Skip to main content Skip to main navigation menu Skip to site footer
  • Register
  • Login
  • Language
    • English
    • Język Polski
  • Menu
  • Home
  • Current
  • Archives
  • Online First Articles
  • About
    • About the Journal
    • Submissions
    • Editorial Team
    • Advisory Board
    • Peer Review Process
    • Logic and Logical Philosophy Committee
    • Open Access Policy
    • Privacy Statement
    • Contact
  • Register
  • Login
  • Language:
  • English
  • Język Polski

Logic and Logical Philosophy

Truth vs. provability – philosophical and historical remarks
  • Home
  • /
  • Truth vs. provability – philosophical and historical remarks
  1. Home /
  2. Archives /
  3. No. 10 (2002) /
  4. Articles

Truth vs. provability – philosophical and historical remarks

Authors

  • Roman Murawski Adam Mickiewicz University, Poznań

DOI:

https://doi.org/10.12775/LLP.2002.006

Abstract

Since Plato, Aristotle and Euclid the axiomatic method was considered as the best method to justify and to organize mathematical knowledge. The first mature and most representative example of its usage in mathematics were Elements of Euclid. They established a pattern of a scientific theory and in particular a paradigm in mathematics.

Author Biography

Roman Murawski, Adam Mickiewicz University, Poznań

Faculty of Mathematics and Computer Science

References

Barwise, J.: 1980, “Infinitary Logics”. In: E. Agazzi (ed.) Modern Logic – A Survey, D. Reidel Publ. Comp., Dordrecht, pp. 3–112.

Carnap, R.: 1934, “Die Antinomien und die Unvollständigkeit der Mathematik”, Monatshefte für Mathematik und Physik 41, 263–284.

Carnap R.: 1963, “Intellectual Autobiography”. In: Paul A. Schilpp (ed.), The Philosophy of Rudolf Carnap, La Salle, Ill., Open Court Publishing Co., 3–84.

Davis, M. (ed.): 1965, The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions, Raven Press, Hewlett, N.Y.

Feferman, S.: 1962, “Transfinite Recursive Progressions of Axiomatic Theories”, Journal of Symbolic Logic 27, 259–316.

Feferman, S.: 1984, “Kurt Gödel: Conviction and Causation”. In: Philosophia Naturalis, a special issue, P. Weingartner et al. (eds.) Philosophy of Science —History of Science. A Selection of Contributed Papers of the 7th International Congress of Logic, Methodology and Philosophy of Science, Salzburg, 1983, Meisenheim/Glan (Verlag Anton Hain). Reprinted in: S.G. Shanker (ed.), Gödel’s Theorem in Focus, Croom Helm, London 1988, 96–114.

Feferman, S.: 1988, “Turing and the Land of O(z)”. In: R. Herken (ed.), The Universal Turing Machine – A Half-Century Survey, Oxford University Press, New York and Oxford, 113–147.

Frege G.: 1976, Wissenschaftlicher Briefwechsel, Hrsg. G. Gabriel, H. Hermes, F. Kambartel, Ch. Thiel, A. Veraart, Felix Meiner Verlag, Hamburg.

Gödel, K.: 1929, “Über die Vollständigkeit des Logikkalküls”, doctoral dissertation; published and translated in: K. Gödel, Collected Works, vol. I, ed. by S. Feferman et al., Oxford University Press, New York and Clarendon Press, Oxford, 1986, 60–101.

Gödel, K.: 1930, “Die Vollständigkeit der Axiome des logischen Funktionenkalküls”, Monatshefte für Mathematik und Physik 37, 349–360. Reprinted with English translation “The Completeness of the Axioms of the Functional Calculus of Logic” in: K. Gödel, Collected Works, vol. I, ed. by S. Feferman et al., Oxford University Press, New York and Clarendon Press, Oxford, 1986, 102–123.

Gödel, K.: 1931, “Über formal unentscheidbare Sätze der ‘Principia Mathematica’ und verwandter Systeme. I”, Monatshefte für Mathematik und Physik 38, 173–198. Reprinted with English translation “On Formally Undecidable Propositions of Principia Mathematica and Related Systems” in: K. Gödel, Collected Works, vol. I, ed. by S. Feferman et al., Oxford University Press, New York and Clarendon Press, Oxford 1986, 144–195.

Gödel, K.: 1931?, “Über unentscheidbare Sätze”; first published (German text and English translation “On undecidable sentences”) in: K. Gödel, Collected Works, 114 Roman Murawski vol. III, ed. by S. Feferman et al., Oxford University Press, New York and Oxford 1995, 30–35.

Gödel, K.: 1933, “The Present Situation in the Foundations of Mathematics”; first published in: K. Gödel, Collected Works, vol. III, ed. by S. Feferman et al., Oxford University Press, New York and Oxford 1995, 45–53.

Gödel, K.: 1934, On Undecidable Propositions of Formal Mathematical Systems (mimeographed lecture notes, taken by S.C. Kleene and J.B. Rosser), Princeton; reprinted with revisions in: M. Davis (ed.), The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions, Hewlett, N.Y. (Raven Press) 1965, 39–74. Also in: K. Gödel, Collected Works,

vol. I, ed. by S. Feferman et al., Oxford University Press, New York and Clarendon Press, Oxford 1986, 346–371.

Gödel, K.: 193?, ’‘Undecidable Diophantine Propositions”, first published in: K. Gödel, Collected Works, vol. III, ed. by S. Feferman et al., Oxford University Press, New York and Oxford 1995, 164–175.

Gödel, K.: 1946, “Remarks Before the Princeton Bicentennial Conference on Problems in Mathematics”, 1–4; first published in: M. Davis (ed.), The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions, Raven Press, Hewlett, N.Y., 1965, 84–88. Reprinted in: K. Gödel, Collected Works, vol. II, ed. by S. Feferman et al., Oxford University

Press, New York and Oxford, 1990, 150–153.

Gödel, K.: 1951, “Some Basic Theorems on the Foundations of Mathematics and Their Implications”; first published in: K. Gödel, Collected Works, vol. III, ed. by S. Feferman et al., Oxford University Press, New York and Oxford 1995, 304–323.

Gödel, K.: 1958, “Über eine bisher noch nicht benützte Erweiterung des finite Standpunktes”, Dialectica 12, 280–287. Reprinted with English translation “On a Hitherto Unutilized Extension of the Finitary Standpoint” in: K. Gödel, Collected Works, vol. II, ed. by S. Feferman et al., Oxford University Press, New York and Oxford, 1990, 240–251.

Gödel, K.: 1970, “The Modern Development of the Foundations of Mathematics in the Light of Philosophy”; first published (German text and English translation) in: K. Gödel, Collected Works, vol. III, ed. by S. Feferman et al., Oxford University Press, New York and Oxford 1995, 374–387.

Gödel, K.: 1972, “On an Extension of Finitary Mathematics Which Has Not Yet Been Used”, revised and expanded English version of (Gödel, 1958), to have appeared in Dialectica, first published in: K. Gödel Collected Works, vol. II, ed. by S. Feferman et al., Oxford University Press, New York-Oxford 1990, 271–280.

Heijenoort, J. van (ed.): 1967, From Frege to Gödel. A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, Mass.

Hilbert D.: 1899, Grundlagen der Geometrie. Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals, B.G. Teubner, Leipzig, 3–92.

Hilbert D.: 1900, “Über den Zahlbegriff”, Jahresbericht der Deutschen Mathematikervereinigung 8, 180–184.

Hilbert, D.: 1901, “Mathematische Probleme”, Archiv der Mathematik und Physik 1, 44–63 and 213–237. Reprinted in: D. Hilbert, Gesammelte Abhandlungen, Verlag von Julius Springer, Berlin, Bd. 3, 290–329. English translation: “Mathematical Problems”, Bulletin of the American Mathematical Society 8 (1901–2), 437–479; also in: F. Browder (ed.), Mathematical Developments Arising from

Hilbert’s Problems, Proceedings of the Symposia in Pure Mathematics 28, American Mathematical Society, Providence, RI, 1976, 1–34.

Hilbert D.: 1902/03, “Über den Satz von der Gleichheit der Basiswinkel im gleichschenkligen Dreieck”, Proceedings of the London Mathematical Society 35, 50–68.

Hilbert D.: 1903, Grundlagen der Geometrie, second edition, Teubner, Leipzig.

Hilbert D.: 1905, “Logische Principien des mathematischen Denkens”, Lecture notes by Ernst Hellinger, Mathematisches Institut, Georg-August-Universität Göttingen, Sommer-Semester 1905. Unpublished manuscript.

Hilbert D.: 1905a, “Über die Grundlagen der Logik und der Arithmetik”. In: A. Krazer (ed.), Verhandlungen des dritten Internationalen Mathematiker-Kongresses in Heidelberg vom 8. bis 13. August 1904, Teubner, Leipzig, 174–185.

English translation: ‘On the Foundations of Logic and Arithmetic’ in: J. van Heijenoort (ed.) 1967, From Frege to Gödel. A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, Mass., 129–138.

Hilbert D.: 1917–18, “Prinzipien der Mathematik”, Lecture notes by Paul Bernays, Mathematisches Institut, Georg-August-Universität Göttingen, Wintersemester 1917–18. Unpublished typescript.

Hilbert D.: 1918, “Axiomatisches Denken”, Mathematische Annalen 78, 405–415.

Reprinted in: D. Hilbert, Gesammelte Abhandlungen, Verlag von Julius Springer, Berlin, Bd. 3, 146–177.

Hilbert D.: 1930, “Probleme der Grundlegung der Mathematik”, Mathematische Annalen 102, 1–9.

Hilbert, D.: 1930a, “Naturerkennen und Logik”, Naturwissenschaften 18, 959–963.

Reprinted in: D. Hilbert, Gesammelte Abhandlungen, Bd. 3, Verlag von Julius Springer, Berlin 1935, 378–387.

Hilbert D.: 1931, “Die Grundlegung der elementaren Zahlentheorie”, Mathematische Annalen 104, 485–494. Reprinted in: D. Hilbert, Gesammelte Abhandlungen, Bd. 3, Verlag von Julius Springer, Berlin 1935, 192–195.

Hilbert, D., and W. Ackermann: 1928, Grundzüge der theoretischen Logik, Verlag von Julius Springer, Berlin. English translation of the second edition: Principles of Mathematical Logic, Chelsea Publishing Company, New York 1950.

Hilbert, D., and P. Bernays: (1934/1939), Grundlagen der Mathematik, Springer-Verlag, Berlin, Bd. I 1934, Bd. II 1939.

Köhler, E.: 1991, “Gödel und der Wiener Kreis”. In: P. Kruntorad (ed.), Jour Fixe der Vernunft, Hölder-Pichler-Tempsky, Wien, 127–158.

Moore, G.H.: 1980, “Beyond First-Order Logic: The Historical Interplay Between Mathematical Logic and Axiomatic Set Theory”, History and Philosophy of Logic 1, 95–137.

Murawski R.: 1998, “Undefinability of Truth. The Problem of the Priority: Tarski vs Gödel”, History and Philosophy of Logic 19, 153–160.

Neumann von, J.: 1966, Theory of Self-Reproducing Automata, ed. A.W. Burks, University of Illinois, Urbana.

Rowe, D.E.: 1989, “Klein, Hilbert, and the Göttingen Mathematical Tradition”, Osiris (2) 5, 186–213.

Rosser, J.B.: 1937, “Gödel Theorems for Non-Constructive Logics”, Journal of Symbolic Logic 2, 129–137.

Tarski, A.: 1930, “Fundamentale Begriffe der Methodologie der deduktiven Wissenschaften. I”, Monatshefte für Mathematik und Physik 37, 361–404. English translation “Fundamental Concepts of the Methodology of the Deductive Sciences” in: Logic, Semantics, Metamathematics. Papers From 1923 To 1938, Clarendon Press, Oxford 1956, 60–109.

Tarski, A.: 1933, Pojęcie prawdy w językach nauk dedukcyjnych, Nakładem Towarzystwa Naukowego Warszawskiego, Warszawa.

Tarski, A.: 1936, “Der Wahrheitsbegriff in den formalisierten Sprachen”, Studia Philosophica 1, 261–405 (offprints dated 1935).

Tarski, A.: 1954, “Contributions to the Discussion of P. Bernays, Zur Beurteilung der Situation in der beweistheoretischen Forschung”, Revue Internationale de Philosophie 8, 16–20.

Tarski, A.: 1956, “The Concept of Truth in Formalized Languages”. In: Logic, Semantics, Metamathematics. Papers From 1923 To 1938, Clarendon Press, Oxford 1956, 152–278.

Turing, A.: 1939, “Systems of Logic Based on Ordinals”, Proc. London Math. Soc., ser. 2, 45, 161–228.

Wang, Hao: 1974, From Mathematics to Philosophy, Routledge and Kegan Paul, London.

Wang, Hao: 1981, “Some Facts About K. Gödel”, Journal of Symbolic Logic 46, 653–659.

Wang, Hao: 1987, Reflections on Kurt Gödel, M.I.T. Press, Cambridge, Mass. Truth vs. provability ... 117

Wang, Hao: 1996, A Logical Journey. From Gödel to Philosophy, The MIT Press, Cambridge, Massachusetts and London, England.

Woleński, J.: 1989, Logic and Philosophy in the Lvov-Warsaw School, Kluwer Academic Publishers, Dordrecht.

Woleński, J.: 1991, “Gödel, Tarski and the Undefinability of Truth”. In: Yearbook 1991 of the Kurt Gödel Society (Jahrbuch 1991 der Kurt-Gödel-Gesellschaft), Wien, 97–108. Reprinted in: J. Woleński, Essays in the History of Logic and Logical Philosophy, Jagiellonian University Press, Kraków 1999, 134–138.

Woleński, J.: 1995, “Mathematical Logic in Poland 1900–1939: People, Circles, Institutions, Ideas”, Modern Logic 5, 363–405.

Downloads

  • PDF

Published

2004-01-19

How to Cite

1.
MURAWSKI, Roman. Truth vs. provability – philosophical and historical remarks. Logic and Logical Philosophy. Online. 19 January 2004. Vol. 10, no. 10, p. 93–117. [Accessed 5 July 2025]. DOI 10.12775/LLP.2002.006.
  • ISO 690
  • ACM
  • ACS
  • APA
  • ABNT
  • Chicago
  • Harvard
  • IEEE
  • MLA
  • Turabian
  • Vancouver
Download Citation
  • Endnote/Zotero/Mendeley (RIS)
  • BibTeX

Issue

No. 10 (2002)

Section

Articles

Stats

Number of views and downloads: 997
Number of citations: 0

Crossref
Scopus
Google Scholar
Europe PMC

Search

Search

Browse

  • Browse Author Index
  • Issue archive

User

User

Current Issue

  • Atom logo
  • RSS2 logo
  • RSS1 logo

Information

  • For Readers
  • For Authors
  • For Librarians

Newsletter

Subscribe Unsubscribe

Language

  • English
  • Język Polski
Up

Akademicka Platforma Czasopism

Najlepsze czasopisma naukowe i akademickie w jednym miejscu

apcz.umk.pl

Partners

  • Akademia Ignatianum w Krakowie
  • Akademickie Towarzystwo Andragogiczne
  • Fundacja Copernicus na rzecz Rozwoju Badań Naukowych
  • Instytut Historii im. Tadeusza Manteuffla Polskiej Akademii Nauk
  • Instytut Kultur Śródziemnomorskich i Orientalnych PAN
  • Instytut Tomistyczny
  • Karmelitański Instytut Duchowości w Krakowie
  • Ministerstwo Kultury i Dziedzictwa Narodowego
  • Państwowa Akademia Nauk Stosowanych w Krośnie
  • Państwowa Akademia Nauk Stosowanych we Włocławku
  • Państwowa Wyższa Szkoła Zawodowa im. Stanisława Pigonia w Krośnie
  • Polska Fundacja Przemysłu Kosmicznego
  • Polskie Towarzystwo Ekonomiczne
  • Polskie Towarzystwo Ludoznawcze
  • Towarzystwo Miłośników Torunia
  • Towarzystwo Naukowe w Toruniu
  • Uniwersytet im. Adama Mickiewicza w Poznaniu
  • Uniwersytet Komisji Edukacji Narodowej w Krakowie
  • Uniwersytet Mikołaja Kopernika
  • Uniwersytet w Białymstoku
  • Uniwersytet Warszawski
  • Wojewódzka Biblioteka Publiczna - Książnica Kopernikańska
  • Wyższe Seminarium Duchowne w Pelplinie / Wydawnictwo Diecezjalne „Bernardinum" w Pelplinie

© 2021- Nicolaus Copernicus University Accessibility statement Shop