Towards Mathematical Philosophy pp 319-343

Part of the Trends in Logic book series (TREN, volume 28) | Cite as

On Meta-Knowledge and Truth

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.

Keywords

meta-knowledge categorial syntax meaning denotation categorial semantics non-standard models truthfulness language knowledge adequacy 

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References

  1. [1]
    Ajdukiewicz, K., 1931, ‘O znaczeniu’ (‘On meaning of expressions’), Księga Pamiątkowa Polskiego Towarzystwa Filozoficznego we Lwowie, Lwów, Google Scholar
  2. [2]
    Ajdukiewicz, K., 1934, ‘Sprache und Sinn’, Erkenntnis, IV: 100–138. CrossRefGoogle Scholar
  3. [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. [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. [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. MATHCrossRefMathSciNetGoogle Scholar
  6. [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. CrossRefGoogle Scholar
  7. [7]
    Bar-Hillel, Y., 1964, Language and Information, Selected Essays on Their Theory and Applications, Addison-Wesley Publishing Co., Reading, Mass. Google Scholar
  8. [8]
    Buszkowski, W., 1988, ‘Three theories of categorial grammar’, in Buszkowski, W., Marciszewski, W., van Benthem, J. (eds.), pp. 57–84. Google Scholar
  9. [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. [10]
    Buszkowski, W., Marciszewski, W., van Benthem, J. (eds.), 1988, Categorial Grammar, John Benjamis Publishing Company, Amsterdam-Philalelphia. MATHGoogle Scholar
  11. [11]
    Cresswell, M.J., 1973, Logics and Languages, Mathuen, London. Google Scholar
  12. [12]
    Cresswell, M.J., 1977, ‘Categorial languages’, Studia Logica, 36: 257–269. CrossRefMathSciNetGoogle Scholar
  13. [13]
    Carnap, R., 1947, Meaning and Necessity, University of Chicago Press, Chicago. MATHGoogle Scholar
  14. [14]
    Chomsky, N., 1957, Syntactic Structure, Mouton and Co., The Hague. Google Scholar
  15. [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. [16]
    Frege, G., 1884, Die Grundlagen der Arithmetik. Eine logisch-mathematische Untersuchung über den Begriff der Zahl, W. Koebner, Breslau. Google Scholar
  17. [17]
    Frege, G., 1892, ‘Über Sinn und Bedeutung’, Zeitschrift für Philosophie und pilosophishe Kritik, 100: 25–50. Google Scholar
  18. [18]
    Frege, G., 1964, Begriffsschrift und andere Ausätze, Angelelli, I. (ed.), Wissenschaftliche Buchgesellschaft/G. Olms, Darmstadt-Hildesheim. Google Scholar
  19. [19]
    Gerhard, C.I. (ed.), 1890, Die philosophische Schriften von Wilhelm Leibniz, vol. 7, Weidmansche Buchhandlung, Berlin. Google Scholar
  20. [20]
    Gödel, K., 1931, ‘Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I’, Monatshefte für Mathematik und Physik, 38: 173–198. CrossRefGoogle Scholar
  21. [21]
    Hendriks, H., 2000, ‘Compositional and model-theoretic interpretation’, Artificial Intelligence Preprint Series, Preprint nr 020. Google Scholar
  22. [22]
    Hodges, W., 1996, ‘Compositional semantics for language of imperfect information’, Logic Journal of the IGPL, 5(4): 539–563. CrossRefMathSciNetGoogle Scholar
  23. [23]
    Hodges, W., 1998, ‘Compositionality is not the problem’, Logic and Logical Philosophy, 6: 7–33. MATHMathSciNetGoogle Scholar
  24. [24]
    Hodges, W., 2001, ‘Formal features of compositionality’, Journal of Logic, Language and Information 10, pp. 7–28, Kluwer Academic Publishers. Google Scholar
  25. [25]
    Husserl, E., 1900–1901, Logische Untersuchungen, vol. I, Halle 1900, vol. II, Halle, 1901. Google Scholar
  26. [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. [27]
    Janssen, T.M.V., 2001, ‘Frege, contextuality and compositionality’, Journal of Logic, Language and Information, 10: 115–136. MATHCrossRefMathSciNetGoogle Scholar
  28. [28]
    Lambek, J., 1958, ‘The mathematics of sentence structure’, American Mathematical Monthly, 65: 154–170. MATHCrossRefMathSciNetGoogle Scholar
  29. [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. [30]
    Leśniewski, S., 1929, ‘Grundzüge eines neuen Systems der Grundlagen der Mathematik’, Fundamenta Mathematicae, 14: 1–81. MATHGoogle Scholar
  31. [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. [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. [33]
    Montague, R., 1970, ‘Universal grammar’, Theoria, 36: 373–398. MathSciNetCrossRefGoogle Scholar
  34. [34]
    Montague, R., 1974, ‘Formal Philosophy’, Thomason, R.H. (ed.), Selected Papers of Richard Montague, Yale University Press, New Haven, Conn. Google Scholar
  35. [35]
    Partee, B.H., ter Meulen, A., Wall, R.E., 1990, Mathematical Methods in Linguistics, Kluwer Academic Publishers, Dordrecht. MATHGoogle Scholar
  36. [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. [37]
    Simons, P., 1989, ‘Combinators and categorial grammar’, Notre Dame Journal of Formal Logic, 30(2): 241–261. MATHCrossRefMathSciNetGoogle Scholar
  38. [38]
    Stanosz, B., Nowaczyk, A., 1976, Logiczne Podstawy Języka (The Logical Foundations of Language), Ossolineum, Wrocław-Warszawa. Google Scholar
  39. [39]
    Suszko, R., 1958, ‘Syntactic structure and semantical reference’, Part I, Studia Logica, 8: 213–144. CrossRefMathSciNetGoogle Scholar
  40. [40]
    Suszko, R., 1960, ‘Syntactic structure and semantical reference’, Part II, Studia Logica, 9: 63–93. CrossRefMathSciNetGoogle Scholar
  41. [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. [42]
    Suszko, R., 1968, ‘Ontology in the tractatus of L. Wittgenstein’, Notre Dame Journal of Formal Logic, 9: 7–33. MATHCrossRefMathSciNetGoogle Scholar
  43. [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. [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. [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. [46]
    Van Benthem, J., 1986, Essays in Logical Semantics, Reidel, Dordrecht. MATHGoogle Scholar
  47. [47]
    Wittgenstein, L., 1953, Philosophical Investigations, Blackwell, Oxford. Google Scholar
  48. [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. [49]
    Wybraniec-Skardowska, U., 1985, Teoria Języków Syntaktycznie Kategorialnych (Theory of Syntactically-Categorial Languages), PWN, Wrocław–Warszawa. Google Scholar
  50. [50]
    Wybraniec-Skardowska, U., 1989, ‘On eliminatibility of ideal linguistic entities’, Studia Logica, 48(4): 587–615. MATHCrossRefMathSciNetGoogle Scholar
  51. [51]
    Wybraniec-Skardowska, U., 1991, Theory of Language Syntax. Categorial Approach, Kluwer Academic Publisher, Dordrecht–Boston–London. Google Scholar
  52. [52]
    Wybraniec-Skardowska, U., 1998, ‘Logical and philosophical ideas in certain approaches to language’, Synthese, 116(2): 231–277. MATHCrossRefMathSciNetGoogle Scholar
  53. [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. [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. [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. [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. [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. [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. [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

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Autonomous Section of Applied Logic and Methodology of SciencesPoznań School of Banking, Department in ChorzówChorzówPoland

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