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On Meta-Knowledge and Truth

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Towards Mathematical Philosophy

Part of the book series: Trends in Logic ((TREN,volume 28))

Abstract

The paper deals with the problem of logical adequacy of language knowledge with cognition of reality. A logical explication of the concept of language knowledge conceived of as a kind of codified knowledge is taken into account in the paper. Formal considerations regarding the notions of meta-knowledge (logical knowledge about language knowledge) and truth are developed in the spirit of some ideas presented in the author’s earlier papers (Theory of Language Syntax. Categorial Approach, 1991; Synthese 116(2): 231–277, 1998; Logical Ideas of Roman Suszko, Proceedings of the Wide-Poland Conference of History of Logic, pp. 89–119, 2001; Bulleting of Symbolic Logic 7(1): 157–158, 2001; Studia Logica 85: 107–134, 263–276, 2007; Gödel Centenary 2006: Posters, Collegium Logicum, pp. 87–91, 2007) treating about the notions of meaning, denotation and truthfulness of well-formed expressions (wfes) of any given categorial language. Three aspects connected with knowledge codified in language are considered, including: 1) syntax and two kinds of semantics: intensional and extensional, 2) three kinds of non-standard language models and 3) three notions of truthfulness of wfes. Adequacy of language knowledge to cognitive objects is understood as an agreement of truthfulness of sentences in these three models.

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References

  1. Ajdukiewicz, K., 1931, ‘O znaczeniu’ (‘On meaning of expressions’), Księga Pamiątkowa Polskiego Towarzystwa Filozoficznego we Lwowie, Lwów,

    Google Scholar 

  2. Ajdukiewicz, K., 1934, ‘Sprache und Sinn’, Erkenntnis, IV: 100–138.

    Article  Google Scholar 

  3. Ajdukiewicz, K., 1935, ‘Die syntaktische Konnexität’, Studia Pholosophica, Leopoli, 1: 1–27. English translation: ‘Syntactic connection’, in McCall, S. (ed.), Polish Logic 1920–1939, Clarendon Press, Oxford, pp. 207–231.

    Google Scholar 

  4. Ajdukiewicz, K., 1960, ‘Związki składniowe między członami zdań oznajmujących (‘Syntactic relation between elements of declarative sentences’)’, Studia Filozoficzne, 6(21): 73–86. First presented in English at the International Linguistic Symposium in Erfurt, September 27–October 2, 1958.

    Google Scholar 

  5. Bar-Hillel, Y., 1950, ‘On syntactical categories’, Journal of Symbolic Logic, 15: 1–16; reprinted in Bar-Hillel, Y., Language and Information, Selected Essays on Their Theory and Applications, Addison-Wesley Publishing Co., Reading, Mass, 1964, pp. 19–37.

    Article  MATH  MathSciNet  Google Scholar 

  6. Bar-Hillel, Y., 1953, ‘A quasi-arithmetical notation for syntactic description’, Language, 63: 47–58; reprinted in Aspects of Language, Jerusalem, pp. 61–74.

    Article  Google Scholar 

  7. Bar-Hillel, Y., 1964, Language and Information, Selected Essays on Their Theory and Applications, Addison-Wesley Publishing Co., Reading, Mass.

    Google Scholar 

  8. Buszkowski, W., 1988, ‘Three theories of categorial grammar’, in Buszkowski, W., Marciszewski, W., van Benthem, J. (eds.), pp. 57–84.

    Google Scholar 

  9. Buszkowski, W., 1989, Logiczne Podstawy Gramatyk Kategorialnych Ajdukiewicza-Lambeka (Logical Foundations of Ajdukiewicz’s-Lambek’s Categorial Grammars), Logika i jej Zastosowania, PWN, Warszawa.

    Google Scholar 

  10. Buszkowski, W., Marciszewski, W., van Benthem, J. (eds.), 1988, Categorial Grammar, John Benjamis Publishing Company, Amsterdam-Philalelphia.

    MATH  Google Scholar 

  11. Cresswell, M.J., 1973, Logics and Languages, Mathuen, London.

    Google Scholar 

  12. Cresswell, M.J., 1977, ‘Categorial languages’, Studia Logica, 36: 257–269.

    Article  MathSciNet  Google Scholar 

  13. Carnap, R., 1947, Meaning and Necessity, University of Chicago Press, Chicago.

    MATH  Google Scholar 

  14. Chomsky, N., 1957, Syntactic Structure, Mouton and Co., The Hague.

    Google Scholar 

  15. Frege, G., 1879, Begriffsschrift, eine der arithmetischen nachbildete Formelsprache des reinen Denkens, Halle; reprinted in Frege, G., Begriffsschrift und andere Ausätze, Angelelli, I. (ed.), Wissenschaftliche Buchgesellschaft/G. Olms, Darmstadt-Hildesheim, 1964.

    Google Scholar 

  16. Frege, G., 1884, Die Grundlagen der Arithmetik. Eine logisch-mathematische Untersuchung über den Begriff der Zahl, W. Koebner, Breslau.

    Google Scholar 

  17. Frege, G., 1892, ‘Über Sinn und Bedeutung’, Zeitschrift für Philosophie und pilosophishe Kritik, 100: 25–50.

    Google Scholar 

  18. Frege, G., 1964, Begriffsschrift und andere Ausätze, Angelelli, I. (ed.), Wissenschaftliche Buchgesellschaft/G. Olms, Darmstadt-Hildesheim.

    Google Scholar 

  19. Gerhard, C.I. (ed.), 1890, Die philosophische Schriften von Wilhelm Leibniz, vol. 7, Weidmansche Buchhandlung, Berlin.

    Google Scholar 

  20. Gödel, K., 1931, ‘Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I’, Monatshefte für Mathematik und Physik, 38: 173–198.

    Article  Google Scholar 

  21. Hendriks, H., 2000, ‘Compositional and model-theoretic interpretation’, Artificial Intelligence Preprint Series, Preprint nr 020.

    Google Scholar 

  22. Hodges, W., 1996, ‘Compositional semantics for language of imperfect information’, Logic Journal of the IGPL, 5(4): 539–563.

    Article  MathSciNet  Google Scholar 

  23. Hodges, W., 1998, ‘Compositionality is not the problem’, Logic and Logical Philosophy, 6: 7–33.

    MATH  MathSciNet  Google Scholar 

  24. Hodges, W., 2001, ‘Formal features of compositionality’, Journal of Logic, Language and Information 10, pp. 7–28, Kluwer Academic Publishers.

    Google Scholar 

  25. Husserl, E., 1900–1901, Logische Untersuchungen, vol. I, Halle 1900, vol. II, Halle, 1901.

    Google Scholar 

  26. Janssen, T.M.V., 1996, ‘Compositionality’, in van Benthem, J., ter Muelen, A. (eds.), Handbook of Logic and Language, Chapter 7, Elsevier Science, Amsterdam–Lausanne–New York, pp. 417–473.

    Google Scholar 

  27. Janssen, T.M.V., 2001, ‘Frege, contextuality and compositionality’, Journal of Logic, Language and Information, 10: 115–136.

    Article  MATH  MathSciNet  Google Scholar 

  28. Lambek, J., 1958, ‘The mathematics of sentence structure’, American Mathematical Monthly, 65: 154–170.

    Article  MATH  MathSciNet  Google Scholar 

  29. Lambek, J., 1961, ‘On the calculus of syntactic types’, in Jakobson, R. (ed.), Structure of Language and its Mathematical Aspects, Proceedings of Symposia in Applied Mathematics, vol. 12, AMS, Providence, Rhode Island.

    Google Scholar 

  30. Leśniewski, S., 1929, ‘Grundzüge eines neuen Systems der Grundlagen der Mathematik’, Fundamenta Mathematicae, 14: 1–81.

    MATH  Google Scholar 

  31. Leśniewski, S., 1930, ‘Über die Grundlagen der Ontologie’, Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie, Classe II, vol. 23, Warszawa, pp. 111–132.

    Google Scholar 

  32. Marciszewski, W., 1988, ‘A chronicle of categorial grammar’, in Buszkowski, W., et al. (eds.), Categorial Grammar, John Benjamis Publishing Company, Amsterdam-Philalelphia, pp. 7–22.

    Google Scholar 

  33. Montague, R., 1970, ‘Universal grammar’, Theoria, 36: 373–398.

    Article  MathSciNet  Google Scholar 

  34. Montague, R., 1974, ‘Formal Philosophy’, Thomason, R.H. (ed.), Selected Papers of Richard Montague, Yale University Press, New Haven, Conn.

    Google Scholar 

  35. Partee, B.H., ter Meulen, A., Wall, R.E., 1990, Mathematical Methods in Linguistics, Kluwer Academic Publishers, Dordrecht.

    MATH  Google Scholar 

  36. Peirce, Ch.S., 1931–1935, Collected Papers of Charles Sanders Peirce, Hartshorne C., Meiss P. (eds.), vols. 1–5, Cambridge, Mass.

    Google Scholar 

  37. Simons, P., 1989, ‘Combinators and categorial grammar’, Notre Dame Journal of Formal Logic, 30(2): 241–261.

    Article  MATH  MathSciNet  Google Scholar 

  38. Stanosz, B., Nowaczyk, A., 1976, Logiczne Podstawy Języka (The Logical Foundations of Language), Ossolineum, Wrocław-Warszawa.

    Google Scholar 

  39. Suszko, R., 1958, ‘Syntactic structure and semantical reference’, Part I, Studia Logica, 8: 213–144.

    Article  MathSciNet  Google Scholar 

  40. Suszko, R., 1960, ‘Syntactic structure and semantical reference’, Part II, Studia Logica, 9: 63–93.

    Article  MathSciNet  Google Scholar 

  41. Suszko, R., 1964, ‘O kategoriach syntaktycznych i denotacjach wyrażeń w językach sformalizowanych’ (‘On syntactic categories and denotation of expressions in formalized languages’), in Rozprawy Logiczne (Logical Dissertations) (to the memory of Kazimierz Ajdukiewicz), Warszawa, pp. 193–204.

    Google Scholar 

  42. Suszko, R., 1968, ‘Ontology in the tractatus of L. Wittgenstein’, Notre Dame Journal of Formal Logic, 9: 7–33.

    Article  MATH  MathSciNet  Google Scholar 

  43. Van Benthem, J., 1980, ‘Universal algebra and model theory. Two excursions on the border’, Report ZW-7908. Department of Mathematics, Groningen University.

    Google Scholar 

  44. Van Benthem, J., 1981, ‘Why is semantics what?’, in Groenendijk, J., Janssen, T., Stokhof, M. (eds.), Formal Methods in the Study of Language, Mathematical Centre Tract 135, Amsterdam, pp. 29–49.

    Google Scholar 

  45. Van Benthem, J., 1984, ‘The logic of semantics’, in Landman, F., Veltman F., (eds.), Varietes of Formal Semantics, GRASS series, vol. 3, Foris, Dordrecht, pp. 55–80.

    Google Scholar 

  46. Van Benthem, J., 1986, Essays in Logical Semantics, Reidel, Dordrecht.

    MATH  Google Scholar 

  47. Wittgenstein, L., 1953, Philosophical Investigations, Blackwell, Oxford.

    Google Scholar 

  48. Wybraniec-Skardowska, U., Rogalski, A.K., 1999, ‘On universal grammar and its formalisation’, Proceedings of 20th World Congress of Philosophy, Boston 1998, http://www.bu.edu/wcp/Papers/Logi/LogiWybr.htm.

    Google Scholar 

  49. Wybraniec-Skardowska, U., 1985, Teoria Języków Syntaktycznie Kategorialnych (Theory of Syntactically-Categorial Languages), PWN, Wrocław–Warszawa.

    Google Scholar 

  50. Wybraniec-Skardowska, U., 1989, ‘On eliminatibility of ideal linguistic entities’, Studia Logica, 48(4): 587–615.

    Article  MATH  MathSciNet  Google Scholar 

  51. Wybraniec-Skardowska, U., 1991, Theory of Language Syntax. Categorial Approach, Kluwer Academic Publisher, Dordrecht–Boston–London.

    Google Scholar 

  52. Wybraniec-Skardowska, U., 1998, ‘Logical and philosophical ideas in certain approaches to language’, Synthese, 116(2): 231–277.

    Article  MATH  MathSciNet  Google Scholar 

  53. Wybraniec-Skardowska, U., 2001a, ‘On denotations of quantifiers’, in Omyła, M. (ed.), Logical Ideas of Roman Suszko, Proceedings of The Wide-Poland Conference of History of Logic (to the memory of Roman Suszko), Kraków 1999, Faculty of Philosophy and Sociology of Warsaw University, Warszawa, pp. 89–119.

    Google Scholar 

  54. Wybraniec-Skardowska, U., 2001b, ‘Three principles of compositionality’, Bulletin of Symbolic Logic, 7(1): 157–158. The complete text of this paper appears in Cognitive Science and Media in Education, vol. 8, 2007.

    Google Scholar 

  55. Wybraniec-Skardowska, U., 2005, ‘Meaning and interpretation’, in Beziau, J.Y., Costa Leite, A. (eds.), Handbook of the First World Congress and School on Universal Logic, Unilog’05, Montreux, Switzerland, 104.

    Google Scholar 

  56. Wybraniec-Skardowska, U., 2006, ‘On the formalization of classical categorial grammar’, in Jadacki, J., Paśniczek, J. (eds.), The Lvov-Warsaw School—The New Generation, Poznań Studies in the Philosophy of Sciences and Humanities, vol. 89, Rodopi, Amsterdam-New York, NY, pp. 269–288.

    Google Scholar 

  57. Wybraniec-Skardowska, U., 2007a, ‘Meaning and interpretation’, Part I, Studia Logica, 85: 107–134. http://dx.doi.org/10.1007/s11225-007-9026-0.

    Google Scholar 

  58. Wybraniec-Skardowska, U., 2007b, “Meaning and interpretation’, Part II, Studia Logica, 85: 263–276. http://dx.doi.org/10.1007/s11225-007-9031-3.

    Google Scholar 

  59. Wybraniec-Skardowska, U., 2007c, ‘Three levels of knowledge’, in Baaz, M., Preining, N. (eds.), Gödel Centenary 2006: Posters, Collegium Logicum, vol. IX, Kurt Gödel Society, Vienna, pp. 87–91.

    Google Scholar 

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Authors and Affiliations

  1. Autonomous Section of Applied Logic and Methodology of Sciences, Poznań School of Banking, Department in Chorzów, Wandy 66, 41–500, Chorzów, Poland

    Urszula Wybraniec-Skardowska

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  1. Urszula Wybraniec-Skardowska
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Correspondence to Urszula Wybraniec-Skardowska .

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Editors and Affiliations

  1. Department of Philosophy, London School of Economics, Houghton Street, London, WC2A 2AE, United Kingdom

    David Makinson

  2. Institute of Philosophy and Sociology, Polish Academy of Sciences, Nowy Swiat 72, 00-330, Warszawa, Poland

    Jacek Malinowski

  3. Institute of Philosophy, Dresden University of Technology, 01062, Dresden, Germany

    Heinrich Wansing

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Wybraniec-Skardowska, U. (2009). On Meta-Knowledge and Truth. In: Makinson, D., Malinowski, J., Wansing, H. (eds) Towards Mathematical Philosophy. Trends in Logic, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9084-4_16

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