Skip to main content
SpringerLink
Log in

Logical Hylomorphism Revisited: Aristotle, Tarski, and Corcoran

  • Chapter
  • First Online:
Universal Logic, Ethics, and Truth

Part of the book series: Studies in Universal Logic ((SUL))

Abstract

This paper proposes an approach to the demarcation of formal ontology and formal epistemology based on the dichotomy between substantial and dynamic models of logical hylomorphism. Substantial hylomorphism considers logic as a theory of higher-order formal objects which turns their properties into rules of inference. Dynamic hylomorphism concerns goals-directed and rules-governed structured actions of reasoning agents rather than objects. The paper shows the significance of Corcoran’s formal methodology for balancing ontologically and epistemologically oriented versions of logical hylomorphism.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Gil Sagi defines isomorphism types as forms of terms: Let t and t' be primitive expressions in a given language L. Form D(t) = form D’(t') if and only if there is a bijection f: D →D' such that f (ext D(t)) = ext D’(t ')) [33, p. 1097]. The forms, in contrast to the extensions, are invariant under isomorphism.

  2. 2.

    Tarski-Sher criterion has received criticism for both overgenerating and undergenerating (see [18, 34]).

References

  1. Alexander of Aphrodisias, On Aristotle’s Prior Analytics 1.1–7. Tr. by J. Barnes, S. Bobzien, K. Flannery, and K. Ierodiakonou (Duckworth, London, 1991)

    Google Scholar 

  2. J. Archambault. Mereological Hylomorphism and the Development of the Medieval Substitutional Account of Formal Consequence, in Hylomorphism and Mereology, ed. by G. Klima and A. Hall (Newcastle upon Tyne, 2018), рр. 81–103

    Google Scholar 

  3. H. Arló-Costa, V. Hendricks, J. van Benthem (eds.) Readings in Formal Epistemology. Sourcebook (Springer Cham, 2016)

    Google Scholar 

  4. J.-Y. Béziau, What is ‘formal logic’? Proceedings of the XXII World Congress of Philosophy, vol. 13, Logic and Philosophy of Logic, 9–22 (2008)

  5. D. Bonnay, Logicality and invariance, Bulletin of Symbolic Logic 14, 29–68 (2008)

    Article  MathSciNet  Google Scholar 

  6. J. Corcoran, A Mathematical Model of Aristotle’s Syllogistic, Archiv für Geschichte der Philosophie 55, 191–219 (1973)

    Article  MathSciNet  Google Scholar 

  7. J. Corcoran, Aristotle’s Natural Deduction System, in: Ancient logic and its modern interpretations, ed. by J. Corcoran (Reidel Publishing Company, Dordrecht – Boston, 1974), 85–132

    Chapter  Google Scholar 

  8. J. Corcoran, The inseparability of logic and ethics, Free Inquiry 9 (2), 37–40 (1989)

    Google Scholar 

  9. J. Corcoran, The founding of logic: Modern Interpretations of Aristotle’s Logic, Ancient Philosophy 14, 9–24 (1994)

    Article  Google Scholar 

  10. J. Corcoran, Aristotle’s Prior Analytics and Boole’s Laws of Thought, History and Philosophy of Logic 24 (4), 261–288 (2003)

    Article  MathSciNet  Google Scholar 

  11. J. Corcoran, Wholistic reference, truth-values, universes of discourse, and formal ontology: tréplica to Oswaldo Chateaubriand, Manuscrito 28 (1), 143–167 (2005)

    Google Scholar 

  12. J. Corcoran, Schemata: The Concept of Schema in the History of Logic. The Bulletin of Symbolic Logic 12 (2), 219–240 (2006)

    Article  MathSciNet  Google Scholar 

  13. J. Corcoran, Notes on the Founding of Logics and Metalogic: Aristotle, Boole, and Tarski, in: Current Issues in Logic/Temas Actuales de Lógica. Imprenta Universidade Santiago de Compostela (University of Santiago de Compostela Press, 2007)

    Google Scholar 

  14. E. Dragalina-Chernaya, Kant’s Dynamic Hylomorphism in Logic, Con-Textos Kantianos. 4, 127–137 (2016)

    Google Scholar 

  15. E. Dragalina-Chernaya E. The Roots of Logical Hylomorphism. Logical Investigations, 22 (2), 59–72 (2016)

    Google Scholar 

  16. E. Dragalina-Chernaya Surprises in Logic: When Dynamic Formality Meets Interactive Compositionality, in: Philosophy of Logic and Mathematics, ed. by G. Mras, P. Weingartner, and B. Ritter (De Gruyter, Berlin – Boston, 2019), pp. 197–212

    Google Scholar 

  17. C. Dutilh Novaes, The Different Ways in which Logic is (Said to Be) Formal, History and Philosophy of Logic, 32, 303–332 (2011)

    Article  MathSciNet  Google Scholar 

  18. C. Dutilh Novaes, The Undergeneration of Permutation Invariance as a Criterion for Logicality, Erkenntnis, 79 (1), 81–97 (2014)

    Article  MathSciNet  Google Scholar 

  19. S. Feferman, Logic, logics, and logicism, Notre Dame Journal of Formal Logic 40, 31–54 (1999)

    Article  MathSciNet  Google Scholar 

  20. S. Feferman, Set-theoretical invariance criteria for logicality, Notre Dame Journal of Formal Logic 51, 3–20 (2010)

    Article  MathSciNet  Google Scholar 

  21. E. Husserl, Introduction to Logic and Theory of Knowledge. Lectures 1906/07, in: Husserliana: Edmund Husserl – Collected Works, Vol. 13 (Springer, Netherlands, 2008)

  22. K. Ierodiakonou, Aristotle’s Use of Examples in the ‘Prior Analytics’, Phronesis 47 (2), 127–152 (2002)

    Article  Google Scholar 

  23. S. Kleene, Introduction to Metamathematics (Van Nostrand, New York, 1952)

    Google Scholar 

  24. P. Lindström, First order predicate logic with generalized quantifiers, Theoria 32, 186–195 (1966)

    Article  MathSciNet  Google Scholar 

  25. J. Łukasiewicz, Aristotle’s Syllogistic from the Standpoint of Modem Formal Logic, 2nd ed., (Oxford University Press, 1957)

    Google Scholar 

  26. J. MacFarlane, What does it mean to say that logic is formal? PhD dissertation, Pittsburgh University (2000)

    Google Scholar 

  27. M. Malink. The Beginnings of Formal Logic: Deduction in Aristotle’s Topics vs. Prior Analytics, Phronesis 60, 267–309 (2015)

    Article  Google Scholar 

  28. V. McGee, Logical operations, Journal of Philosophical Logic 25, 567–580 (1996)

    Article  MathSciNet  Google Scholar 

  29. Z. Mikeladze, On a Class of Logical Concepts, in: Logical Inference (Moscow, Nauka, 1979), pp. 287–299 (In Russian)

    Google Scholar 

  30. A. Mostowski, On a generalization of quantifiers. Fundamenta Mathematicae 44, 12–35 (1957)

    Article  MathSciNet  Google Scholar 

  31. J. Piaget, Judgement and Reasoning in the Child (Routledge, London, 1999)

    Google Scholar 

  32. G. Ryle, Knowing How and Knowing That, Proceedings of the Aristotelian Society 46, 1–16 (1945–1946)

    Google Scholar 

  33. G. Sagi, Extensionality and Logicality, Synthese 198, 1095–1119 (2021)

    Article  MathSciNet  Google Scholar 

  34. G. Sagi, J. Woods (eds.) The Semantic Conception of Logic. Essays on Consequence, Invariance, and Meaning (Cambridge University Press, 2021)

    Google Scholar 

  35. H. Scholz, Concise History of Logic, tr. K. Leidecker (New York, 1961)

    Google Scholar 

  36. G. Sher, The bounds of logic: A generalized viewpoint (MIT Press, Cambridge, 1991)

    Google Scholar 

  37. G. Sher, Did Tarski Commit ‘Tarski’s Fallacy’? The Journal of Symbolic Logic 61, 653–686 (1996)

    Article  MathSciNet  Google Scholar 

  38. G. Sher, Is logic in the mind or in the world? Synthese 181, 353–365 (2011)

    Article  Google Scholar 

  39. A. Tarski, What are logical notions? History and Philosophy of Logic 7, 143–154 (1986)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

Support from the Basic Research Program of the National Research University Higher School of Economics is gratefully acknowledged.

Author information

Authors and Affiliations

  1. National Research University Higher School of Economics, International Laboratory for Logic, Linguistics and Formal Philosophy, Moscow, Russia

    Elena Dragalina-Chernaya

Authors
  1. Elena Dragalina-Chernaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. St. John Fisher University, Philosophy, Rochester, NY, USA

    Timothy J. Madigan

  2. Departement of Philosophy, Federal University of Rio de Janeiro, Rio de Janeiro, Rio de Janeiro, Brazil

    Jean-Yves Béziau

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Dragalina-Chernaya, E. (2024). Logical Hylomorphism Revisited: Aristotle, Tarski, and Corcoran. In: Madigan, T.J., Béziau, JY. (eds) Universal Logic, Ethics, and Truth. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-44461-6_8

Download citation

Publish with us

Policies and ethics

Search

Navigation