Synthese

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A measure of inferential-role preservation

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Abstract

The point of formalisation is to model various aspects of natural language. Perhaps the main use to which formalisation is put is to model and explain inferential relations between different sentences. Judged solely by this objective, a formalisation is successful in modelling the inferential network of natural language sentences to the extent that it mirrors this network. There is surprisingly little literature on the criteria of good formalisation, and even less on the question of what it is for a formalisation to mirror the inferential network of a natural language or some fragment of it. This paper takes some exploratory steps towards a quantitative account of the main ingredient in the goodness of a formalisation. We introduce and critically examine a mathematical model of how well a formalisation mirrors natural-language inferential relations.

Keywords

Formalisation Inferential-role preservation Mathematical modelling Adequacy of formalisation Logical form 

References

  1. Baumgartner, M., & Lampert, T. (2008). Adequate formalization. Synthese, 164(1), 93–115.CrossRefGoogle Scholar
  2. Blau, U. (1977). Die dreiwertige Logik der Sprache: Ihre Syntax, Semantik und Anwendung in der Sprachanalyse. Berlin: de Gruyter.Google Scholar
  3. Brun, G. (2004). Die richtige Formel: Philosophische Probleme der logischen Formalisierung (2nd ed.). New York: Ontos.Google Scholar
  4. Brun, G. (2008). Formalization and the objects of logic. Erkenntnis, 69, 1–30.CrossRefGoogle Scholar
  5. Chipman, J. S., Hurwicz, L., Richter, M. K., & Sonnenschein, H. F. (1971). Preferences, utility, and demand: A Minnesota symposium. New York: Harcourt Brace Jovanovich.Google Scholar
  6. Davidson, D. (1976). Inquiries into truth & interpretation, 1976. Oxford: Clarendon Press.Google Scholar
  7. Davidson, D. (1980). The logical form of action sentences. In N. Rescher (ed.), The logic of decision and action. (U. of Pittsburgh Press, reprint with criticism, comment and defence in his Essays on actions & events, pp. 105–148, 1967). Oxford: Oxford University Press.Google Scholar
  8. Epstein, R. L. (2001). Predicate logic. Belmont: Wadsworth.Google Scholar
  9. Heim, I., & Kratzer, A. (1998). Semantics in generative grammar. Oxford: Blackwell.Google Scholar
  10. Lepore, E., & Ludwig, K. (2002). What is logical form? In G. Preyer & G. Peter (Eds.), Logical form and language (pp. 54–96). Oxford: Oxford University Press.Google Scholar
  11. Machina, K. (1976). Truth, belief, and vagueness. Journal of Philosophical Logic, 5, 47–78.CrossRefGoogle Scholar
  12. Mates, B. (1972). Elementary logic (2nd ed.). Oxford: Oxford University Press.Google Scholar
  13. Oliver, A. D. (2010). The matter of form: Logic’s beginnings. In J. Lear & A. D. Oliver (Eds.), The force of argument: Essays in honor of timothy smiley (pp. 165–185). New York: Routledge.Google Scholar
  14. Peregrin, J., & Svoboda, V. (2013). Criteria for logical formalization. Synthese, 190, 2897–2924.CrossRefGoogle Scholar
  15. Quine, W. V. (1960). Word and object, 1960. Cambridge: The MIT Press.Google Scholar
  16. Quine, W. V. (1971). Methodological reflections on current lingustic theory. In D. Davidson & G. Harman (Eds.), Semantics of natural language (pp. 442–454). Dordrecht: Reidel.Google Scholar
  17. Read, S. (1994). Formal and material consequence. Journal of Philosophical Logic, 23, 247–265.CrossRefGoogle Scholar
  18. Russell, B. (1905). On denoting. Mind, 14(1905), 479–493.CrossRefGoogle Scholar
  19. Russell, G. (2008). One true logic? Journal of Philosophical Logic, 37, 593–611.CrossRefGoogle Scholar
  20. Sainsbury, M. R. (2001). Logical forms (2nd ed.). Oxford: Blackwell.Google Scholar
  21. Shapiro, S. (1998). Logical consequence: Models and modality. In M. Schirn (Ed.), The philosophy of mathematics today (pp. 131–156). Oxford: University Press.Google Scholar
  22. Strawson, P. F. (1952). Introduction to logical theory. London: Methuen.Google Scholar
  23. Williamson, T. (2007). The philosophy of philosophy. Oxford: Oxford University Press.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Wadham CollegeOxford UniversityOxfordUK

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