la logique abstraite”,
Boletim da Sociedade Paranaense de Matem ل tica, 14, 41-50.
- B 94b Béziau, J.-Y. (1994), “Universal logic”, in T.Childers & O.Majer (eds),
Logica’94 - Proceedings of the 8th International Symposium, Philosophia,
Prague, pp.73-93.
- B 95b Jean-Yves B´eziau, Recherches sur la logique universelle, PhD Thesis,
Universit´e Denis Diderot (Paris 7), 1995.
- B 97b Béziau, J.-Y. (1997), “Logic may be simple - Logic, congruence and
algebra”, Logic and Logical Philosophy, 5, 129-147.
- B 98 Béziau, J.-Y. (1998), “Do sentences have identity ?”, in The Paideia Project -
Proceedings of the XXth World Congress of Philosophy, http://www.bu.edu/wcp/
MainLogi.htm.
- B 99b Béziau, J.-Y. (1999), “The future of paraconsistent logic”, to appear in
Logical Studies, 2.
- B 99c Béziau, J.-Y. (1999), “The mathematical structure of logical syntax”, to
appear in Carnielli, W.A. and D’Ottaviano, I.M.L. (eds.), Proceedings of the
XIth Brazilian Conference on Mathematical Logic, AMS, Providence.
- Barwise, J. and Hammer, E. (1994),“Diagrams and the concept of logical system”
in (Gabbay 1994, pp.73-106).
- Birkhoff, G. (1940), Lattice theory, AMS, Providence.
- Birkhoff, G. (1946), “Universal algebra”, in Comptes Rendus du Premier Congrès
Canadien de Mathématiques, University of Toronto Press, Toronto, pp.310-326.
- Birkhoff, G. (1976), “The rise of modern algebra to 1936” in Man and Institutions
in American Mathematics, Graduate Studies, Texas Technical Studies, 13, 65-85
- Birkhoff, G. (1987), “Universal algebra”, in Rota, G.-C. and Oliveira, J.S. (eds.),
Selected papers on algebra and topology by Garret Birkhoff, Birkh نuser, Basel,
pp.111-115.
- Bloom, S. (1984), “Roman Suszko : a reminiscence”, Studia Logica, 43, 313.
منطقِ کلی به مثابه ی نظریه ی عمومیِ منطق 61
- Bourbaki, N. (1950), “The architecture of mathematics”, American Mathematical
Monthly, 57: 4, pp. 221-232. {http://www. math.lsa.umich. edu/~mduchin/ UCD
/111/ readings/architecture.pdf}
- Brady, Ross (2001), Universal Logic, California: Center for the Study of Language
and Information.
- Dzik, W. (1981), “The existence of Lindenbaum’s extension is equivalent to the
axiom of choice”, Reports on Mathematica Logic, 13, 29-31.
-Feferman, Solomon (2006) "What kind of logic is "Independence Friendly" logic?",
in Randall E. Auxier and Lewis Edwin Hahn (eds.) The Philosophy of Jaakko
Hintikka, Library of Living Philosophers vol. 30, Open Court, 453-469.
- Gabbay, D.M. (1994b) (ed.), What is a Logical System ?, Oxford, Clarendon
- Gabbay, D.M. (1996), Labelled Deductive Systems, vol.1, Oxford, Clarendon
- Girard, Jean-Yves (1987), Linear logic, Theoretical Computer Science, London
Mathematical 50:1, pp. 1–102.
- Luschei, Eugene (1962), The Logical Systems of Lesniewski. North-Holland.
- Porte, J. (1965), Recherches sur la théorie générale des systèmes formels et sur les
systèmes connectifs, Gauthier-Villars, Paris & Nauwelaerts, Louvain.
- Scott, D.S. (1974), “Completeness and axiomatizability in many-valued logic” in
L.Henkin (ed.), Proceedings of the Tarski Symposium, AMS, Providence, 1974,
pp.411-435.
SORITES, ISSN 1135-1349, Issue #12. May 2001. pp. 5-32, On-line
Version,{http://www.sorites.org/Issue_12/beziau.htm}, Accessed March 12,
2009
- B 06 B-eziau, J.-Y. (2006), “13 Questions about Universal Logic: 13 questions to
Jean-Yves B´eziau, by Linda Eastwood”, Bulletin of the Section of Logic,
Volume 35:2/3 (2006), pp. 133–150
- B 09 Beziau, J.-Y. “Is Logic Universal?”
{http://philo.at/pipermail/philweb/2009-March/003485.html}, accessed 15/10/2009.
- B 90 Béziau, J.-Y. (1990), “Logiques construites suivant les méthodes de da
Costa”, Logique et Analyse, 131-132, 259-272.
- B 93 Béziau, J.-Y. (1993), “La logique abstraite au sein de la mathématique
moderne”, Ruch Filosoficzny, 50 (1993), pp.289-293.
- B 94a Béziau, J.-Y. (1994), “De la logique formelle à la logique abstraite”,
Boletim da Sociedade Paranaense de Matem ل tica, 14, 41-50.
- B 94b Béziau, J.-Y. (1994), “Universal logic”, in T.Childers & O.Majer (eds),
Logica’94 - Proceedings of the 8th International Symposium, Philosophia,
Prague, pp.73-93.
- B 95b Jean-Yves B´eziau, Recherches sur la logique universelle, PhD Thesis,
Universit´e Denis Diderot (Paris 7), 1995.
- B 97b Béziau, J.-Y. (1997), “Logic may be simple - Logic, congruence and
algebra”, Logic and Logical Philosophy, 5, 129-147.
- B 98 Béziau, J.-Y. (1998), “Do sentences have identity ?”, in The Paideia Project -
Proceedings of the XXth World Congress of Philosophy, http://www.bu.edu/wcp/
MainLogi.htm.
- B 99b Béziau, J.-Y. (1999), “The future of paraconsistent logic”, to appear in
Logical Studies, 2.
- B 99c Béziau, J.-Y. (1999), “The mathematical structure of logical syntax”, to
appear in Carnielli, W.A. and D’Ottaviano, I.M.L. (eds.), Proceedings of the
XIth Brazilian Conference on Mathematical Logic, AMS, Providence.
- Barwise, J. and Hammer, E. (1994),“Diagrams and the concept of logical system”
in (Gabbay 1994, pp.73-106).
- Birkhoff, G. (1940), Lattice theory, AMS, Providence.
- Birkhoff, G. (1946), “Universal algebra”, in Comptes Rendus du Premier Congrès
Canadien de Mathématiques, University of Toronto Press, Toronto, pp.310-326.
- Birkhoff, G. (1976), “The rise of modern algebra to 1936” in Man and Institutions
in American Mathematics, Graduate Studies, Texas Technical Studies, 13, 65-85
- Birkhoff, G. (1987), “Universal algebra”, in Rota, G.-C. and Oliveira, J.S. (eds.),
Selected papers on algebra and topology by Garret Birkhoff, Birkh نuser, Basel,
pp.111-115.
- Bloom, S. (1984), “Roman Suszko : a reminiscence”, Studia Logica, 43, 313.
منطقِ کلی به مثابه ی نظریه ی عمومیِ منطق 61
- Bourbaki, N. (1950), “The architecture of mathematics”, American Mathematical
Monthly, 57: 4, pp. 221-232. {http://www. math.lsa.umich. edu/~mduchin/ UCD
/111/ readings/architecture.pdf}
- Brady, Ross (2001), Universal Logic, California: Center for the Study of Language
and Information.
- Dzik, W. (1981), “The existence of Lindenbaum’s extension is equivalent to the
axiom of choice”, Reports on Mathematica Logic, 13, 29-31.
-Feferman, Solomon (2006) "What kind of logic is "Independence Friendly" logic?",
in Randall E. Auxier and Lewis Edwin Hahn (eds.) The Philosophy of Jaakko
Hintikka, Library of Living Philosophers vol. 30, Open Court, 453-469.
- Gabbay, D.M. (1994b) (ed.), What is a Logical System ?, Oxford, Clarendon
- Gabbay, D.M. (1996), Labelled Deductive Systems, vol.1, Oxford, Clarendon
- Girard, Jean-Yves (1987), Linear logic, Theoretical Computer Science, London
Mathematical 50:1, pp. 1–102.
- Luschei, Eugene (1962), The Logical Systems of Lesniewski. North-Holland.
- Porte, J. (1965), Recherches sur la théorie générale des systèmes formels et sur les
systèmes connectifs, Gauthier-Villars, Paris & Nauwelaerts, Louvain.
- Scott, D.S. (1974), “Completeness and axiomatizability in many-valued logic” in
L.Henkin (ed.), Proceedings of the Tarski Symposium, AMS, Providence, 1974,
pp.411-435.
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