Vindicating the Frege Project. The Priority of the Propositions and the Expressive Character of Logic
Keywords:
Compositionality, Concept-script, Inferentialism, Judgeable Content, Logical Constant, Logical Expressivism
Abstract
Frege is widely considered as the father of contemporary logic and analytical philosophy. Nevertheless, a closer look to Frege’s work makes clear that the formalist paroxysm which defines contemporary logic and formal semantics has overlooked substantial parts of Frege’s original project. For this reason, it becomes urgent to re-examine that project in search of illumination about what we are doing when doing logic. The purpose of this paper is to study in particular how Frege dealt with logical constants while developing his ideography as an instrument for the representation of inferences. We expect to obtain thus a new and better understanding of the contributions that Frege made to the development of logic and semantics that overcome the limits drawn by the Hilbert-Tarskian tradition.
References
Bell, David (1979). Frege’s Theory of Judgement. Oxford: Oxford University Press.
Bolzano, Bernard (1837). The Theory of Science. Die Wissenschaftslehre oder Versuch einer Neuen Darstellung der Logik / Attempt at a Detailed and in the Main Novel Exposition of Logic with Constant Attention to Earlier Authors. Editado y traducido por Rolf George. Berkeley–Los Angeles: The Univesity of California Press, 1972.
Boolos, George (1999). Logic, Logic, Logic. Introducción de John P. Burgess y edición de Richard Jeffrey. Cambridge, MA: Harvard University Press.
Brandom, Robert (1994). Making it Explicit. Reasoning, Representing, and Discoursive Committment. Cambridge, MA: Harvard University Press
Brandom, Robert (2000). Articulating Reasons. An Introduction to Inferentialism. Cambridge, MA: Harvard University Press
Carnap, Rudolf (1947). Meaning and Necessity, A Sudy in Semantics and Modal Logic. Chicago, IL: The University of Chicago Press
Dedekind, Richard (1888). «Was sind und was sollen die Zahlen?». En: Gesammelte mathematische Werke. Vol. 3. Braunschweig: Vieweg, 1932, pp. 335–391.
Dedekind, Richard (1901). «Continuity and irrational numbers». En: Essays on the Theory of Numbers: I. Continuity and irrational numbers, II. The nature and meaning of numbers. Traducción autorizada por Wooster Woodruff Beman. Chicago: The Open Court Publishing Company, pp. 1–27.
Dummett, Michael (1973). Frege. Philosophy of Language. New York: Haper and Row Publishers.
Frápolli, María J. (2005). Frank Plumpton Ramsey. Obra Filosófica Completa. Edición, introducción y traducción. Granada: Comares
Frápolli, María J. y Villanueva, Neftalí (2016). «Pragmatism. Propositional Priority and The Organic Model of Propositional Individuation». Disputatio 43: pp. 203–217.
Frápolli, María J. y Villanueva, Neftalí (2015). «Expressivism, Relativism, and the Analytic Equivalence Test». Frontiers in psychology. doi: 10.3389/fpsyg.2015.01788
Frege, Gottlob (1879). Conceptografía. Los fundamentos de la aritmética. Otros estudios filosóficos. Traducción de Hugo Padilla. Instituto de Investigaciones Filosóficas, Universidad nacional Autónoma de México, 1972
Frege, Gottlob (1884). «Los Fundamentos de la Aritmética». En: Escritos Filosóficos. Barcelona: Crítica, 1996, pp. 31–144.
Frege, Gottlob (1974). Escritos lógico–semánticos. Traducción de Carlos R. Luis y Carlos Pereda Madrid, Tecnos
Frege, Gottlob (1996). Escritos Filosóficos. Edición e introducción de Jesús Mosterín. Traducción de Ulises Moulines y Andrés Rivadulla. Barcelona: Crítica
Frege, Gottlob (1998). Ensayos de semántica y filosofía de la lógica. Edición, introducción, traducción y notas de Luis M. Valdés Villanueva. Madrid: Tecnos
Frege, Gottlob (1879). «Begriffsschrift, a formula language modeled upon that of arithmetic, for pure thought». En: From Frege to Gödel. A source book on mathematical logic, 1879–1931, editado por Jean van Heijenoort. Cambridge, MA: Harvard University Press, 1967. p. 1–82.
Frege, Gottlob (1880–1). «Boole’s logical Calculus and the Concept–script». En: Posthumous Writings. Oxford: Basil Blackwell, 1979, pp. 9–46.
Frege, Gottlob (1879–1891). «Logic». En: Posthumous Writings. Oxford: Basil Blackwell, 1979, pp. 1–8.
Frege, Gottlob (1892). «On sense and meaning». En: Collected papers on Mathematics, Logic and Philosophy. Oxford: Basil Blackwell, 1984, pp. 57–177.
Frege, Gottlob (1914). «My basic logical insights». En: Posthumous Writings. Oxford: Basil Blackwell, 1979, pp. 251–252.
Frege, Gottlob (1915). «Logic in Mathematics». En: Posthumous Writings. Oxford: Basil Blackwell, 1979, pp. 203–250.
Frege, Gottlob (1918–19a). «Thought». En: Collected papers on Mathematics, Logic and Philosophy. Oxford: Basil Blackwell, 1984, pp. 351–372.
Frege, Gottlob (1918–19b). «Negation». En: Collected papers on Mathematics, Logic and Philosophy. Oxford: Basil Blackwell, 1984, pp. 373–389.
Frege, Gottlob (1923–6). «Compound Thoughts». En: Collected papers on Mathematics, Logic and Philosophy. Oxford: Basil Blackwell, 1984, pp. 390–406.
Frege, Gottlob (1923). «Logical generality». En: Posthumous Writings. Oxford: Basil Blackwell, 1979, pp. 258–262.
Frege, Gottlob (1979). Posthumous Writings. Edición de Hans Hermes, Friedrich Kambartel y Friedrich Kaulbach. Traducción de Peter Long y Roger White. Oxford: Basil Blackwell.
Frege, Gottlob (1984). Collected papers on Mathematics, Logic and Philosophy. Editado por Brian McGuinness. Traducción de Max Black, V. H. Dudman, Peter Geach, Hans Kaal, E. H. W. Kluge, Brian McGuinness y R. H. Stoothoff. Oxford: Basil Blackwell.
Frege, Gottlob (1884). The Foundations of Mathematics. A logico–mathematical enquiry on the concept of number. Traducción de J. L. Austin. New York: Harper Torchbook, 1960.
Frege, Gottlob (1980). Philosophical and Mathematical Correspondence. Edición de Gottfried Gabriel, Hans Hermes, Friedrich Kambartel, Christian Thiel, Albert Veraart. Edición abreviada de la alemana de Brian McGuinness. Traducción de Hans Kaal. Chicago, IL: University of Chicago Press.
Geach, Peter y Black, Max (1960). Translations from the Philosophical Writings of Gottlob Frege. Oxford: Basil Blackwell.
Haack, Susan. (1978). Filosofía de las Lógicas. Madrid: Tecnos, 1982.
Haaparanta, Leila (ed.) (2009). The Development of Modern Logic. Oxford–Nueva York: Oxford University Press. doi: 10.1093/acprof:oso/9780195137316.001.0001
Hacker, Peter Michael Stephan y Baker, Gordon Park (1984). Frege: Logical Excavations. Oxford: Basil Blackwell.
Klima, Gyula (2005). «Syncategoremata». En: Encyclopedia of Language and Linguistic, editada por Keith Brown. Vol. 12. 2da. Ed. Boston: Elsevier Science, pp. 353–356
Kneale, William y Kneale, Martha (1962). The Development of Logic. Oxford: Clarendon Press
Kripke, Saul (1980). Naming and Necessity. Cambridge, MA: Harvard Univesity Press.
Linsky, Leonard (1977). Names and Descriptions. Chicago, IL: University of Chicago Press.
Margalit, Avishai (1978). «The «Platitude» Principle of Semantics». Erkenntnis, 13 (3): pp. 377–395. doi: 10.1007/BF00160904
Pelletier, Francis Jeffry (2001). «Did Frege believe in Frege’s Principle?». Journal of Logic, Language, and Information 10: pp. 87–114. doi: 10.1023/A:1026594023292
Pelletier, Francis Jeffry (2012). «Holism and Compositionality». En: The Oxford Handbook of Compositionality, editado por Markus Werning, Wolfram Hinzen, y Edouard Machery, Oxford–Nueva York: Oxford University Press. doi: 10.1093/oxfordhb/9780199541072.013.0007
Prior, Arthur N. (1963). «Is the Concept of Referential Opacity Really Necessary?». Acta Philosophica Fennica 16: pp. 189–98.
Putnam, Hilary (1990). Realism with a Human Face. Cambridge, MA: Harvard University Press.
Russell, Bertrand y Whitehead, Alfred North (1927). Principia Mathematica. Cambridge: Cambridge University Press.
Salmon, Nathan U. (1986). Frege’s Puzzle. Cambridge, MA: MIT Press.
Sandu, Gabriel y Hintikka, Jaakko (2001). «Aspects of Compositionality». Journal of Logic, Language, and Information 10: pp. 49–61. doi: 10.1023/A:1026530709583
Schiffrin, Deborah (1987). Discourse Markers. Cambridge: Cambridge University Press. doi: 10.1017/CBO9780511611841
Sundholm, Göran (2009). «A Century of Judgment and Inference, 1837–1936: Some Strands in the Development of Logic». En: The Development of Modern Logic, editado por Leila Haaparanta. Oxford–Nueva York: Oxford University Press: pp. 263–317. doi: 10.1093/acprof:oso/9780195137316.003.0028
Thiel, Christian (2009). «Gottlob Frege and the Interplay between Logic and Mathematics». En: The Development of Modern Logic, editado por Leila Haaparanta. Oxford–Nueva York: Oxford University Press: pp. 196–202. doi: 10.1093/acprof:oso/9780195137316.003.0020
Tarski, Alfred (1934/1983). «On the concept of logical consequence». En: Logic, semantics, metamathematics. Edición, introducción e índice de John Corcoran. Traducción de J. H. Woodger. Indianapolis: Hackett Publishing Company.
Van Heijenoort, Jean (ed.) (1967). From Frege to Gödel. A source book on mathematical logic, 1879–1931. Cambridge, MA: Harvard University Press.
Warmbrõd, Ken (1999). «Logical Constants». Mind 108 (431): pp. 503–538. doi: 10.1093/mind/108.431.503
Wiggins, David (1965). «Identity Statements». En: Analytical Philosophy, editado por R. J. Butler. 2da. Ed. Oxford: Basil Blackwell, pp. 40–71.
Wiggins, David (1976). «Frege’s Problem of the Morning Star and the Evening Star». En: Studien zu Frege II Logik und Sprachphilosophie. Studies on Frege II Logic and Philosophy of Language, editado por Matthias Schirn. Stuttgart–Bad Cannstatt: Günthner Holzboog, pp. 221–225.
Taschek, William W. (1992). «Frege’s Puzzle, Sense, and Information Content». Mind 101: pp. 767–791. doi: 10.1093/mind/101.404.767
Wittgenstein, Ludwig. (1996). «Notes on Logic». En: Editing Wittgenstein’s «Notes on Logic» (Vol. 2), editado por Michael A. R. Biggs. Working papers from the Wittgenstein Archives at the University of Bergen 11: pp. 5–152.
Bolzano, Bernard (1837). The Theory of Science. Die Wissenschaftslehre oder Versuch einer Neuen Darstellung der Logik / Attempt at a Detailed and in the Main Novel Exposition of Logic with Constant Attention to Earlier Authors. Editado y traducido por Rolf George. Berkeley–Los Angeles: The Univesity of California Press, 1972.
Boolos, George (1999). Logic, Logic, Logic. Introducción de John P. Burgess y edición de Richard Jeffrey. Cambridge, MA: Harvard University Press.
Brandom, Robert (1994). Making it Explicit. Reasoning, Representing, and Discoursive Committment. Cambridge, MA: Harvard University Press
Brandom, Robert (2000). Articulating Reasons. An Introduction to Inferentialism. Cambridge, MA: Harvard University Press
Carnap, Rudolf (1947). Meaning and Necessity, A Sudy in Semantics and Modal Logic. Chicago, IL: The University of Chicago Press
Dedekind, Richard (1888). «Was sind und was sollen die Zahlen?». En: Gesammelte mathematische Werke. Vol. 3. Braunschweig: Vieweg, 1932, pp. 335–391.
Dedekind, Richard (1901). «Continuity and irrational numbers». En: Essays on the Theory of Numbers: I. Continuity and irrational numbers, II. The nature and meaning of numbers. Traducción autorizada por Wooster Woodruff Beman. Chicago: The Open Court Publishing Company, pp. 1–27.
Dummett, Michael (1973). Frege. Philosophy of Language. New York: Haper and Row Publishers.
Frápolli, María J. (2005). Frank Plumpton Ramsey. Obra Filosófica Completa. Edición, introducción y traducción. Granada: Comares
Frápolli, María J. y Villanueva, Neftalí (2016). «Pragmatism. Propositional Priority and The Organic Model of Propositional Individuation». Disputatio 43: pp. 203–217.
Frápolli, María J. y Villanueva, Neftalí (2015). «Expressivism, Relativism, and the Analytic Equivalence Test». Frontiers in psychology. doi: 10.3389/fpsyg.2015.01788
Frege, Gottlob (1879). Conceptografía. Los fundamentos de la aritmética. Otros estudios filosóficos. Traducción de Hugo Padilla. Instituto de Investigaciones Filosóficas, Universidad nacional Autónoma de México, 1972
Frege, Gottlob (1884). «Los Fundamentos de la Aritmética». En: Escritos Filosóficos. Barcelona: Crítica, 1996, pp. 31–144.
Frege, Gottlob (1974). Escritos lógico–semánticos. Traducción de Carlos R. Luis y Carlos Pereda Madrid, Tecnos
Frege, Gottlob (1996). Escritos Filosóficos. Edición e introducción de Jesús Mosterín. Traducción de Ulises Moulines y Andrés Rivadulla. Barcelona: Crítica
Frege, Gottlob (1998). Ensayos de semántica y filosofía de la lógica. Edición, introducción, traducción y notas de Luis M. Valdés Villanueva. Madrid: Tecnos
Frege, Gottlob (1879). «Begriffsschrift, a formula language modeled upon that of arithmetic, for pure thought». En: From Frege to Gödel. A source book on mathematical logic, 1879–1931, editado por Jean van Heijenoort. Cambridge, MA: Harvard University Press, 1967. p. 1–82.
Frege, Gottlob (1880–1). «Boole’s logical Calculus and the Concept–script». En: Posthumous Writings. Oxford: Basil Blackwell, 1979, pp. 9–46.
Frege, Gottlob (1879–1891). «Logic». En: Posthumous Writings. Oxford: Basil Blackwell, 1979, pp. 1–8.
Frege, Gottlob (1892). «On sense and meaning». En: Collected papers on Mathematics, Logic and Philosophy. Oxford: Basil Blackwell, 1984, pp. 57–177.
Frege, Gottlob (1914). «My basic logical insights». En: Posthumous Writings. Oxford: Basil Blackwell, 1979, pp. 251–252.
Frege, Gottlob (1915). «Logic in Mathematics». En: Posthumous Writings. Oxford: Basil Blackwell, 1979, pp. 203–250.
Frege, Gottlob (1918–19a). «Thought». En: Collected papers on Mathematics, Logic and Philosophy. Oxford: Basil Blackwell, 1984, pp. 351–372.
Frege, Gottlob (1918–19b). «Negation». En: Collected papers on Mathematics, Logic and Philosophy. Oxford: Basil Blackwell, 1984, pp. 373–389.
Frege, Gottlob (1923–6). «Compound Thoughts». En: Collected papers on Mathematics, Logic and Philosophy. Oxford: Basil Blackwell, 1984, pp. 390–406.
Frege, Gottlob (1923). «Logical generality». En: Posthumous Writings. Oxford: Basil Blackwell, 1979, pp. 258–262.
Frege, Gottlob (1979). Posthumous Writings. Edición de Hans Hermes, Friedrich Kambartel y Friedrich Kaulbach. Traducción de Peter Long y Roger White. Oxford: Basil Blackwell.
Frege, Gottlob (1984). Collected papers on Mathematics, Logic and Philosophy. Editado por Brian McGuinness. Traducción de Max Black, V. H. Dudman, Peter Geach, Hans Kaal, E. H. W. Kluge, Brian McGuinness y R. H. Stoothoff. Oxford: Basil Blackwell.
Frege, Gottlob (1884). The Foundations of Mathematics. A logico–mathematical enquiry on the concept of number. Traducción de J. L. Austin. New York: Harper Torchbook, 1960.
Frege, Gottlob (1980). Philosophical and Mathematical Correspondence. Edición de Gottfried Gabriel, Hans Hermes, Friedrich Kambartel, Christian Thiel, Albert Veraart. Edición abreviada de la alemana de Brian McGuinness. Traducción de Hans Kaal. Chicago, IL: University of Chicago Press.
Geach, Peter y Black, Max (1960). Translations from the Philosophical Writings of Gottlob Frege. Oxford: Basil Blackwell.
Haack, Susan. (1978). Filosofía de las Lógicas. Madrid: Tecnos, 1982.
Haaparanta, Leila (ed.) (2009). The Development of Modern Logic. Oxford–Nueva York: Oxford University Press. doi: 10.1093/acprof:oso/9780195137316.001.0001
Hacker, Peter Michael Stephan y Baker, Gordon Park (1984). Frege: Logical Excavations. Oxford: Basil Blackwell.
Klima, Gyula (2005). «Syncategoremata». En: Encyclopedia of Language and Linguistic, editada por Keith Brown. Vol. 12. 2da. Ed. Boston: Elsevier Science, pp. 353–356
Kneale, William y Kneale, Martha (1962). The Development of Logic. Oxford: Clarendon Press
Kripke, Saul (1980). Naming and Necessity. Cambridge, MA: Harvard Univesity Press.
Linsky, Leonard (1977). Names and Descriptions. Chicago, IL: University of Chicago Press.
Margalit, Avishai (1978). «The «Platitude» Principle of Semantics». Erkenntnis, 13 (3): pp. 377–395. doi: 10.1007/BF00160904
Pelletier, Francis Jeffry (2001). «Did Frege believe in Frege’s Principle?». Journal of Logic, Language, and Information 10: pp. 87–114. doi: 10.1023/A:1026594023292
Pelletier, Francis Jeffry (2012). «Holism and Compositionality». En: The Oxford Handbook of Compositionality, editado por Markus Werning, Wolfram Hinzen, y Edouard Machery, Oxford–Nueva York: Oxford University Press. doi: 10.1093/oxfordhb/9780199541072.013.0007
Prior, Arthur N. (1963). «Is the Concept of Referential Opacity Really Necessary?». Acta Philosophica Fennica 16: pp. 189–98.
Putnam, Hilary (1990). Realism with a Human Face. Cambridge, MA: Harvard University Press.
Russell, Bertrand y Whitehead, Alfred North (1927). Principia Mathematica. Cambridge: Cambridge University Press.
Salmon, Nathan U. (1986). Frege’s Puzzle. Cambridge, MA: MIT Press.
Sandu, Gabriel y Hintikka, Jaakko (2001). «Aspects of Compositionality». Journal of Logic, Language, and Information 10: pp. 49–61. doi: 10.1023/A:1026530709583
Schiffrin, Deborah (1987). Discourse Markers. Cambridge: Cambridge University Press. doi: 10.1017/CBO9780511611841
Sundholm, Göran (2009). «A Century of Judgment and Inference, 1837–1936: Some Strands in the Development of Logic». En: The Development of Modern Logic, editado por Leila Haaparanta. Oxford–Nueva York: Oxford University Press: pp. 263–317. doi: 10.1093/acprof:oso/9780195137316.003.0028
Thiel, Christian (2009). «Gottlob Frege and the Interplay between Logic and Mathematics». En: The Development of Modern Logic, editado por Leila Haaparanta. Oxford–Nueva York: Oxford University Press: pp. 196–202. doi: 10.1093/acprof:oso/9780195137316.003.0020
Tarski, Alfred (1934/1983). «On the concept of logical consequence». En: Logic, semantics, metamathematics. Edición, introducción e índice de John Corcoran. Traducción de J. H. Woodger. Indianapolis: Hackett Publishing Company.
Van Heijenoort, Jean (ed.) (1967). From Frege to Gödel. A source book on mathematical logic, 1879–1931. Cambridge, MA: Harvard University Press.
Warmbrõd, Ken (1999). «Logical Constants». Mind 108 (431): pp. 503–538. doi: 10.1093/mind/108.431.503
Wiggins, David (1965). «Identity Statements». En: Analytical Philosophy, editado por R. J. Butler. 2da. Ed. Oxford: Basil Blackwell, pp. 40–71.
Wiggins, David (1976). «Frege’s Problem of the Morning Star and the Evening Star». En: Studien zu Frege II Logik und Sprachphilosophie. Studies on Frege II Logic and Philosophy of Language, editado por Matthias Schirn. Stuttgart–Bad Cannstatt: Günthner Holzboog, pp. 221–225.
Taschek, William W. (1992). «Frege’s Puzzle, Sense, and Information Content». Mind 101: pp. 767–791. doi: 10.1093/mind/101.404.767
Wittgenstein, Ludwig. (1996). «Notes on Logic». En: Editing Wittgenstein’s «Notes on Logic» (Vol. 2), editado por Michael A. R. Biggs. Working papers from the Wittgenstein Archives at the University of Bergen 11: pp. 5–152.
Published
2017-12-22
How to Cite
[1]
Frápolli, M.J. 2017. Vindicating the Frege Project. The Priority of the Propositions and the Expressive Character of Logic. Disputatio. 6, 7 (Dec. 2017), 1-42. DOI:https://doi.org/10.5281/zenodo.1488197.
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