Matters of Logic

  • Jan WoleńskiEmail author
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 45)


Since STT is a logical theory, its relation to logic are very close. The task of this chapter consists in presenting logical concepts and theories relevant for the further discussion of STT. Particular sections are devoted to propositional calculus, first-order logic, metalogic, definitions of logic (the universality of logic is its essential attribute) and historical notes on metalogic and metamathematics.


  1. Agazzi, E. (Ed.) (1981). Modern Logic. Dordrecht: Reidel.Google Scholar
  2. Anderson, C. A., Zeleny, M. (Eds.) (2001). Logic, Meaning and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer.Google Scholar
  3. Andréka, H., Madárasz, J., Németi, I. (2003). Why first-order logic? (unpublished).Google Scholar
  4. Barwise, J. (1985). Model-theoretic logics: Background and aims. In Barwise, Feferman (1985), 3–23.Google Scholar
  5. Barwise, J., Feferman, S. (Eds.) (1985). Model-Theoretic Logics. Berlin: Springer.Google Scholar
  6. Beall, J. C., Restall, G. (2006). Logical Pluralism. Oxford: Clarendon Press.Google Scholar
  7. Benmakhlouf, A. (Ed.). (2004). Sémantique et épistemologie. Casablanca: Editions Le Fennec.Google Scholar
  8. Beziau, J.-Y. (Ed.) (2007). Logica Universalis. Toward a General Theory of Logic. Basel: Birkhäuser.Google Scholar
  9. Boolos, G. (1975). On second-order logic. Journal of Philosophy, 72, 509–527; repr. in Shapiro (1996), 70–87.Google Scholar
  10. Borkowski, L. (1991). Characterization of quantifiers in the axiomatic theory of consequence. In Borkowski, Stępień (1991), 37–39.Google Scholar
  11. Church, A. (1956). Introduction to Mathematical Logic. Princeton: Princeton University Press.Google Scholar
  12. Corcoran, J. (2001). Second-order logic. In Anderson, Zeleny (2001), 61–75.Google Scholar
  13. Feferman, S. (2004). Tarski’s conceptual analysis of semantical notions. In Benmakhlouf (2004), 79–108.Google Scholar
  14. Flum, J. (1985). Characterizing logic. In Barwise, Feferman (1985), 77–120.Google Scholar
  15. Font, J. M. (2016). Abstract Algebraic Logic. An Introductory Textbook. London: College Publications.Google Scholar
  16. Frege, G. (1891). Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, 100; 25–50; Eng. tr . (by M. Black) in Frege (1984), 155–177.Google Scholar
  17. Frege, G. (1892). Über Begriff und Gegenstand. Vierteljahrsschrift für Wissenschaftliche Philosophie, 16, 192–205; Eng. tr. (by P. Geach), in Frege (1984), 182–194.Google Scholar
  18. Frege, G. (1984). Collected Papers on Mathematics, Logic and Philosophy. Oxford: Blackwell.Google Scholar
  19. Gödel, K. (1944). Russell’s mathematical logic. In Schillp (1944), 125–153; repr. in Gödel (1989), 119–141.Google Scholar
  20. Gödel, K. (1989). Collected papers (v. II). Oxford: Oxford University Press.Google Scholar
  21. Goldblatt, R. (1979). Topoi. The Categorial Analysis of Logic. Amsterdam: North-Holland.Google Scholar
  22. Haack, S. (1978). Philosophy of Logics. Cambridge: Cambridge University Press.Google Scholar
  23. Halbach, V. (2011). Axiomatic Theories of Truth. Cambridge: Cambridge University Press.Google Scholar
  24. Hendricks, V., Neuhaus, F., Pedersen, S. A., Scheffler, U., Wansing, H. (Eds.) (2004). First-Order Logic Revisited. Berlin: Logos.Google Scholar
  25. Hintikka, J. (Ed.) (1995). From Dedekind to Gödel. Dordrecht: KluwerGoogle Scholar
  26. Hintikka, J. (1996). The Principles of Mathematics Revisited. Cambridge: Cambridge University Press.Google Scholar
  27. Hintikka, J. (1998). Language, Truth and Logic in Mathematics. Dordrecht: Kluwer.Google Scholar
  28. Hodges, W. (2004). Which languages have Tarski truth-definition. In Adamowicz, Z., Artemov, S., Niwiński, D., Orłowska, E. Romanowska, A, Woleński, J. (2004), 77–92.Google Scholar
  29. Lyndon, R. C. (1966). Notes on Logic. New York: Van Nostrand.Google Scholar
  30. Mann, A. L., Sandu, G., Sevenster, M. (2011). Independence-Friendly Logic: A Game-Theoretic Approach. Cambridge: Cambridge University Press.Google Scholar
  31. Manzano, M. (1999). Model Theory. Oxford: Clarendon Press.Google Scholar
  32. Murawski, R. (1999). Recursive Functions and Metamathematics. Problems of Completeness and Decidability. Dordrecht: Kluwer.Google Scholar
  33. Parsons, D. (2016). Theories of Intensionality. A Critical Survey. Dordrecht: Springer.Google Scholar
  34. Pogorzelski, W. A. (1994). Notions and Theorems of Elementary Formal Logic. Białystok: Białystok University Press.Google Scholar
  35. Quine, W. v. O. (1970). Philosophy of Logic. Englewood Cliffs: Prentice Hall.Google Scholar
  36. Schillp, P. A. (Ed.) (1944). The Philosophy of Bertrand Russell. La Salle: Open CourtGoogle Scholar
  37. Shapiro, S. (1991). Foundations without Foundationalism. Oxford: Oxford University Press.Google Scholar
  38. Shapiro, S. (Ed.) (1996). The Limits of Logic. Higher-Order Logic and the Löwenheim–Skolem Theorem. Aldershot: Dartmouth.Google Scholar
  39. Shapiro, S. (1996a). Introduction. In Shapiro (1996), XI–XXII.Google Scholar
  40. Shapiro, S. (2014). Varieties of Logic. Oxford: Oxford University Press.Google Scholar
  41. Simpson, S. G. (1999). Subsystems of Second-Order Arithmetic. Berlin: Springer.Google Scholar
  42. Stelmach, J., Brożek, B., Kwiatek, Ł. (Eds.) (2016). The Normative Mind. Kraków: Copernicus Center.Google Scholar
  43. Surma, S. J. (1981). The growth of logic out of the foundational research in the foundations of mathematics. In Agazzi (1981), 15–33.Google Scholar
  44. Tarski, A. (1930). Über einige fundamentale Begriffe der Metamathematik. Comptes Rendus des séances de la Société des Sciences et de Lettres de Varsovie, 23, 22–39; Eng. tr. in Tarski (1956), 30–37.Google Scholar
  45. Tarski, A. (1933). Pojęcie prawdy w językach nauk dedukcyjnych (The concept of truth in languages of deductive sciences). Warszawa: Towarzystwo Naukowe Warszawskie; Germ. tr. (with additions) as Tarski (1935).Google Scholar
  46. Tarski, A. (1935). Der Wahrheitsbegriff in den formalisierten Sprachen. Studia Philosophica, 1, 261–405; repr. in Tarski (1986), v. 2, 51–198; Engl. tr. (The Concept of Truth in Formalized Languages) in Tarski (1956), 152–278 (page-references Tarski (1933)).Google Scholar
  47. Tarski, A. (1936). Über den Begriff der logischen Folgerung. In Actes du Congès International de Philosophie Scientifique, v. 7, 1–11. Paris: Herman; Eng. tr. in Tarski (1956), 409–420.Google Scholar
  48. Tarski, A. (1956). Logic, Semantics, Metamathematics. Papers of 1923 to 1938 (tr. by J. H. Woodger). Oxford: Clarendon Press; 2nd ed., Indianapolis: Hackett Publishing Company 1983.Google Scholar
  49. Tarski, A. (1986). What are logical notions? History and Philosophy of Logic, 7, 143–154.Google Scholar
  50. Tarski, A., Vaught, R. (1957). Arithmetical extensions of relational systems. Compositio Mathematica, 13, 81–102; repr. in Tarski (1986), v. 4, 651–682.Google Scholar
  51. Vänäänen, J. (2001). Second-order logic and the foundations of mathematics. Bulletin of Symbolic Logic, 7, 504–520.Google Scholar
  52. Westerståhl, D. (1976). Some Philosophical Aspects of Abstract Model Theory. Göteborg: Institutionen för Filosofi, Göteborgs Universitet.Google Scholar
  53. Woleński, J. (1995a). On Tarski’s Background. In Hintikka (1995), 331–341; repr. in Woleński (1999), 126–133.Google Scholar
  54. Woleński, J. (1999). Essays in the History of Logic and Logical Philosophy. Kraków: Jagiellonian University Press.Google Scholar
  55. Woleński, J. (2004). First-order logic: (philosophical) pro and contra. In Hendricks, Neuhaus, Pedersen, Scheffer, Wansing (2004), 369–399; repr. in Woleński (2011), 61–80.Google Scholar
  56. Woleński, J. (2011). Essays on Logic and Its Applications in Philosophy. Frankfurt a. M.: Peter Lang.Google Scholar
  57. Woleński, J. (2016a). Normativity of logic. In Stelmach, Brożek, Kwiatek (2016), 169–195; repr. in Woleński (2018), 177–194.Google Scholar
  58. Woleński, J. (2018). Logic and Its Philosophy. Frankfurt a. M.: Peter Lang.Google Scholar
  59. Wójcicki, R. (1988). Theory of Logical Calculi. Basic Theory of Consequence Operations. Dordrecht: Kluwer.Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Jagiellonian University (prof. emeritus)KrakówPoland
  2. 2.University of Information, Technology and ManagementRzeszowPoland

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