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Artículos

Vol. 16 No. 1 (2025)

Topology, Logic and Philosophy: For an Interdisciplinary Work

DOI
https://doi.org/10.5281/zenodo.15644617
Submitted
November 2, 2024
Published
2025-05-30

Abstract

This paper provides a contemporary historical overview of the relationship between topology and philosophy, and the concepts that bridge the two areas. Formal limitations and philosophical problems of possible worlds semantics are examined. Subsequently, the work of philosophers of science, Daniel Kostić and Thommas Mormann, is examined, who vindicate the use of topology in philosophy, specifically in epistemology and metaphysics. Finally, a thesis vindicating the use of topology in philosophy is proposed through the text.

References

  1. Baltag, A., Bezhanishvili, N., Özgün, A., & Smets, S. (2022). Justified belief, knowledge, and the topology of evidence. Synthese, 200(512), 512. https://doi.org/10.1007/s11229-022-03967-6
  2. Bayart, A. (1958). La Correction de la Logique Modale du Premier et Second Ordre S5. Logique et Analyse, 1(1), 28-45. https://www.jstor.org/stable/44083329
  3. Bayart, A. (1959). Quasi-adéquation de la Logique Modale de Second Ordre S5 et Adéquation de la Logique Modale de Premier Ordre S5. Logique et Analyse, 2(6/7), 99-121. https://www.jstor.org/stable/44083456
  4. Bjorndahl, A., & Özgün, A. (2020). Logic and topology for knowledge, knowability, and belief. The Review of Symbolic Logic, 13(4), 748-775. https://doi.org/10.1017/S1755020319000509
  5. Carnap, R. (1922). Der Raum. Ein Beitrag zur Wissenschaftslehre. Kantstudien Ergän-zunghefte. PhD. Thesis. Berlin: Reuther & Reichard.
  6. Carnap, R. (1946). Modalities and Quantification. The Journal of Symbolic Logic, 11(2), 33-64. https://doi.org/10.2307/2268610
  7. Carnap, R. (1947). Meaning and Necessity. Chicago: University of Chicago Press.
  8. Cassirer, E. (1953). The Philosophy of Symbolic Forms. New Heaven: Yale Universi-ty Press.
  9. Cresswell, M. (2013, June 15-20). Carnap and McKinsey: Topics in the Pre-History of Possible-Worlds Semantics. Proceedings of the 12th Asian Logic Conference, 53-75. Wellington, New Zealand: World Scientific Publishing Company. https://doi.org/10.1142/8701
  10. Cresswell, M. (2014). The Completeness of Carnap's Predicate Logic. Australasian Journal of Logic, 11(1), 46-61. https://doi.org/10.26686/ajl.v11i1.2017
  11. Cresswell, M. (2015). Arnould Bayart’s modal completeness theorems: translated with an introduction and commentary. Logique et Analyse, 58(229), 89-142. https://www.jstor.org/stable/44085332
  12. Cresswell, M. (2016). Worlds and Models in Bayart and Carnap. The Australasian Journal of Logic, 13(1), 1-10. https://doi.org/10.26686/ajl.v13i1.3927
  13. Cresswell, M. (2019). Modal Logic before Kripke. Organon F, 26(3), 323-339. https://doi.org/10.31577/orgf.2019.26302
  14. Cresswell, M. (2020). Revisiting McKinsey's 'Syntactical' Construction of Modality. The Australasian Journal of Logic, 17(2), 123-140. https://doi.org/10.26686/ajl.v17i2.4073
  15. Haack, S. (1978). Philosophy of Logics. Cambridge: Cambridge University Press.
  16. Hintikka, J. (1969). Semantics for Propositional Attitudes. In J. Hintikka, Models for Modalities. Selected Essays (Vol. 23, pp. 87-111). Dordrecht: Springer. https://doi.org/10.1007/978-94-010-1711-4_6
  17. Hughes, G., & Cresswell, M. (1996). A New Introduction to Modal Logic. London: Routledge. https://doi.org/10.4324/9780203028100
  18. Kostić, D. (2018). The topological realization. Synthese, 196, 79-98. https://doi.org/10.1007/s11229-016-1248-0
  19. Kostić, D. (2020). General theory of topological explanations and explanatory asymmetry. Philosophical Transactions of the Royal Society B, 375, 1-8. https://doi.org/10.1098/rstb.2019.0321
  20. Kostić, D. (2022). Topological Explanations: An Opinionated Appraisal. In I. Lawler, K. Khalifa, & E. Shech (Eds.), Scientific Understanding and Representation: Model-ing in the Physical Sciences (pp. 96-115). New York: Routledge.
  21. Kostić, D. (2024). On the Role of Erotetic Constraints in Noncausal Explanations. Philosophy of Science, 91(5), 1078-1088. https://doi.org/10.1017/psa.2023.114
  22. Kostić, D., & Khalifa, K. (2021). The directionality of topological explanations. Synthese, 199, 14143-14165. https://doi.org/10.1007/s11229-021-03414-y
  23. Kostić, D., & Khalifa, K. (2023). Decoupling Topological Explanations from Mecha-nisms. Philosophy of Science, 90(2), 245-268. https://doi.org/10.1017/psa.2022.29
  24. Kripke, S. A. (1959). A completeness theorem in modal logic. The Journal of Symbolic Logic , 24(1), 1-14. https://doi.org/10.2307/2964568
  25. Kripke, S. A. (1963a). Semantical Analysis of Modal Logic I Normal Modal Proposi-tional Calculi. Zeitschrift für mathematische Logik und Grundlagen der Mathema-tik , 9(5-6), 67-96. https://doi.org/10.1002/malq.19630090502
  26. Kripke, S. A. (1963b). Semantical Considerations on Modal Logic. Acta Philosophi-ca Fennica, 16, 83-94.
  27. Kripke, S. A. (1965). Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi. In J. W. Addison, L. Henkin, & A. Tarski (Eds.), The theory of models (pp. 206-220). Amsterdam: North-Holland Publishing Company.
  28. Kripke, S. A. (1980). Naming and Necessity: Lectures Given to the Princeton University Philosophy Colloquium. (D. Byrne, & M. Kölbel, Eds.) Cambridge: Harvard University Press.
  29. Kuratowski, K. (1966). Topology. Vol. I. New York: Academic Press.
  30. Lewis, D. (1968). Counterpart Theory and Quantified Modal Logic. The Journal of Philosophy, 65(5), 113-126. https://doi.org/10.2307/2024555
  31. Lewis, D. (1973). Counterfactuals. Cambridge: Harvard University Press.
  32. Lewis, D. (1986). On the Plurality of Worlds. Oxford: Basil Blackwell.
  33. McKinsey, J. C. (1941). A solution of the decision problem for the Lewis systems S2 and S4, with an application to topology. Journal of Symbolic Logic, 6(4), 117-134. https://doi.org/10.2307/2267105
  34. McKinsey, J. C., & Tarski, A. (1944). The Algebra of Topology. Annals of Mathemat-ics, 45(1), 141-191. https://doi.org/10.2307/1969080
  35. Mormann, T. (2013). Topology as an Issue for History of Philosophy of Science. In H. Andersen, D. Dieks, W. J. Gonzalez, T. Uebel, & G. Wheeler (Eds.), New Chal-lenges to Philosophy of Science (Vol. 4, pp. 423-434). Dordrecht: Springer.
  36. Mormann, T. (2014). Set Theory, Topology, and the Possibility of Junky Worlds. Notre Dame Journal of Formal Logic, 55(1), 79-90. https://doi.org/10.1215/00294527-1960497
  37. Mormann, T. (2020). Topological Aspects of Epistemology and Metaphysics. In A. Peruzzi, & S. Zipoli Caiani (Eds.), Structures Mères: Semantics, Mathematics, and Cognitive Science (Vol. 57, pp. 135-152). Cham: Springer. https://doi.org/10.1007/978-3-030-51821-9_7
  38. Mormann, T. (2021). Prototypes, poles, and tessellations: towards a topological theory of conceptual spaces. Synthese, 199, 3675-3710. https://doi.org/https://doi.org/10.1007/s11229-020-02951-2
  39. Mormann, T. (2022). Topological Models of Columnar Vagueness. Erkenntnis, 87, 693-716. https://doi.org/10.1007/s10670-019-00214-2
  40. Mosterín, J. & Torretti, R, (2010). Diccionario de Lógica y Filosofía de la Ciencia. (Segunda ed.). Madrid: Alianza Editorial.
  41. Russell, B. (1915). Our Knowledge of the External World: As a Field for Scientific Method in Philosophy. Chicago and London: The Open Court Publishing Company.
  42. Russell, B. (1927). The Analysis of Matter. London: Kegan Paul, Trench, Trubner & Co. Ltd.
  43. Russell, B. (1936). On order in time. Proceedings of the Cambridge Philosophical Society, 32, 216-228.
  44. Stone, M. H. (1936). The Theory of Representation for Boolean Algebras. Transac-tions of the American Mathematical Society, 40(1), 37-111. https://doi.org/10.2307/1989664
  45. Tarski, A. (1938). Der Aussagenkalkül und die Topologie. Fundamenta Mathemati-cae, 31, 103-134. https://doi.org/10.4064/fm-31-1-103-134
  46. Tsao-Chen, T. (1938). Algebraic postulates and a geometric interpretation for the Lewis calculus of strict implication. Bulletin of the American Mathematical Socie-ty, 44(10), 737-744. https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-44/issue-10/Algebraic-postulates-and-a-geometric-interpretation-for-the-Lewis-calculus/bams/1183500884.full