How to make tautologies clear?
##plugins.themes.bootstrap3.article.sidebar##
Published:
21.05.2019
##plugins.themes.bootstrap3.article.main##
Abstract
The paper shows how the first part of Peirce’s Existential Graphs theory answers Wittgenstein's question: “how must a system of signs be constituted in order to make every tautology recognizable as such in one and the same way?” Existential Graphs theory or Graphs theory is a diagrammatical system. Its basic unit is a graph or diagram that reminds Euler’s diagrams. The first part of the theory, which is alpha, corresponds, approximately, to classical propositional logic. The theory provides graphic or iconic syntax. So, it is clear why Wittgenstein's problem is also solved in an iconic way. Graphs let observe tautologies. No transformations are required to identify a formula type. The possibility to observe tautologies is due to not only the diagrammatical syntax peculiarities but also its minimalism. The cut (it is the boundary of a diagram) is the only sign of the alpha-graphs. It plays both technical and logical functions. The theory is even more concise than approaches with NAND or NOR operators. In light of the talk about tautologies, the paper concerns the problem of cut evolution. The cut is treated as negation, but it is a generated implication. Thus, implication but not negation and conjunction or disjunction is a primitive and most analytic sign. At first glance, it might look strange as the implication is the most complex logical connective. However, the implication tracks the idea of logical consequence and reflects its main properties, such as antisymmetry and transitivity.
##plugins.generic.usageStats.downloads##
##plugins.generic.usageStats.noStats##
##plugins.themes.bootstrap3.article.details##
How to Cite
Bobrova A. S. How to make tautologies clear? // Logicheskie Issledovaniya / Logical Investigations. 2019. VOL. 25. № 1. C. 20-36.
Issue
Section
Philosophy and Logic
References
Боброва, 2016 – Боброва А.С. Графы Пирса: особенности их построения и прочтения // Логико-философские штудии. Ежегодник Ассоциации логиков СанктПетербурга. Т. 14. СПб.: Изд-во РХГА, 2016. С. 76–90.
Боброва, 2018 – Боброва А.С. Диаграмматические теории (Дж. Венн, Ч.С. Пирс) и логическое следование. Учебное пособие. М.: ВАВТ, 2018. 48 с.
Боброва, 2019 – Боброва А.С. Обучение графами. Диаграммы Ч.С. Пирса и преподавание логики (в печати).
Витгенштейн, 1994 – Витгенштейн Л. Витгенштейн Л. Логико-философский трактат //Витгенштейн Л. Философские работы (часть I) / Пер. с нем. М.С. Козловой и Ю.А. Асеева. Ч. I. М.: Гнозис, 1994. С. 3–73. Цитируется как Тр. с последующим указанием номера части и параграфа.
Лихтарников, 1999 – Лихтарников Л.М., Сукачева Т.Г. Математическая логика. Курс лекций. М., 1999.
Bellucci, Pietarinen, 2016 – Bellucci F., Pietarinen A.-V. Existential Graphs As an Instrument of Logical Analysis: Part I. Alpha // The Review of Symbolic Logic. Vol. 9. No. 2. 2016. P. 209–237.
Bellucci, Pietarinen, 2017 – Bellucci F., Pietarinen A.-V. Two Dogmas of Diagrammatic Reasoning: a View from Existential Graphs // Peirce on Perception and Reasoning: From Icons to Logic /Ed. by K.A. Hull, R.K. Atkins. New York. NY: Routledge, 2017. P. 174–196.
D¨orfler, 2016 – D¨orfler W. Signs and Their Use: Peirce and Wittgenstein. Springer, Cham, 2016.
Kauffman, 2001 – Kauffman L. The Mathematics of Charles Sanders Peirce // Cybernetics & Human Knowing. Vol. 8. No. 1–2. 2001. P. 79–110.
Misak, 2016 – Misak C. Cambridge Pragmatism: From Peirce and James to Ramsey and Wittgenstein. Oxford University Press, 2016.
Nubiola, 1996 – Nubiola J. Scholarship On the Relations Between Ludwig Wittgenstein and Charles S. Peirce // Studies on the History of Logic. Proceedings of the III Symposium on History of Logic / Ed. by I. Angelelli y M. Cerezo. Berlin: Gruyter, 1996. P. 281–294.
Peirce, 1931–1958 – Peirce C.S. Collected Papers. Vols. 1–8. Cambridge: Belknap Press of Harvard University Press, 1931–1958. Цитируется как СР с номером тома и параграфа.
Peirce, 1967 – Peirce C.S. Peirce C.S. Manuscripts in the Houghton Library of Harvard University, as identified by Richard Robin // Annotated Catalogue of the Papers of Charles S. Peirce. Amherst. 1967. Цитируется как MS или R с номером манускрипта.
Pietarinen, 2005 – Pietarinen A.-V. Compositionality, Relevance and Peirce’s Logic of Existential Graphs // Axiomathes. No. 15, 2005. P. 513–540.
Pietarinen, 2006 – Pietarinen A.-V. Signs of Logic. Peircean Themes on the Philosophy of Language, Games, and Communication. Dordrecht: Springer, 2006. Pietarinen, 2015 – Pietarinen A.-V. Two Papers on Existential Graphs by Charles Peirce // Synthese. Vol. 192. No. 4. 2015. P. 881–922.
Roberts, 1973 – Roberts D. The Existential Graphs of Charles S. Peirce. The Hague: Mouton, 1973.
Wittgenstein, 2012 – Wittgenstein L. Wittgenstein in Cambridge. Letters and documents 1911–1951 / Ed. by B. McGuinness. Oxford: Blackwell, 2012.
Zeman, 1964 – Zeman J. The Graphical Logic of C.S. Peirce, dissertation, University of Chicago, 1964. Online edition, 2002. URL: users.clas.ufl.edu/jzeman/ (дата обращения: 15.01.2019).
Боброва, 2018 – Боброва А.С. Диаграмматические теории (Дж. Венн, Ч.С. Пирс) и логическое следование. Учебное пособие. М.: ВАВТ, 2018. 48 с.
Боброва, 2019 – Боброва А.С. Обучение графами. Диаграммы Ч.С. Пирса и преподавание логики (в печати).
Витгенштейн, 1994 – Витгенштейн Л. Витгенштейн Л. Логико-философский трактат //Витгенштейн Л. Философские работы (часть I) / Пер. с нем. М.С. Козловой и Ю.А. Асеева. Ч. I. М.: Гнозис, 1994. С. 3–73. Цитируется как Тр. с последующим указанием номера части и параграфа.
Лихтарников, 1999 – Лихтарников Л.М., Сукачева Т.Г. Математическая логика. Курс лекций. М., 1999.
Bellucci, Pietarinen, 2016 – Bellucci F., Pietarinen A.-V. Existential Graphs As an Instrument of Logical Analysis: Part I. Alpha // The Review of Symbolic Logic. Vol. 9. No. 2. 2016. P. 209–237.
Bellucci, Pietarinen, 2017 – Bellucci F., Pietarinen A.-V. Two Dogmas of Diagrammatic Reasoning: a View from Existential Graphs // Peirce on Perception and Reasoning: From Icons to Logic /Ed. by K.A. Hull, R.K. Atkins. New York. NY: Routledge, 2017. P. 174–196.
D¨orfler, 2016 – D¨orfler W. Signs and Their Use: Peirce and Wittgenstein. Springer, Cham, 2016.
Kauffman, 2001 – Kauffman L. The Mathematics of Charles Sanders Peirce // Cybernetics & Human Knowing. Vol. 8. No. 1–2. 2001. P. 79–110.
Misak, 2016 – Misak C. Cambridge Pragmatism: From Peirce and James to Ramsey and Wittgenstein. Oxford University Press, 2016.
Nubiola, 1996 – Nubiola J. Scholarship On the Relations Between Ludwig Wittgenstein and Charles S. Peirce // Studies on the History of Logic. Proceedings of the III Symposium on History of Logic / Ed. by I. Angelelli y M. Cerezo. Berlin: Gruyter, 1996. P. 281–294.
Peirce, 1931–1958 – Peirce C.S. Collected Papers. Vols. 1–8. Cambridge: Belknap Press of Harvard University Press, 1931–1958. Цитируется как СР с номером тома и параграфа.
Peirce, 1967 – Peirce C.S. Peirce C.S. Manuscripts in the Houghton Library of Harvard University, as identified by Richard Robin // Annotated Catalogue of the Papers of Charles S. Peirce. Amherst. 1967. Цитируется как MS или R с номером манускрипта.
Pietarinen, 2005 – Pietarinen A.-V. Compositionality, Relevance and Peirce’s Logic of Existential Graphs // Axiomathes. No. 15, 2005. P. 513–540.
Pietarinen, 2006 – Pietarinen A.-V. Signs of Logic. Peircean Themes on the Philosophy of Language, Games, and Communication. Dordrecht: Springer, 2006. Pietarinen, 2015 – Pietarinen A.-V. Two Papers on Existential Graphs by Charles Peirce // Synthese. Vol. 192. No. 4. 2015. P. 881–922.
Roberts, 1973 – Roberts D. The Existential Graphs of Charles S. Peirce. The Hague: Mouton, 1973.
Wittgenstein, 2012 – Wittgenstein L. Wittgenstein in Cambridge. Letters and documents 1911–1951 / Ed. by B. McGuinness. Oxford: Blackwell, 2012.
Zeman, 1964 – Zeman J. The Graphical Logic of C.S. Peirce, dissertation, University of Chicago, 1964. Online edition, 2002. URL: users.clas.ufl.edu/jzeman/ (дата обращения: 15.01.2019).