Investigações em semânticas construtivas

Detalhes bibliográficos
Autor(a) principal: Oliveira, Hermogenes Hebert Pereira
Data de Publicação: 2014
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/3103
Resumo: Proof-theoretic Semantics provides a new approach to the semantics of logical constants. It has compelling philosophical motivations which are rooted deeply in the philosophy of language and the philosophy of mathematics. We investigate this new approach of logical semantics and its perspective on logical validity in the light of its own philosophical aspirations, especially as represented by the work of Dummett (1991). Among our findings, we single out the validity of Peirce’s rule with respect to a justification procedure based on the introduction rules for the propositional logical constants. This is an undesirable outcome since Peirce’s rule is not considered to be constructively acceptable. On the other hand, we also establish the invalidity of the same inference rule with respect to a justification procedure based on the elimination rules for the propositional logical constants. We comment on the implications of this scenario to Dummett’s philosophical programme and to proof-theoretic semantics in general.
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spelling Sanz, Wagner de Camposhttp://lattes.cnpq.br/5046432111036307http://lattes.cnpq.br/7965659331229634Oliveira, Hermogenes Hebert Pereira2014-09-19T13:19:45Z2014-02-14OLIVEIRA, Hermogenes Hebert Pereira. Investigações em semânticas construtivas. 2014. 77 f. Dissertação (Mestrado em Filosofia) - Universidade Federal de Goiás, Goiânia, 2014.http://repositorio.bc.ufg.br/tede/handle/tede/3103ark:/38995/0013000003t6gProof-theoretic Semantics provides a new approach to the semantics of logical constants. It has compelling philosophical motivations which are rooted deeply in the philosophy of language and the philosophy of mathematics. We investigate this new approach of logical semantics and its perspective on logical validity in the light of its own philosophical aspirations, especially as represented by the work of Dummett (1991). Among our findings, we single out the validity of Peirce’s rule with respect to a justification procedure based on the introduction rules for the propositional logical constants. This is an undesirable outcome since Peirce’s rule is not considered to be constructively acceptable. On the other hand, we also establish the invalidity of the same inference rule with respect to a justification procedure based on the elimination rules for the propositional logical constants. We comment on the implications of this scenario to Dummett’s philosophical programme and to proof-theoretic semantics in general.As semânticas construtivas oferecem uma nova abordagem semântica para as constantes lógicas. Essas semânticas gozam de fortes motivações filosóficas advindas da filosofia da linguagem e da filosofia da matemática. Nós investigamos essa nova abordagem semântica da lógica e sua concepção de validade lógica sob a luz de suas próprias aspirações filosóficas, em especial aquelas representadas pelo trabalho de Dummett (1991). Dentre nossos resultados, destacamos a validade da Regra de Peirce em relação ao procedimento justificatório baseado nas regras de introdução para as constantes lógicas proposicionais. Essa é uma situação indesejável, pois a Regra de Peirce não é considerada aceitável de um ponto de vista construtivo. Por outro lado, verificamos que o procedimento justificatório baseado nas regras de eliminação atesta a invalidade dessa mesma regra. Tecemos alguns comentários a respeito das consequências desse cenário para o projeto filosófico de Dummett e para as semânticas construtivas em geral.Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-09-19T13:14:21Z No. of bitstreams: 2 Dissertacao Hermogenes Hebert Pereira Oliveira.pdf: 452221 bytes, checksum: b2469cc663d70c03f4dcf9dbea202fb2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-19T13:19:45Z (GMT) No. of bitstreams: 2 Dissertacao Hermogenes Hebert Pereira Oliveira.pdf: 452221 bytes, checksum: b2469cc663d70c03f4dcf9dbea202fb2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2014-09-19T13:19:45Z (GMT). No. of bitstreams: 2 Dissertacao Hermogenes Hebert Pereira Oliveira.pdf: 452221 bytes, checksum: b2469cc663d70c03f4dcf9dbea202fb2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-02-14Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfhttp://repositorio.bc.ufg.br/tede/retrieve/8067/Dissertacao%20Hermogenes%20Hebert%20Pereira%20Oliveira.pdf.jpgporUniversidade Federal de GoiásPrograma de Pós-graduação em Filosofia (FAFIL)UFGBrasilFaculdade de Filosofia - FAFIL (RG)ARISTOTLE. On interpretation. In: . Aristotle. Cambridge, Massachusetts: Harvard University Press, 1938. (Loeb Classical Library, 1), cap. 2. Translated by Harold P. Cooke. BROUWER, L. E. J. De onbetrouwbaarheid der logische principes. Tijdschrift voor Wijsbegeerte, v. 2, p. 152–158, 1908. Translated in Brouwer (1975). BROUWER, L. E. J. Collected Works: Philosophy and foundations of mathematics. Amsterdam: North Holland, 1975. CARNAP, R. The Logical Syntax of Language. London: Routledge and Kegan Paul, 1964. DEVITT, M. Dummett’s anti-realism. The Journal of Philosophy, v. 80, n. 2, p. 73–99, 1983. DÍEZ, G. F. Five observations concerning the intended meaning of the intuitionistic logical constants. Journal of Philosophical Logic, v. 29, p. 409–424, 2000. DUMMETT, M. The justification of deduction. Proceedings of the British Academy, LIX, p. 201–232, 1975. Reprinted in Dummett (1978). DUMMETT, M. The philosophical basis of intuitionistic logic. In: ROSE, H.; SHEPHERDSON, J. (Ed.). Logic Colloquium ’73 Proceedings of the Logic Colloquium. Amsterdam: North Holland, 1975, (Studies in Logic and the Foundations of Mathematics, v. 80). p. 5–40. Reprinted in Dummett (1978). DUMMETT, M. Truth and Other Enigmas. Cambridge, Massachussetts: Harvard University Press, 1978. DUMMETT, M. The Logical Basis Of Metaphysics. Cambridge, Massachusetts: Harvard University Press, 1991. DUMMETT, M. Elements of Intuitionism. 2. ed. Great Claredon Street, Oxford: Oxford University Press, 2000. (Oxford Logic Guides, v. 39). DUMMETT, M. Reply to Dag Prawitz. In: AUXIER, R. E.; HAHN, L. E. (Ed.). The Philosophy of Michael Dummett. Chicago and La Salle, Illinois: Open Court Publishing Company, 2007, (The Library of Living Philosophers, XXXI). cap. 13, p. 482–489. GENTZEN, G. Untersuchungen über das logische schließen I. Mathematische Zeitschrift, v. 39, n. 1, p. 176–210, 1935. Translated in Gentzen (1969). GENTZEN, G. The Collected Papers of Gerhard Gentzen. Amsterdam: North-Holland Publishing Company, 1969. GÖDEL, K. In what sense is intuitionistic logic constructive? In: FEFERMAN, S. (Ed.). Collected Works. [S.l.]: Oxford University Press, 1995. III, p. 189–200. GRISS, G. F. C. Negationless intuitionistic mathematics. Indagationes Mathematicae, v. 8, p. 675–681, 1946. HEIJENOORT, J. van (Ed.). From Frege to Gödel: A source book in mathematical logic: 1879–1931. Cambridge, Massachusetts: Harvard University Press, 1967. HEYTING, A. Die formalen regeln der intuitionische logik. Sitzungsberichte der Preuszischen Akademie der Wissenschaften, p. 42–56, 1930. HEYTING, A. Intuitionism: An Introduction. 3. ed. Amsterdam: North-Holland Publishing Company, 1971. HILBERT, D. Die grundlagen der mathematik. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, v. 6, n. 1, p. 65–85, 1928. Translated in Heijenoort (1967). KAHLE, R.; SCHROEDER-HEISTER, P. Introduction: Proof-theoretic semantics. Synthese, Springer, v. 148, n. 3, p. 503–506, 2006. KLEENE, S. C. Introduction to Metamathematics. Amsterdam: North Holland, 1952. KOLMOGOROFF, A. Zur deutung der intuitionistischen logik. Mathematische Zeitschrift, v. 35, n. 1, p. 58–65, 1932. KRIPKE, S. A. Semantical analysis of intuitionistic logic I. In: DUMMETT, M.; CROSSLEY, J. N. (Ed.). Formal Systems and Recursive Functions. Amsterdam: North Holland Publishing Company, 1965, (Studies in Logic and The Foundations of Mathematics, v. 40). p. 92–130. KUTSCHERA, F. von. Die vollständigkeit des operatorsystems f:;^;_; g für die intuitionistische aussagenlogik im rahmen der gentzensemantik. Archiv für Matematische Logik und Grundlagenforschung, v. 12, p. 3–16, 1968. LORENZEN, P. Einführung in die Operative Logik und Mathematik. 2. ed. Berlin: Springer, 1969. First edition published in 1955. MARTIN-LÖF, P. On the meanings of the logical constants and the justifications of the logical laws. Nordic Journal of Philosophical Logic, v. 1, n. 1, p. 11–60, 1996. MINTS, G. E. Derivability of admissible rules. Journal of Mathematical Sciences, v. 6, n. 4, p. 417–421, 1976. First published in Russian in 1972. PAGIN, P. Bivalence: Meaning theory vs metaphysics. Theoria, v. 64, n. 2-3, p. 157–186, 1998. PLATO, J. von. Gentzen’s proof systems: Byproducts in a work of genius. The Bulletin of Symbolic Logic, v. 18, n. 3, p. 313–367, September 2012. PRAWITZ, D. Natural Deduction: A Proof-Theoretical Study. Stockholm: Almqvist & Wiksell, 1965. PRAWITZ, D. Ideas and results in proof theory. Studies in Logic and the Foundations of Mathematics, v. 66, p. 235–307, 1971. PRAWITZ, D. Towards a foundation of a general proof theory. In: SUPPES, P. et al. (Ed.). Logic, Methodology and Philosophy of Science IV. Amsterdam: North Holland, 1973. (Studies in Logic and the Foundations of Mathematics, v. 74), p. 225–250. PRAWITZ, D. On the ideia of a general proof theory. Synthese, v. 27, n. 1, p. 63–77, 1974. PRAWITZ, D. Meaning approached via proofs. Synthese, v. 148, n. 3, p. 507–524, 2006. PRAWITZ, D. Pragmatist and verificationist theories of meaning. In: AUXIER, R. E.; HAHN, L. E. (Ed.). The Philosophy of Michael Dummett. Chicago and La Salle, Illinois: Open Court Publishing Company, 2007, (The Library of Living Philosophers, XXXI). cap. 13, p. 455–481. SANDQVIST, T. Classical logic without bivalence. Analisys, v. 69, n. 2, p. 211–218, April 2009. SANZ, W. de C. Uma Investigação Acerca das Regras para a Negação e o Absurdo em Dedução Natural. Tese (Doutorado) — Universidade Estadual de Campinas, Campinas, 2006. SANZ, W. de C.; PIECHA, T.; SCHROEDER-HEISTER, P. Constructive semantics, admissibility of rules and the validity of Peirce’s law. Logic Journal of the IGPL, 2013. SCHROEDER-HEISTER, P. Proof-theoretic semantics. In: ZALTA, E. N. (Ed.). The Stanford Encyclopedia of Philosophy. Spring 2013. [S.l.: s.n.], 2013. TARSKI, A. On the concept of logical consequence. In: Logic, Semantics, Metamathematics. Oxford: The Claredon Press, 1956. p. 409–420. TENNANT, N. Anti-Realism and Logic: Truth as eternal. Oxford: Claredon Press, 1987. TROELSTRA, A. S.; DALEN, D. van. Constructivism in Mathematics: An Introduction. 1. ed. Amsterdam: Elsevier, 1988. (Studies in Logic and the Foundations of Mathematics, v. 121). 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dc.title.por.fl_str_mv Investigações em semânticas construtivas
dc.title.alternative.eng.fl_str_mv Investigations on proof-theoretic semantics
title Investigações em semânticas construtivas
spellingShingle Investigações em semânticas construtivas
Oliveira, Hermogenes Hebert Pereira
Validade lógica
Intuicionismo lógico
Teoria das demonstrações
Teoria do significado
Logical validity
Logical intuitionism
Proof theory
Meaning theory
CIENCIAS HUMANAS::FILOSOFIA
title_short Investigações em semânticas construtivas
title_full Investigações em semânticas construtivas
title_fullStr Investigações em semânticas construtivas
title_full_unstemmed Investigações em semânticas construtivas
title_sort Investigações em semânticas construtivas
author Oliveira, Hermogenes Hebert Pereira
author_facet Oliveira, Hermogenes Hebert Pereira
author_role author
dc.contributor.advisor1.fl_str_mv Sanz, Wagner de Campos
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/5046432111036307
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/7965659331229634
dc.contributor.author.fl_str_mv Oliveira, Hermogenes Hebert Pereira
contributor_str_mv Sanz, Wagner de Campos
dc.subject.por.fl_str_mv Validade lógica
Intuicionismo lógico
Teoria das demonstrações
Teoria do significado
topic Validade lógica
Intuicionismo lógico
Teoria das demonstrações
Teoria do significado
Logical validity
Logical intuitionism
Proof theory
Meaning theory
CIENCIAS HUMANAS::FILOSOFIA
dc.subject.eng.fl_str_mv Logical validity
Logical intuitionism
Proof theory
Meaning theory
dc.subject.cnpq.fl_str_mv CIENCIAS HUMANAS::FILOSOFIA
description Proof-theoretic Semantics provides a new approach to the semantics of logical constants. It has compelling philosophical motivations which are rooted deeply in the philosophy of language and the philosophy of mathematics. We investigate this new approach of logical semantics and its perspective on logical validity in the light of its own philosophical aspirations, especially as represented by the work of Dummett (1991). Among our findings, we single out the validity of Peirce’s rule with respect to a justification procedure based on the introduction rules for the propositional logical constants. This is an undesirable outcome since Peirce’s rule is not considered to be constructively acceptable. On the other hand, we also establish the invalidity of the same inference rule with respect to a justification procedure based on the elimination rules for the propositional logical constants. We comment on the implications of this scenario to Dummett’s philosophical programme and to proof-theoretic semantics in general.
publishDate 2014
dc.date.accessioned.fl_str_mv 2014-09-19T13:19:45Z
dc.date.issued.fl_str_mv 2014-02-14
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv OLIVEIRA, Hermogenes Hebert Pereira. Investigações em semânticas construtivas. 2014. 77 f. Dissertação (Mestrado em Filosofia) - Universidade Federal de Goiás, Goiânia, 2014.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/3103
dc.identifier.dark.fl_str_mv ark:/38995/0013000003t6g
identifier_str_mv OLIVEIRA, Hermogenes Hebert Pereira. Investigações em semânticas construtivas. 2014. 77 f. Dissertação (Mestrado em Filosofia) - Universidade Federal de Goiás, Goiânia, 2014.
ark:/38995/0013000003t6g
url http://repositorio.bc.ufg.br/tede/handle/tede/3103
dc.language.iso.fl_str_mv por
language por
dc.relation.program.fl_str_mv -7401176116358064379
dc.relation.confidence.fl_str_mv 600
600
600
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dc.relation.department.fl_str_mv 5585255767972561168
dc.relation.cnpq.fl_str_mv -672352020940167053
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dc.relation.references.por.fl_str_mv ARISTOTLE. On interpretation. In: . Aristotle. Cambridge, Massachusetts: Harvard University Press, 1938. (Loeb Classical Library, 1), cap. 2. Translated by Harold P. Cooke. BROUWER, L. E. J. De onbetrouwbaarheid der logische principes. Tijdschrift voor Wijsbegeerte, v. 2, p. 152–158, 1908. Translated in Brouwer (1975). BROUWER, L. E. J. Collected Works: Philosophy and foundations of mathematics. Amsterdam: North Holland, 1975. CARNAP, R. The Logical Syntax of Language. London: Routledge and Kegan Paul, 1964. DEVITT, M. Dummett’s anti-realism. The Journal of Philosophy, v. 80, n. 2, p. 73–99, 1983. DÍEZ, G. F. Five observations concerning the intended meaning of the intuitionistic logical constants. Journal of Philosophical Logic, v. 29, p. 409–424, 2000. DUMMETT, M. The justification of deduction. Proceedings of the British Academy, LIX, p. 201–232, 1975. Reprinted in Dummett (1978). DUMMETT, M. The philosophical basis of intuitionistic logic. In: ROSE, H.; SHEPHERDSON, J. (Ed.). Logic Colloquium ’73 Proceedings of the Logic Colloquium. Amsterdam: North Holland, 1975, (Studies in Logic and the Foundations of Mathematics, v. 80). p. 5–40. Reprinted in Dummett (1978). DUMMETT, M. Truth and Other Enigmas. Cambridge, Massachussetts: Harvard University Press, 1978. DUMMETT, M. The Logical Basis Of Metaphysics. Cambridge, Massachusetts: Harvard University Press, 1991. DUMMETT, M. Elements of Intuitionism. 2. ed. Great Claredon Street, Oxford: Oxford University Press, 2000. (Oxford Logic Guides, v. 39). DUMMETT, M. Reply to Dag Prawitz. In: AUXIER, R. E.; HAHN, L. E. (Ed.). The Philosophy of Michael Dummett. Chicago and La Salle, Illinois: Open Court Publishing Company, 2007, (The Library of Living Philosophers, XXXI). cap. 13, p. 482–489. GENTZEN, G. Untersuchungen über das logische schließen I. Mathematische Zeitschrift, v. 39, n. 1, p. 176–210, 1935. Translated in Gentzen (1969). GENTZEN, G. The Collected Papers of Gerhard Gentzen. Amsterdam: North-Holland Publishing Company, 1969. GÖDEL, K. In what sense is intuitionistic logic constructive? In: FEFERMAN, S. (Ed.). Collected Works. [S.l.]: Oxford University Press, 1995. III, p. 189–200. GRISS, G. F. C. Negationless intuitionistic mathematics. Indagationes Mathematicae, v. 8, p. 675–681, 1946. HEIJENOORT, J. van (Ed.). From Frege to Gödel: A source book in mathematical logic: 1879–1931. Cambridge, Massachusetts: Harvard University Press, 1967. HEYTING, A. Die formalen regeln der intuitionische logik. Sitzungsberichte der Preuszischen Akademie der Wissenschaften, p. 42–56, 1930. HEYTING, A. Intuitionism: An Introduction. 3. ed. Amsterdam: North-Holland Publishing Company, 1971. HILBERT, D. Die grundlagen der mathematik. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, v. 6, n. 1, p. 65–85, 1928. Translated in Heijenoort (1967). KAHLE, R.; SCHROEDER-HEISTER, P. Introduction: Proof-theoretic semantics. 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Nordic Journal of Philosophical Logic, v. 1, n. 1, p. 11–60, 1996. MINTS, G. E. Derivability of admissible rules. Journal of Mathematical Sciences, v. 6, n. 4, p. 417–421, 1976. First published in Russian in 1972. PAGIN, P. Bivalence: Meaning theory vs metaphysics. Theoria, v. 64, n. 2-3, p. 157–186, 1998. PLATO, J. von. Gentzen’s proof systems: Byproducts in a work of genius. The Bulletin of Symbolic Logic, v. 18, n. 3, p. 313–367, September 2012. PRAWITZ, D. Natural Deduction: A Proof-Theoretical Study. Stockholm: Almqvist & Wiksell, 1965. PRAWITZ, D. Ideas and results in proof theory. Studies in Logic and the Foundations of Mathematics, v. 66, p. 235–307, 1971. PRAWITZ, D. Towards a foundation of a general proof theory. In: SUPPES, P. et al. (Ed.). Logic, Methodology and Philosophy of Science IV. Amsterdam: North Holland, 1973. (Studies in Logic and the Foundations of Mathematics, v. 74), p. 225–250. PRAWITZ, D. On the ideia of a general proof theory. Synthese, v. 27, n. 1, p. 63–77, 1974. PRAWITZ, D. Meaning approached via proofs. Synthese, v. 148, n. 3, p. 507–524, 2006. PRAWITZ, D. Pragmatist and verificationist theories of meaning. In: AUXIER, R. E.; HAHN, L. E. (Ed.). The Philosophy of Michael Dummett. Chicago and La Salle, Illinois: Open Court Publishing Company, 2007, (The Library of Living Philosophers, XXXI). cap. 13, p. 455–481. SANDQVIST, T. Classical logic without bivalence. Analisys, v. 69, n. 2, p. 211–218, April 2009. SANZ, W. de C. Uma Investigação Acerca das Regras para a Negação e o Absurdo em Dedução Natural. Tese (Doutorado) — Universidade Estadual de Campinas, Campinas, 2006. SANZ, W. de C.; PIECHA, T.; SCHROEDER-HEISTER, P. Constructive semantics, admissibility of rules and the validity of Peirce’s law. Logic Journal of the IGPL, 2013. SCHROEDER-HEISTER, P. Proof-theoretic semantics. In: ZALTA, E. N. (Ed.). The Stanford Encyclopedia of Philosophy. Spring 2013. [S.l.: s.n.], 2013. TARSKI, A. On the concept of logical consequence. In: Logic, Semantics, Metamathematics. Oxford: The Claredon Press, 1956. p. 409–420. TENNANT, N. Anti-Realism and Logic: Truth as eternal. Oxford: Claredon Press, 1987. TROELSTRA, A. S.; DALEN, D. van. Constructivism in Mathematics: An Introduction. 1. ed. Amsterdam: Elsevier, 1988. (Studies in Logic and the Foundations of Mathematics, v. 121). Volume I.
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