The Paradox of Inference and the Non-Triviality of Analytic Information
Tóm tắt
The classical theory of semantic information (ESI), as formulated by Bar-Hillel and Carnap in 1952, does not give a satisfactory account of the problem of what information, if any, analytically and/or logically true sentences have to offer. According to ESI, analytically true sentences lack informational content, and any two analytically equivalent sentences convey the same piece of information. This problem is connected with Cohen and Nagel’s paradox of inference: Since the conclusion of a valid argument is contained in the premises, it fails to provide any novel information. Again, ESI does not give a satisfactory account of the paradox. In this paper I propose a solution based on the distinction between empirical information and analytic information. Declarative sentences are informative due to their meanings. I construe meanings as structured hyperintensions, modelled in Transparent Intensional Logic as so-called constructions. These are abstract, algorithmically structured procedures whose constituents are sub-procedures. My main thesis is that constructions are the vehicles of information. Hence, although analytically true sentences provide no empirical information about the state of the world, they convey analytic information, in the shape of constructions prescribing how to arrive at the truths in question. Moreover, even though analytically equivalent sentences have equal empirical content, their analytic content may be different. Finally, though the empirical content of the conclusion of a valid argument is contained in the premises, its analytic content may be different from the analytic content of the premises and thus convey a new piece of information.
Tài liệu tham khảo
Abramsky, S. (2008). Information, processes and games. In P. Adriaans & J. van Benthem (Eds.), Philosophy of information: Handbook of the philosophy of science (pp. 483–550). Amsterdam: Elsevier Science.
Allo, P. (2007). Logical pluralism and semantic information. Journal of Philosophical Logic, 36, 659–694.
Anderson, C. A. (1998). Alonzo Church’s contributions to philosophy and intensional logic. The Bulletin of Symbolic Logic, 4(2), 129–171.
Bar-Hillel, Y., & Carnap, R. (1952). An outline of a theory of semantic information, rep. in Bar-Hillel (1964) (ed.), Language and Information (pp. 221–274). Addison-Wesley, Reading, MA.
Bolzano, B. (1837). Wissenschaftslehre I, II. Sulzbach.
Carnap, R. (1947). Meaning and necessity. Chicago University Press.
Church, A. (1941). The calculi of lambda conversion. Princeton: Princeton University Press.
Church, A. (1954). Intensional isomorphism and identity of belief. Philosophical Studies, 5, 65–73.
Cohen, M. R., & Nagel, E. (1934). An introduction to logic and scientific method. London: Routledge and Kegan Paul.
Cook, S. A. (1971). The complexity of theorem-proving procedures. In: STOC ’71: Proceedings of the third annual ACM symposium on Theory of computing (pp. 151–158). New York: ACM.
Cresswell, M. J. (1985). Structured meanings. Cambridge, Mass: MIT.
Duží, M. (1992). Semantic information connected with data. In J. Biskup & R. Hull (Eds.), Database theory ICDT’92 (pp. 376–390). Berlin: Springer, Lecture Notes in Computer Science.
Duží, M. (2006). Informativnost matematických či analyticky pravdivých tvrzení a paradox inference’ (in Czech). Filosofický časopis, 54(4), 501–522.
Duží, M. (2009). Topic-focus articulation from the semantic point of view, In A. Gelbukh (Ed.), Computational linguistics and intelligent text processing (pp. 220–232). Springer, LNCS 5449.
Duží, M., & Materna, P. (2004). A procedural theory of concepts and the problem of the synthetic a priori. Korean Journal of Logic, 7, 1–22.
Duží, M., & Materna, P. (2005). Logical form. In G. Sica (Ed.), Essays on the foundations of mathematics and logic, vol. 1 (pp. 115–153). Monza: Polimetrica International Scientific.
Duží, M., Jespersen B., Materna P. (2010). Procedural semantics for hyperintensional logic; Foundations and applications of transparent intensional logic. Series Logic, Epistemology and the Unity of Science. Berlin: Springer.
D’Agostino, M., & Floridi, L. (2009). The enduring scandal of deduction. Is propositional logic really uninformative? Synthese, 167, 271–315.
Floridi, L. (2004). Outline of a theory of strongly semantic information. Minds & Machines, 14, 197–222.
Floridi, L. (2005). ‘Is information meaningful data’? Philosophy and Phenomenological Research, 70, 351–370.
Frege, G. (1892). Über Sinn and Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, 100, 25–50.
Gärdenfors, P. (1988): Knowledge in flux: Modelling the dynamics of epistemic states, A Bradford Book, Cambridge Massachusetts: The MIT.
Hintikka, J. (1970). Surface information and depth information. In J. Hintikka & O. Suppes (Eds.), Information and inference (pp. 263–297). Reidel: Dordrecht.
Jespersen, B. (2003). Why the tuple theory of structured propositions isn’t a theory of structured propositions. Philosophia, 31, 171–183.
Jespersen, B. (2005). Explicit intensionalisation, anti-actualism, and how Smith’s murderer might not have murdered Smith. Dialectica, 59, 285–314.
Jespersen, B. (2008). Predication and extensionalization. Journal of Philosophical Logic, 37, 479–499.
Jespersen, B. (2010). Hyperintensions and procedural isomorphism: Alternative (½). In The Analytical Way. Proceedings of the 6th European Congress of Analytic Philosophy. Tadeusz Czarnecki, K. Kijania-Placek, O. Poller, and J. Woleński (eds.), College Publications, London, pp. 301–322.
Johnson-Laird, P. N. (1977). Procedural semantics. Cognition, 5, 189–214.
Kaufmann, W. (1906). ‘Über die Konstitution des Elektrons’, Annalen der Physik, 19, 487–553, <http://gallica.bnf.fr/ark:/12148/bpt6k15326w/f497.chemindefer>
King, J. C. (1995). Structured propositions and complex predicates. Nous, 29(4), 516–535.
King, J. C. (2001). Structured propositions, http://plato.stanford.edu/entries/propositionsstructured/, version as of 8 August 2001.
Materna, P. (1998). Concepts and objects. Acta Philosophica Fennica, 63, Helsinki.
Materna, P. (2004). Conceptual systems. Berlin: Logos Verlag.
Materna, P., & Duží, M. (2005). The Parmenides principle. Philosophia, 32, 155–180.
Mates, B. (1950). ‘Synonymity’, in: University of California Publications in Philosophy, 25, 201–226.
Moschovakis, Y. N. (1994). Sense and denotation as algorithm and value. In J. Väänänen & J. Oikkonen (Eds.), Lecture Notes in Logic (Vol. 2, pp. 210–249). Berlin: Springer.
Moschovakis, Y. N. (2006). A logical calculus of meaning and synonymy. Linguistics and Philosophy, 29, 27–89.
Sequoiah-Grayson, S. (2006). Information flow and impossible situations. Logique et Analyse, 196, 371–398.
Sequoiah-Grayson, S. (2008). The scandal of deduction (Hintikka on the information yield of deductive inferences). Journal of Philosophical Logic, 37(1), 67–94.
Sundholm, G. (1997). Inference vs. consequence. In T. Childers (Ed.), The logica yearbook 1997 (pp. 26–36). Prague 1998.
Tichý, P. (1966). K explikaci pojmu obsah věty. Filosofický časopis 14, pp. 364–372. Translation ‘On explication of the notion “the content of a sentence’, reprinted in: Tichý (2004), pp. 53–68.
Tichý, P. (1988). The foundations of Frege’s logic. Berlin: De Gruyter.
Tichý, P. (2004). Collected papers in logic and philosophy. In V. Svoboda, B. Jespersen, C. Cheyne (Eds.), Prague: Filosofia, Czech Academy of Sciences, and Dunedin: University of Otago Press.
van Benthem, J., & Martinez, M.-C. (2008). The stories of logic and information. In P. Adriaans & J. van Benthem (Eds.), Philosophy of information: handbook of the philosophy of science (pp. 217–280). Amsterdam: Elsevier Science.
Wagner, S. J. (1986). California semantics meets the Great Fact. Notre Dame Journal of Formal Logic, 27(3), 430–455.
Wittgenstein, L. (1922). Tractatus Logico-Philosophicus. London: Routlege.