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points out that this last step is too short and contains a gap. A recently published (2006) clarification by the authors shows that their intent was to exhibit a conditional result that was dependent on what they call a "naĂŻvely plausible condition". The 2003 conditional result can be reformulated,
500:
states that "the absence of rigor led to numerous errors (and ambiguities)"; he also rejects da Costa's "naĂŻvely plausible condition", as this assumption is "based partly on the possible non-totality of F and partly on an axiom equivalent to the totality of F".
457:
Basically da Costa and Doria define a formal sentence ' which is the same as P = NP in the standard model for arithmetic; however, because ' by its very definition includes a disjunct that is not refutable in ZFC, ' is not refutable in ZFC, so ZFC + ' is
413:
Da Costa believes that the significant progress in the field of logic will give rise to new fundamental developments in computing and technology, especially in connection with non-classical logics and their applications.
674:
Shyam
Wuppuluri, N.C.A. da Costa (Eds.), "Wittgensteinian (adj.) : Looking at the World from the Viewpoint of Wittgenstein's Philosophy" Springer — The Frontiers Collection, 2019.
927:
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454:(consistency of P = NP with fragments of arithmetic) and those of Sazonov and Maté (conditional proofs of the consistency of P = NP with strong systems).
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Da Costa was co-discoverer of the truth-set principle and co-creator of the classical logic of variable-binding term operators—both with
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is undecidable within that axiomatics. They later exhibited similar results for systems in other areas, such as mathematical economics.
875:
869:
772:
http://hps.master.univ-paris-diderot.fr/sites/hps.master.univ-paris-diderot.fr/files/users/fcontami/Paty,M-2000d-QuantClasDom.pdf
590:. In Stanisław Jaškowski Memorial Symposium, pp. 29–35. Department of Logic, Nicholas Copernicus University of Toruń. 1998.
426:. He is also co-author with Chris Mortensen of the definitive pre-1980 history of variable-binding term operators in classical
387:. He received many awards and held numerous visiting scholarships at universities and centers of research in all continents.
383:. He served as the President of the Brazilian Association of Logic and the Director of the Institute of Mathematics at the
548:. Non-Classical Logics, Model Theory and Computability, North-Holland Publishing Company, Amsterdam, pp. 37–56, 1977.
35:
832:
126:
104:
64:
604:. In P Weingartner (ed.), Alternative Logics: Do Sciences Need them? Berlin: Springer-Verlag, 2004, pp. 95–114.
291:
97:
430:: “Notes on the theory of variable-binding term operators”, History and Philosophy of Logic, vol.4 (1983) 63–72.
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in
Computability, Complexity and Constructivity in Economic Analysis, ed. K. V. Velupillai, Blackwell, 2005.
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439:
391:
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406:, chaotic properties of those systems are undecidable and Gödel-incomplete, that is, a sentence like
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184:
91:
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Wittgensteinian (adj.) : Looking at the World from the
Viewpoint of Wittgenstein's Philosophy
569:. Philosophia – The Philos. Quarterly of Israel, vol.16, numbers 3 and 4, pp. 293–305, 1988.
328:
890:
108:
736:
722:
796:"Matemático e filósofo Newton da Costa, criador da lógica paraconsistente, morre aos 94 anos"
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335:. In addition, he constructed the theory of quasi-truth that constitutes a generalization of
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462:(assuming that ZFC is). The paper then continues by an informal proof of the implication
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Review of the article by
Corcoran, Hatcher, and Herring on variable-binding term operators
8:
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442:, Da Costa published two papers with conditional relative proofs of the consistency of
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So far no formal argument has been constructed to show that ZFC + ' is ω-consistent.
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Paraconsistent logic as a formalism for reasoning about inconsistent knowledge bases
402:' predicates. They used that technique to show that for the axiomatized version of
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Science and
Partial Truth: A Unitary Approach to Models and Scientific Reasoning
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N.C.A. da Costa, J.M. Abe, J.I. da Silva Filho, A.C. Murolo and C.F.S. Leite
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352:
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671:. (Oxford Studies in Philosophy of Science), Oxford University Press, 2003.
348:
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Carlos
Caleiro and Ricardo Gonçalves; pages 7–8 contain a section titled
372:
315:
Da Costa's international recognition came especially through his work on
228:
459:
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611:. Applied Mathematics and Computation, vol. 145 (2003), 655–665, and
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450:. The results they obtain are similar to the results of DeMillo and
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282:(16 September 1929 – 16 April 2024) was a Brazilian mathematician,
176:
931:, which contains a description of da Costa’s paraconsistent logic.
615:. Applied Mathematics and Computation, vol. 172 (2006), 1364–1367.
583:, International J. Theoretical Physics, vol. 30 (1991), 1041–1073.
339:'s theory of truth, and applied it to the foundations of science.
152:
443:
367:, and abstract logics. Da Costa significantly contributed to the
555:, History and Philosophy of Logic, vol.4, pp. 63–72, 1983.
785:(Bulletin of Symbolic Logic, v. 10 no. 1, March 2004, p. 118f)
224:
613:
Addendum to "Consequences of an exotic formulation for P=NP"
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Applied
Mathematics and Computation, vol. 178 (2006) 83–92.
534:, Zentralblat fur Mathematik, vol. 247, pp. 8–9, 1973.
319:
and its application to various fields such as philosophy,
870:
Talk on the foundations of
Physics (videos in Portuguese)
527:. Curitiba, Brazil: Universidade Federal do Paraná, 1963.
447:
320:
882:, 2nd edition, volume 14, pages 15–107. Springer-Verlag.
581:
Undecidability and incompleteness in classical mechanics
576:. Artificial Intelligence in Medicine 1989; 1: 167–174.
541:. Notre Dame Journal of Formal Logic 1974; 15: 497–510.
342:
821:
Wuppuluri, Shyam; Costa, N.C.A. da (1 November 2012).
761:. Metaphysics Research Lab, Stanford University. 2018.
743:. Metaphysics Research Lab, Stanford University. 2018.
553:
Notes on the theory of variable-binding term operators
904:
34:
may contain excessive or inappropriate references to
16:
Brazilian philosopher and mathematician (1929–2024)
985:Academic staff of the Federal University of Paraná
921:
509:Da Costa died on 16 April 2024, at the age of 94.
417:
686:Sulla teoria delle valutazioni di N.C.A. da Costa
600:N.C.A. da Costa (with O. Bueno and A.G. Volkov),
298:and the title of his 1961 Ph.D. dissertation was
936:
597:History and Philosophy of Logic 1998; 19: 41–54.
496:of the da Costa/Doria papers on P=NP, logician
290:, he studied engineering and mathematics at the
657:. SĂŁo Paulo, Discurso Editorial, 2a. Ed., 1999.
609:Consequences of an exotic definition for P = NP
593:N.C.A. da Costa (with O. Bueno and S. French),
820:
678:
975:Academic staff of the University of SĂŁo Paulo
874:Carnielli, W., Coniglio, M.E., e Marcos, J.,
688:. Naples: Liguori Editore, 1990. Pp. 75.
466:If ZFC + ' is consistent, then so is ZFC + .
891:On the algebraization of many-sorted logics⋆
539:On the theory of inconsistent formal systems
602:Outline of a paraconsistent category theory
300:Topological spaces and continuous functions
864:Newton da Costa, ou: a matemática com arte
643:. Hucitec-EdUSP, 2a. ed., SĂŁo Paulo, 1993.
572:N.C.A. da Costa (with V.S. Subrahmanian),
857:Newton da Costa: Pensador da Contradição
565:N.C.A. da Costa (with Walter Carnielli),
475:according to da Costa and Doria 2006, as
127:Learn how and when to remove this message
65:Learn how and when to remove this message
802:(in Brazilian Portuguese). 17 April 2024
517:
512:
347:The scope of his research also includes
90:This article includes a list of general
759:The Stanford Encyclopedia of Philosophy
741:The Stanford Encyclopedia of Philosophy
937:
783:Schindler's review of the P = NP paper
544:N.C.A. da Costa (with L. Dubikajtis),
955:20th-century Brazilian mathematicians
551:N.C.A. da Costa (with C. Mortensen),
446:with the usual set-theoretic axioms
331:. He was one of the founders of this
45:by removing references to unreliable
851:Biography at Unicamp (in Portuguese)
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715:
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625:N.C.A. da Costa (with F. A. Doria),
618:N.C.A. da Costa (with F. A. Doria),
607:N.C.A. da Costa (with F. A. Doria),
343:Other fields; foundations of physics
76:
49:where they are used inappropriately.
18:
990:Federal University of Paraná alumni
960:20th-century Brazilian philosophers
579:N.C.A. da Costa (with F.A. Doria),
13:
922:{\displaystyle {\mathcal {C}}_{1}}
908:
648:Logique Classique et Non-Classique
627:Some thoughts on hypercomputation,
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96:it lacks sufficient corresponding
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1001:
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898:Example 3 (Paraconsistent Logic
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662:LĂłgica Paraconsistente Applicada
280:Newton Carneiro Affonso da Costa
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145:Newton Carneiro Affonso da Costa
81:
23:
880:Handbook of Philosophical Logic
667:N.C.A. da Costa and S. French,
641:LĂłgica Indutiva e Probabilidade
562:. Erkenntnis 1986; 25: 141–162.
546:On Jaskowski's Discussive Logic
525:Sistemas Formais Inconsistentes
418:Variable-binding term operators
876:Logics of Formal Inconsistency
814:
788:
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394:axiomatized large portions of
1:
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567:Paraconsistent deontic logics
679:Essays on N. C. A. da Costa
483:, then ZFC + is consistent.
292:Federal University of Paraná
286:, and philosopher. Born in
7:
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355:, axiomatic foundations of
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664:. SĂŁo Paulo, Atlas, 1999.
655:O conhecimento cientĂfico
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404:dynamical systems theory
595:Is there a Zande Logic?
440:Francisco AntĂ´nio DĂłria
392:Francisco AntĂ´nio DĂłria
390:Da Costa and physicist
385:University of SĂŁo Paulo
329:artificial intelligence
305:
111:more precise citations.
923:
886:Google scholar profile
755:"Paraconsistent Logic"
737:"Paraconsistent Logic"
650:. Paris, Masson, 1997.
36:self-published sources
924:
620:Computing the future,
560:Pragmatic probability
518:Articles and lectures
513:Selected publications
470:However, a review by
381:philosophy of science
255:Marcelo Samuel Berman
237:Philosophy of Science
980:Paraconsistent logic
970:People from Curitiba
902:
588:Paraconsistent logic
493:Mathematical Reviews
317:paraconsistent logic
208:Paraconsistent logic
965:Brazilian logicians
490:In his reviews for
369:philosophy of logic
333:non-classical logic
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653:N.C.A. da Costa,
646:N.C.A. da Costa,
639:N.C.A. da Costa,
586:N.C.A. da Costa,
558:N.C.A. da Costa,
537:N.C.A. da Costa,
530:N.C.A. da Costa,
523:N.C.A. da Costa,
428:first-order logic
398:with the help of
396:classical physics
371:, paraconsistent
365:complexity theory
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265:Itala D'Ottaviano
243:Doctoral students
215:Scientific career
173:16 September 1929
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250:Jean-Yves BĂ©ziau
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117:January 2013
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41:Please help
33:
950:2024 deaths
945:1929 births
229:Mathematics
109:introducing
939:Categories
723:"Cle-Aips"
705:References
460:consistent
361:relativity
233:Philosophy
169:1929-09-16
92:references
55:April 2024
43:improve it
325:computing
806:17 April
693:See also
377:ontology
296:Curitiba
288:Curitiba
284:logician
177:Curitiba
105:improve
47:sources
831:
452:Lipton
444:P = NP
434:P = NP
379:, and
327:, and
221:Fields
185:Brazil
181:Paraná
94:, but
634:Books
505:Death
225:Logic
829:ISBN
808:2024
359:and
306:Work
235:and
192:Died
163:Born
448:ZFC
321:law
294:in
941::
894:by
878:.
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757:.
739:.
712:^
375:,
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