The House that Carroll Built: Regress and Adoption in Formal Justification
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26.06.2022
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Abstract
This paper addresses Lewis Carroll's infinite justification regress described in his essay “What the Tortoise said to Achilles”. It demonstrates that the discussions on justification regress, which is caused by turning а rule of inference into an additional premise of that inference, roots in the problem of topical justification in ancient and medieval logic. It is shown that Charles S. Peirce’s doctrine on guiding principles of reasoning, which was elaborated under a direct influence of scholastic logic, does not allow stopping the regress of justification. The paper also demonstrates the limitations of overcoming this regress in Gilbert Ryle’s dispositional interpretation of the logical knowing as knowing how. Special attention is paid to Sol Kripke's adoption problem, which questions the possibility of rationally adopting and revising the basic principles of logic. The paper reveals the inconsistency that Kripke’s interpretation of the “Cartesian” procedure of revising logical laws and principles has with Descartes’ theories of deduction and eternal truths. It argues for a dynamic approach to resolving the problem of adoption, which is related to overcoming the dichotomy of rules of inference, constitutive and non-constitutive for the meaning of logical constants in logical theory (logica docens). It also overcomes the opposition of the exhaustive logical knowing how and its total absence in the practice of real cognitive agents’ reasoning (logica utens). It is shown that the structural realignment of the logical system and the conceptual design of its key concepts are not being carried out in a sequential manner, but synchronically, due to the internal relations between these concepts. It attempts to provide a dynamic interpretation of a principle of compositionality, based on Ludwig Wittgenstein’s doctrine of internal relations.
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How to Cite
Dragalina-Chernaya E. G. The House that Carroll Built: Regress and Adoption in Formal Justification // Logicheskie Issledovaniya / Logical Investigations. 2022. VOL. 28. № 1. C. 27-49.
Issue
Section
Philosophy and Logic
Copyright (c) 2022 Елена Григорьевна Драгалина
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
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Декарт, 1989 – Декарт Р. Правила для руководства ума // Декарт Р. Соч. Т. 1. М.: Мысль, 1989. С. 80–153.
Декарт, 1994 – Декарт Р. Беседа с Бурманом // Декарт Р. Соч. Т. 2. М.: Мысль, 1994. С. 447–488.
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Bellucci, 2016 – Bellucci F. Charles S. Peirce and the Medieval Doctrine of consequentiae // History and Philosophy of Logic. 2016. Vol. 37. No. 3. P. 244–268.
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Boghossian, 2014 – Boghossian P. What is Inference? // Philosophical Studies. 2014.Vol. 169. No. 1. P. 1–18.
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Cohen, 2002 – Cohen S. Basic Knowledge and the Problem of Easy Knowledge // Philosophy and Phenomenological Research. 2002. Vol. 65. P. 309–329.
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Eklund, 2017 – Eklund M. Choosing Normative Concepts. Oxford: Oxford University Press, 2017. 224 p.
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Floridi, 2017 – Floridi L. The Logic of Design as a Conceptual Logic of Information // Minds and Machines. 2017. Vol. 28. P. 495–519.
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Hjortland, 2014 – Hjortland T. Verbal Disputes in Logic: Against Minimalism for Logical Connectives // Logique et Analyse. 2014. Vol. 57. No. 227. P. 463–486.
Kilwardby, 1989 – Kilwardby R. The Nature of Logic: Dialectic and Demonstration // Kretzmann N., Stump E. The Cambridge Translations of Medieval Philosophical Texts. Cambridge: Cambridge University Press, 1989. Р. 262–282.
MacFarlane, 2015 – MacFarlane J. Abelard’s Argument for Formality // Formal Approaches and Natural Language in Medieval Logic: Proceedings of the XIXth European Symposium of Medieval Logic and Semantics, Geneva, 12–16, June 2012. Turnhout: Brepols, 2015. P. 41–57.
Malink, 2015 – Malink M. The Beginnings of Formal Logic: Deduction in Aristotle’s Topics vs. Prior Analytics // Phronesis. 2015. Vol. 60. P. 267–309.
Padr´o, 2015 – Padr´o R. What the Tortoise Said to Kripke: the Adoption Problem and the Epistemology of Logic. A dissertation submitted to the Graduate Faculty in Philosophy. The City University of New York, 2015. 247 р.
Paoli, 2003 – Paoli F. Quine and Slater on Paraconsistency and Deviance // Journal of Philosophical Logic. 2003. Vol. 32. No. 9. P. 531–548.
Peirce, 1984 – Peirce C.S. Writings of Charles S. Peirce. A Chronological Edition. Vol. 2 (1867–1871) / Ed. by E.C. Moore. Indianapolis: Indiana Univ. Press, 1984. 649 р.
Pietarinen, Bellucci, 2015 – Pietarinen A.-V., Bellucci F. Habits of Reasoning: On the Grammar and Critics of Logical Habits // Habit: Before and Beyond Consciousness / Ed. By D. West, M. Anderson. Dordrecht: Springer, 2015. Р. 265–282.
Putnam, 1976 – Putnam H. The Logic of Quantum Mechanics // Putnam H. Mathematics, Matter and Method, Cambridge: Cambridge University Press, 1976. P. 174–197.
Quine, 1936 – Quine W.V.O. Truth by Convention // Philosophical Essays for A.N. Whitehead. Longmans, 1936. P. 90–124.
Quine, 1951 – Quine W.V.O. Two Dogmas of Empiricism // The Philosophical Review. 1951. Vol. 60. P. 20–43.
Restall, 2002 – Restall G. Carnap’s Tolerance, Language Change, and Logical Pluralism // Journal of Philosophy. 2002. Vol. 99. No. 8. P. 426–443.
Ryle, 1945–1946 – Ryle G. Knowing How and Knowing That // Proceedings of the Aristotelian Society, 1945–1946. Vol. 46. P. 1–16.
Ryle, 2009 – Ryle G. ‘If ’, ‘So’, and ‘Because’ // Ryle G. Collected Essays 1929–1968. Vol. 2. Routledge, 2009. Р. 244–260.
Sosa, 2009 – Sosa E. Reflective Knowledge. Oxford: Oxford University Press. 2009. 240 р.
Stanovich, West, 2000 – Stanovich K., West R. Individual Differences in Reasoning: Implications for the Rationality Debate // Behavioral and Brain Sciences. 2000. Vol. 23. No. 5. P. 645–665.
Stjernfelt, 2015 – Stjernfelt F. Blocking Evil Infinites: A note on a Note on a Peircean Strategy // Sign Systems Studies. 2015. Vol. 43. No. 4. P. 518–522.
Thom, 2013 – Thom P. Robert Kilwardby on Syllogistic Form // Ed. by P. Thom. A Companion to the Philosophy of Robert Kilwardby. Brill, Leiden/Boston, 2013. P. 131–163.
Van Benthem, 2007a – van Benthem J. Logic in Philosophy // Philosophy of Logic / Ed. by D. Jacquette, et al. Amsterdam: Elsevier, 2007. P. 65–99.
Van Benthem, 2007b – van Benthem J. Abduction at the Interface of Logic and Philosophy of Science // Theoria. 2007. Vol. 22. No. 3. P. 271–273.
Wansing, 2000 – Wansing H. The Idea of a Proof-Theoretic Semantics and the Meaning of the Logical Operations // Studia Logica. 2000. Vol. 64. P. 3–20. Williamson, 2017 – Williamson T. Semantic Paradoxes and Abductive Methodology // The Relevance of the Liar / Ed. by B. Armour-Garb. Oxford: OUP, 2017. P. 325–346.
Wittgenstein, 1976 – Wittgenstein L. Wittgenstein’s Lectures on the Foundations of Mathematics, Cambridge 1939 / Ed. by C. Diamond. The Harvester Press Ltd., Hassocks, Sussex, 1976. 300 р.
Wittgenstein, 1979 – Wittgenstein L. Wittgenstein’s Lectures, Cambridge, 19321935 / Ed. by A. Ambrose. Basil Blackwell, Oxford, 1979. 238 p.
Wright, 2007 – Wright C. Rule-following without Reasons: Wittgenstein’s Quietism and the Constitutive Question // Ratio. 2007. Vol. 20. No. 4. P. 481–502.
Аристотель, 1978b – Аристотель. Вторая Аналитика // Аристотель. Соч.: В 4 т.Т. 2. М.: Мысль, 1978. С. 255–376.
Витгенштейн, 1994а – Витгенштейн Л. Философские исследования // Витгенштейн Л. Философские работы (часть 1). М.: Гнозис, 1994. С. 75–319.
Витгенштейн, 1994b – Витгенштейн Л. О достоверности //Витгенштейн Л. Философские работы (часть 1). М.: Гнозис, 1994. С. 321–406.
Витгенштейн, 1994с – Витгенштейн Л. Замечания по основаниям математики // Витгенштейн Л. Философские работы (часть II, книга 1). М.: Гнозис, 1994. 207 с.
Витгенштейн, 2008 – Витгенштейн Л. Логико-философский трактат. М.: Канон+, 2008. 288 с.
Витгенштейн, 2020 – Витгенштейн Л. Заметки о цвете (избранные фрагменты) // Вопросы философии. 2020. № 6. С. 157–168.
Декарт, 1989 – Декарт Р. Правила для руководства ума // Декарт Р. Соч. Т. 1. М.: Мысль, 1989. С. 80–153.
Декарт, 1994 – Декарт Р. Беседа с Бурманом // Декарт Р. Соч. Т. 2. М.: Мысль, 1994. С. 447–488.
Драгалина-Черная, 2020 – Драгалина-Черная Е.Г. Материальное следование и формальное обоснование // Эпистемология и философия науки. 2020. Т. 57. № 2. С. 79–95.
Коэн, Нагель, 2010 – Коэн М., Нагель Э. Введение в логику и научный метод. Челябинск: Социум, 2010. 655 с.
Куайн, 2000 – Куайн У. Слово и объект. М.: Логос, Пракисис, 2000. 386 с. Кэрролл, 1985 – Кэрролл Л. Что Черепаха сказала Ахиллу // Кэрролл Л. История с узелками. М.: Мир, 1985. С. 368–372.
Лакофф, 2004 – Лакофф Дж. Женщины, огонь и опасные вещи. Что категории языка говорят нам о мышлении. М.: Языки славянской культуры, 2004. 792 с.
Пирс, 2005 – Пирс Ч.С. Рассуждение и логика вещей. М.: РГГУ, 2005. 371 с. Райл, 1999 – Райл Г. Понятие познания. М.: Идея-Пресс, 1999. 408 с.
Abelard, 1970 – Abelard P. Dialectica / Ed. by L.M. de Rijk. Assen: Van Gorcum & Co, 1970. 669 p.
Aho, Yrjonsuuri, 2009 – Aho Т., Yrj¨onsuuri М. Late Medieval Logic // The Development of Modern Logic / Ed. by L. Haaparanta, Oxford: Oxford University Press, 2009. P. 11–77.
Arnold, Shapiro, 2007 – Arnold J., Shapiro S. Where in the (World Wide) Web of Belief Is the Law of Non-contradiction? // Noˆus. 2007. Vol. 41. No. 2. P. 276–297.
Allo, 2017 – Allo P. A Constructionist Philosophy of Logic // Minds and Machines. 2017. Vol. 27. P. 545–564.
Bellucci, 2016 – Bellucci F. Charles S. Peirce and the Medieval Doctrine of consequentiae // History and Philosophy of Logic. 2016. Vol. 37. No. 3. P. 244–268.
Boghossian, 2000 – Boghossian P. Knowledge of Logic // New Essays on the A Priori / Ed. by P. Boghossian, C.Peacocke, Oxford: Oxford University Press, 2000. Р. 229–254.
Boghossian, 2014 – Boghossian P. What is Inference? // Philosophical Studies. 2014.Vol. 169. No. 1. P. 1–18.
Carnap, 1937 – Carnap R. The Logical Syntax of Language. London: Kegan Paul, 1937. 352 p.
Cohen, 2002 – Cohen S. Basic Knowledge and the Problem of Easy Knowledge // Philosophy and Phenomenological Research. 2002. Vol. 65. P. 309–329.
Dicher, 2016 – Dicher В. A Proof-Theoretic Defence of Meaning-Invariant Logical Pluralism // Mind. 2016. Vol. 125. No. 499. P. 727–757.
Dogson, 1977 – Dogson C.L. Lewis Carroll’s Symbolic Logic. New York: Clarkson Potter, 1977. 496 p.
Dragalina-Chernaya, 2019 – Dragalina-Chernaya E. Surprises in Logic: When Dynamic Formality Meets Interactive Compositionality // Philosophy of Logic and Mathematics / Ed. by G. Mras, P. Weingartner, B. Ritter. Berlin, Boston: De Gruyter, 2019. P. 197–212.
Eklund, 2017 – Eklund M. Choosing Normative Concepts. Oxford: Oxford University Press, 2017. 224 p.
Engel, 1998 – Engel P. La logique peut-elle mouvoir l’esprit? // Dialogue. 1998. Vol. 37. No. 1. P. 1–27.
Floridi, 2008 – Floridi L. The Method of Levels of Abstraction // Minds and Machines. 2008. Vol. 18. No. 3. P. 303–329.
Floridi, 2017 – Floridi L. The Logic of Design as a Conceptual Logic of Information // Minds and Machines. 2017. Vol. 28. P. 495–519.
Floridi, 2019 – Floridi L. The Logic of Information: A Theory of Philosophy as Conceptual Design. Oxford, 2019. 272 p.
Hjortland, 2014 – Hjortland T. Verbal Disputes in Logic: Against Minimalism for Logical Connectives // Logique et Analyse. 2014. Vol. 57. No. 227. P. 463–486.
Kilwardby, 1989 – Kilwardby R. The Nature of Logic: Dialectic and Demonstration // Kretzmann N., Stump E. The Cambridge Translations of Medieval Philosophical Texts. Cambridge: Cambridge University Press, 1989. Р. 262–282.
MacFarlane, 2015 – MacFarlane J. Abelard’s Argument for Formality // Formal Approaches and Natural Language in Medieval Logic: Proceedings of the XIXth European Symposium of Medieval Logic and Semantics, Geneva, 12–16, June 2012. Turnhout: Brepols, 2015. P. 41–57.
Malink, 2015 – Malink M. The Beginnings of Formal Logic: Deduction in Aristotle’s Topics vs. Prior Analytics // Phronesis. 2015. Vol. 60. P. 267–309.
Padr´o, 2015 – Padr´o R. What the Tortoise Said to Kripke: the Adoption Problem and the Epistemology of Logic. A dissertation submitted to the Graduate Faculty in Philosophy. The City University of New York, 2015. 247 р.
Paoli, 2003 – Paoli F. Quine and Slater on Paraconsistency and Deviance // Journal of Philosophical Logic. 2003. Vol. 32. No. 9. P. 531–548.
Peirce, 1984 – Peirce C.S. Writings of Charles S. Peirce. A Chronological Edition. Vol. 2 (1867–1871) / Ed. by E.C. Moore. Indianapolis: Indiana Univ. Press, 1984. 649 р.
Pietarinen, Bellucci, 2015 – Pietarinen A.-V., Bellucci F. Habits of Reasoning: On the Grammar and Critics of Logical Habits // Habit: Before and Beyond Consciousness / Ed. By D. West, M. Anderson. Dordrecht: Springer, 2015. Р. 265–282.
Putnam, 1976 – Putnam H. The Logic of Quantum Mechanics // Putnam H. Mathematics, Matter and Method, Cambridge: Cambridge University Press, 1976. P. 174–197.
Quine, 1936 – Quine W.V.O. Truth by Convention // Philosophical Essays for A.N. Whitehead. Longmans, 1936. P. 90–124.
Quine, 1951 – Quine W.V.O. Two Dogmas of Empiricism // The Philosophical Review. 1951. Vol. 60. P. 20–43.
Restall, 2002 – Restall G. Carnap’s Tolerance, Language Change, and Logical Pluralism // Journal of Philosophy. 2002. Vol. 99. No. 8. P. 426–443.
Ryle, 1945–1946 – Ryle G. Knowing How and Knowing That // Proceedings of the Aristotelian Society, 1945–1946. Vol. 46. P. 1–16.
Ryle, 2009 – Ryle G. ‘If ’, ‘So’, and ‘Because’ // Ryle G. Collected Essays 1929–1968. Vol. 2. Routledge, 2009. Р. 244–260.
Sosa, 2009 – Sosa E. Reflective Knowledge. Oxford: Oxford University Press. 2009. 240 р.
Stanovich, West, 2000 – Stanovich K., West R. Individual Differences in Reasoning: Implications for the Rationality Debate // Behavioral and Brain Sciences. 2000. Vol. 23. No. 5. P. 645–665.
Stjernfelt, 2015 – Stjernfelt F. Blocking Evil Infinites: A note on a Note on a Peircean Strategy // Sign Systems Studies. 2015. Vol. 43. No. 4. P. 518–522.
Thom, 2013 – Thom P. Robert Kilwardby on Syllogistic Form // Ed. by P. Thom. A Companion to the Philosophy of Robert Kilwardby. Brill, Leiden/Boston, 2013. P. 131–163.
Van Benthem, 2007a – van Benthem J. Logic in Philosophy // Philosophy of Logic / Ed. by D. Jacquette, et al. Amsterdam: Elsevier, 2007. P. 65–99.
Van Benthem, 2007b – van Benthem J. Abduction at the Interface of Logic and Philosophy of Science // Theoria. 2007. Vol. 22. No. 3. P. 271–273.
Wansing, 2000 – Wansing H. The Idea of a Proof-Theoretic Semantics and the Meaning of the Logical Operations // Studia Logica. 2000. Vol. 64. P. 3–20. Williamson, 2017 – Williamson T. Semantic Paradoxes and Abductive Methodology // The Relevance of the Liar / Ed. by B. Armour-Garb. Oxford: OUP, 2017. P. 325–346.
Wittgenstein, 1976 – Wittgenstein L. Wittgenstein’s Lectures on the Foundations of Mathematics, Cambridge 1939 / Ed. by C. Diamond. The Harvester Press Ltd., Hassocks, Sussex, 1976. 300 р.
Wittgenstein, 1979 – Wittgenstein L. Wittgenstein’s Lectures, Cambridge, 19321935 / Ed. by A. Ambrose. Basil Blackwell, Oxford, 1979. 238 p.
Wright, 2007 – Wright C. Rule-following without Reasons: Wittgenstein’s Quietism and the Constitutive Question // Ratio. 2007. Vol. 20. No. 4. P. 481–502.