Advertisement

Synthese

pp 1–36 | Cite as

On causality as the fundamental concept of Gödel’s philosophy

  • Srećko Kovač
Article

Abstract

This paper proposes a possible reconstruction and philosophical-logical clarification of Gödel’s idea of causality as the philosophical fundamental concept. The results are based on Gödel’s published and non-published texts (including Max Phil notebooks), and are established on the ground of interconnections of Gödel’s dispersed remarks on causality, as well as on the ground of his general philosophical views. The paper is logically informal but is connected with already achieved results in the formalization of a causal account of Gödel’s onto-theological theory. Gödel’s main causal concepts are analysed (will, force, enjoyment, God, time and space, life, form, matter). Special attention is paid to a possible causal account of some of Gödel’s logical concepts (assertion, privation, affirmation, negation, whole, part, general, particular, subject, predicate, necessary, possible, implication), as well as of logical antinomies. The problem of mechanical and non-mechanical procedures in the work with and on concepts is addressed in terms of Gödel’s causal view.

Keywords

Kurt Gödel Causality Primitive concepts Will Force Logic General Whole Subject Human mind 

Mathematics Subject Classification

01260 03A05 

Notes

Acknowledgements

This work was supported by the Croatian Science Foundation under the project IP-2014-09-9378. Works of Kurt Gödel used with permission of the Institute for Advanced Study. Unpublished Copyright Institute for Advanced Study. All rights reserved. The author is grateful to Professor Gabriella Crocco (Aix-Marseille University) for permission to quote Gödel’s Max Phil notebooks from the transcription of Max Phil X in Crocco et al. (2017), from the draft transcriptions of notebooks Phil XIV and Max XV in Gödel (2016), and from Crocco and Engelen (2016a), as well as to add or slightly modify the translations of the quotations. In particular, thanks are due to Gabriella Crocco and to Anaïs Mauriceau (Library Granger-Guillermit at the Aix-Marseille University) for the availability of the above-mentioned draft transcription (Gödel 2016). The author would like to thank the audiences of a seminar at the Department of Philosophy of the Cardinal S. Wyszyński University, Warsaw, May 2013, and of the conference Kurt Gödel Philosopher: From Logic to Cosmology, Aix-en-Provence, 11–13 July 2013, where initial drafts of the paper were presented, for valuable comments and discussions.

References

  1. Artemov, S., Yavorskaya (Sidon), T. (2011). First-order logic of proofs. Technical Report TR-2011005, CUNY Ph.D. Program in Computer Science.Google Scholar
  2. Audireau, É. (2016). Gödel: From the pure theory of gravitation to Newton’s absolute (pp. 57–79). In Crocco and Engelen (2016a).Google Scholar
  3. Bernard, J. (2016). From the physical existence of tuples to quantum materia prima (pp. 81–105). In Crocco and Engelen (2016a).Google Scholar
  4. Crocco, G. (2016). Sinn/Bedeutung and intension/extension in Gödel’s Max Phil IX (pp. 127–152). In Crocco and Engelen (2016a).Google Scholar
  5. Crocco, G., & Engelen, E. M. (Eds.). (2016a). Kurt Gödel philosopher–scientist. Aix-en-Provence: Presses Universitaires de Provence.Google Scholar
  6. Crocco, G., & Engelen, E. M. (2016b). Kurt Gödel’s Philosophical remarks (Max Phil) (pp. 33–54). In Crocco and Engelen (2016a).Google Scholar
  7. Crocco, G., van Atten, M., Cantù, P., Engelen, E.M. (2017). Kurt Gödel Maxims and philosophical remarks volume X. https://hal.archives-ouvertes.fr/hal-01459188.
  8. Engelen, E. M. (2013). Hat Kurt Gödel Thomas von Aquins Kommentar zu Aristoteles’ De Anima rezipiert? Philosophia Scientiae, 17, 167–188.CrossRefGoogle Scholar
  9. Engelen, E. M. (2016). What is the link between Aristotle’s philosophy of mind, the iterative conception of set, Gödel’s incompleteness theorems and God: About the pleasure and the difficulties of interpreting Kurt Gödel’s Philosophical remarks (pp. 171–188). In Crocco and Engelen (2016a).Google Scholar
  10. Fitting, M. (2014). Possible world semantics for first order \({\sf LP}\). Annals of Pure and Applied Logic, 165, 225–240.CrossRefGoogle Scholar
  11. Futch, M. (2008). Leibniz’s metaphysics of time and space. Berlin: Springer.CrossRefGoogle Scholar
  12. Gödel, K. (1986). On formally undecidable propositions of Principia mathematica and related systems I (pp. 145–195). Vol. 1 of Gödel (1986–2003).Google Scholar
  13. Gödel, K. (1986–2003). Collected works (Vol. 1–5) Feferman, S. et al. (Eds.). Oxford: Oxford University Press.Google Scholar
  14. Gödel, K. (1990a). On an extension of finitary mathematics which has not yet been used (pp. 271–280). Vol. 2 of Gödel (1986–2003).Google Scholar
  15. Gödel, K. (1990b). A remark about the relationship between relativity theory and idealistic philosophy (pp. 202–207). Vol. 2 of Gödel (1986–2003).Google Scholar
  16. Gödel, K. (1990c). Remarks before the Princeton bicentennial conference on problems in mathematics (pp. 150–153). Vol. 2 of Gödel (1986–2003).Google Scholar
  17. Gödel, K. (1990d). Russell’s mathematical logic (pp. 119–141). Vol. 2 of Gödel (1986–2003).Google Scholar
  18. Gödel, K. (1990e). What is Cantor’s continuum problem (1964) (pp. 254–270). Vol 2 of Gödel (1986–2003).Google Scholar
  19. Gödel, K. (1995a). Is mathematics syntax of language? (pp. 334–362). Vol 3 of Gödel (1986–2003).Google Scholar
  20. Gödel, K. (1995b). Lecture on rotating universes (pp. 269–287). Vol 3 of Gödel (1986–2003).Google Scholar
  21. Gödel, K. (1995c). The modern development of the foundations of mathematics in the light of philosophy (pp. 374–387). Vol 3 of Gödel (1986–2003).Google Scholar
  22. Gödel, K. (1995d). Ontological proof/Appendix B: Texts relating to the ontological proof (pp. 403–404, 429–437). Vol 3 of Gödel (1986–2003).Google Scholar
  23. Gödel, K. (1995e). The present situation in the foundations of mathematics (pp. 45–53). Vol 3 of Gödel (1986–2003).Google Scholar
  24. Gödel, K. (1995f). Some basic theorems on the foundations of mathematics and their implications (pp. 304–323). Vol 3 of Gödel (1986–2003).Google Scholar
  25. Gödel, K. (1995g). Some observations about the relationship between theory of relativity and Kantian philosophy (pp. 230–259). Vol 3 of Gödel (1986–2003).Google Scholar
  26. Gödel, K. (1995h). Vortrag bei Zilsel (pp. 86–113). Vol 3 of Gödel (1986–2003).Google Scholar
  27. Gödel, K. (2016). Volume XIV of the Max Phil notebooks, draft, Gabriella Crocco (Editor-in-chief), Mark van Atten, Paola Cantù, Eva-Maria Engelen (Eds.), contains Philosophy Notebook “Max XV, Letztes”.Google Scholar
  28. Gomperz, H. (1897). Zur Psychologie der logischen Grundtatsachen. Leipzig: Deuticke.Google Scholar
  29. Husserl, E. (1995). Cartesianische Meditationen (3rd ed.). Hamburg: Meiner.Google Scholar
  30. Husserl, E. (2002). Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie. Tübingen: Niemeyer.CrossRefGoogle Scholar
  31. Kant, I. (1968). Kritik der reinen Vernunft, 2nd ed. 1787, Kants Werke, Vol. 3 (1st ed. in vol. 4). Berlin: de Gruyter.Google Scholar
  32. Kant, I. (1998). Critique of pure reason. (P. Guyer & A. W. Wood, Trans.). Cambridge: Cambridge University Press.Google Scholar
  33. Kennedy, J. (2014). Gödel’s 1946 Princeton bicenntenial lecture: An appreciation. In J. Kennedy (Ed.), Interpreting Gödel: Critical essays (pp. 109–130). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  34. Kovač, S. (2008). Gödel, Kant, and the path of a science. Inquiry, 51, 147–169.CrossRefGoogle Scholar
  35. Kovač, S. (2012). Modal collapse in Gödel’s ontological proof. In M. Szatkowski (Ed.), Ontological proofs today (pp. 323–343). Frankfurt: Ontos.Google Scholar
  36. Kovač, S. (2015). Causal interpretation of Gödel’s ontological proof. In K. Świętorzecka (Ed.), Gödel’s ontological argument: History, modifications, and controversies (pp. 163–201). Warszawa: Semper.Google Scholar
  37. Kovač, S., & Świętorzecka, K. (2015). Gödel’s ‘slingshot’ argument and his onto-theological system. In K. Świętorzecka (Ed.), Gödel’s ontological argument: History, modifications, and controversies (pp. 123–162). Warszawa: Semper.Google Scholar
  38. Leibniz, G. W. (1863). Initia rerum mathematicarum metaphysica. In C. I. Gerhardt (Ed.), Leibnizens mathematische Schriften, zweite Abt. (Vol. 3, pp. 17–29). Halle: Schmidt.Google Scholar
  39. Leibniz, G. W. (1978a). Monadologie. In: Gerhardt, C. I. (Ed.), Die philosophischen Schriften (Vol. 6, pp. 607–623), transl. in http://www.earlymoderntexts.com/pdf/leibmona.pdf.
  40. Leibniz, G. W. (1978b). Principes de la nature et de la grâce, fondés en raison. In Gerhardt, C. I. (Ed.), Die philosophischen Schriften (Vol. 6, pp. 598–606).Google Scholar
  41. Leibniz, G. W. (1989). Philosophical essays (R. Ariew & D. Garber, Trans.). Indianapolis: HackettGoogle Scholar
  42. Leibniz, G.W. (1999a). Definitiones: ens, possibile, existens. In Leibniz, G. W., Sämtliche Schriften und Briefe. Philosophische Schriften (Vol. VI 4, pp. 867–870). Berlin: Akademie Verlag. http://www.uni-muenster.de/Leibniz/DatenVI4/VI4a2.pdf.
  43. Leibniz, G. W. (1999b). Definitiones. Notiones. Characteres. In Leibniz, G. W., Sämtliche Schriften und Briefe. Philosophische Schriften (Vol. VI 4, pp. 870–879). Berlin: Akademie Verlag. http://www.uni-muenster.de/Leibniz/DatenVI4/VI4a2.pdf.
  44. Leibniz, G. W. (1999c). Sämtliche Schriften und Briefe. Philosophische Schriften (Vol. VI 4). Berlin: Akademie Verlag.Google Scholar
  45. Mertens, A. (2016). Gödel’s distinction between objective and subjective concepts: taken from the analysis of the remark on page 16 in the Max Phil XI (pp. 189–201). In Crocco and Engelen (2016a).Google Scholar
  46. Plato. (1964–1978). Plato in twelve volumes (Vol. 1–12). Cambridge: Harvard University Press.Google Scholar
  47. Reich, K. (1948). Die Vollständigkeit der kantischen Urteilstafel. Berlin: Schoetz.Google Scholar
  48. Sobel, J. H. (2004). Logic and theism: Arguments for and against beliefs in God. Cambridge: Cambridge University Press.Google Scholar
  49. Świętorzecka, K. (Ed.). (2015). Gödel’s ontological argument: History, modifications, and controversies. Warszawa: Semper.Google Scholar
  50. Tieszen, R. (2016). Leibniz, Husserl and Gödelian monadology (pp. 447–463). In Crocco and Engelen (2016a).Google Scholar
  51. Toledo, S. (2011). Sue Toledo’s notes of her conversations with Gödel in 1972–5. In J. Kennedy & R. Kossak (Eds.), Set theory, arithmetic and foundations of mathematics: Theorems, philosophies (pp. 200–207). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  52. van Atten, M. (2015). Essays on Gödel’s reception of Leibniz, Brouwer, and Husserl. Heidelberg: Springer.CrossRefGoogle Scholar
  53. van Atten, M., & Kennedy, J. (2003). On the philosophical development of Kurt Gödel. Bulletin of Symbolic Logic, 9, 425–476.CrossRefGoogle Scholar
  54. Wang, H. (1987). Reflections on Kurt Gödel. Cambridge: The MIT Press.Google Scholar
  55. Wang, H. (1996). A logical journey: From Gödel to philosophy. Cambridge: The MIT Press.Google Scholar
  56. Weingartner, P. (2016). The need for pluralism of causality. Logic and Logical Philosophy, 25, 461–498.Google Scholar
  57. Yourgrau, P. (1999). Gödel meets Einstein: Time travel in the Gödel’s universe. Chicago: Open Court.Google Scholar
  58. Yourgrau, P. (2005). A world without time: The forgotten legacy of Gödel and Einstein. New York: Basic Books.Google Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Philosophy, a public research institute of the Republic of CroatiaZagrebCroatia

Personalised recommendations