PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2020 | 49 | 2 |
Tytuł artykułu

Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Husserl's two notions of "definiteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "definite" axiom system has been interpreted as a syntactically complete theory, and also as a categorical one. I discuss whether and how far these readings manage to capture Husserl's goal of elucidating the problem of imaginary numbers, raising objections to both positions. Then, I suggest an interpretation of "absolute definiteness" as semantic completeness and argue that this notion does not suffice to explain Husserl's solution to the problem of imaginary numbers.
Rocznik
Tom
49
Numer
2
Opis fizyczny
Daty
wydano
2020-06-30
Twórcy
  • Universidad Autónoma de Madrid, Departamento de Lingüística General, Lenguas Modernas, Lógica y Filosofía de la Ciencia
Bibliografia
  • [1] S. Awodey, E. Reck, Completeness and Categoricity. Part I, History and Philosophy of Logic, vol. 23 (2002), pp. 1–30.
  • [2] R. Carnap, Untersuchungen zur allgemeinen Axiomatik, Wissenschaftliche Buchgesellschaft, Darmstadt (2000).
  • [3] S. Centrone, Logic and philosophy of mathematics in the early Husserl, Springer, Dordrecht (2010).
  • [4] J. J. Da Silva, Husserl's two notions of completeness, Synthese, vol. 125 (2000), pp. 417–438.
  • [5] J. J. Da Silva, Husserl and Hilbert on completeness, still, Synthese, vol. 193 (2016), pp. 1925–1947.
  • [6] A. Fraenkel, Einleitung in die Megenlehre (3rd edition), Springer, Berlin (1928).
  • [7] H. Hankel, Theorie der complexen Zahlensysteme (vol. 1), Leopold Voss, Leipzig (1867).
  • [8] M. Hartimo, Towards completeness: Husserl on theories of manifolds 1890–1901, Synthese, vol. 156 (2007), pp. 281–310.
  • [9] M. Hartimo, Husserl on completeness, definitely, Synthese, vol. 195 (2018), pp. 1509–1527.
  • [10] C. O. Hill, Husserl and Hilbert on completeness, From Dedekind to Gödel, Springer (1995), pp. 143–163.
  • [11] W. Hodges, Truth in a structure, Proceedings of the Aristotelian Society, vol. 86 (1986), pp. 135–151.
  • `2] [12] W. Hodges, Model Theory, Cambridge University Press, Cambridge (1993).
  • [13] E. Husserl, Formal and Trascendental Logic, Springer+Bussiness Media, Dordrecht (1969).
  • [14] E. Husserl, Philosophy of Arithmetic, Kluwer Academic Publishers, Dordrecht (2003).
  • [15] A. Lindenbaum and A. Tarski, On the limitations of the means of expression of deductive theories, Logic, semantics, metamathematics, Hackett, Indianapolis (1983), pp. 384–392.
  • [16] L. Löwenheim, On possibilities in the calculus of relatives, From Frege to Gödel, Harvard University Press, Harvard (1967), pp. 228–251.
  • [17] U. Majer, Husserl and Hilbert on completeness, Synthese, vol. 110 (1997), pp. 37–56.
  • [18] P. Mancosu, The Adventure of Reason, Oxford University Press, Oxford (2010).
  • [19] M. Manzano, Extensions of First Order Logic, Cambridge University Press, Cambridge (1996).
  • [20] M. Manzano, Model Theory, Oxford University Press, Oxford (1999).
  • [21] A. Tarski, On the concept of logical consequence, Logic, semantics, metamathematics, Hackett, Indianapolis (1983), pp. 409–420.
  • [22] A. Tarski, On the completeness and categoricity of deductive systems, The Adventure of Reason, Oxford University Press, Oxford (2010), pp. 485–492.
  • [23] N. Tennant, Deductive versus expressive power: A pre-Gödelian predicament, The Journal of Philosophy, vol. 97 (2000), pp. 257–277.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_18778_0138-0680_2020_07
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.