Abstract
For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I then develop an account on which informational contents are indeterminate in their membership. This allows there to be cases in which it is indeterminate whether a given deduction is informative. Nevertheless, on the picture I present, there are determinate cases of informative (and determinate cases of uninformative) inferences. I argue that the model I offer is the best way for an account of content to respect the meaning of the logical constants and the inference rules associated with them without collapsing into a classical picture of content, unable to account for informative deductive inferences.
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References
Buss, S. (1998). Handbook of proof theory (Vol. 137). Amsterdam: Elsevier Science.
Chalmers, D. (2002). The components of content. In: D. Chalmers (Ed.), Philosophy of mind: classical and contemporary readings (pp. 608–633). Oxford University Press.
Chalmers, D. (2010). The nature of epistemic space. In: A. Egan & B. Weatherson (Eds.), Epistemic modality. Oxford University Press.
Dummett, M. (1978). The justification of deduction. In: Truth and other enigmas (pp. 166–185). Cambridge, MA: Harvard University Press.
Henkin, L. (1961). Some remarks on infinitely long formulas. In: Infinitistic methods (pp. 167–183). Oxford: Pergamon Press.
Hintikka, J. (1962) Knowledge and belief: an introduction to the logic of the two notions. Ithaca, N.Y.: Cornell University Press.
Hintikka, J. (1970). Surface information and depth information. In: J. Hintikka & P. Suppes (Eds.), Information and inference. Dordrecht: D. Reidel.
Hintikka, J. (1973). Logic, language-games and information: Kantian themes in the philosophy of logic. Oxford: Clarendon Press.
Hintikka, J. (1973). Surface semantics and its motivation. In: H. Leblanc (Ed.), Truth, syntax and modality. Amsterdam: North-Holland.
Hintikka, J. (1975) Impossible possible worlds vindicated. Journal of Philisophical Logic, 4, 475–484.
Jago, M. (2009) Epistemic Logic for rule-based agents. Journal of Logic, Language and Information, 18(1), 131–158.
Jago, M. (2009) Logical information and epistemic space. Synthese, 167(2), 327–341.
Jago, M. (2009) Resources in epistemic logic. In: J.-Y. Béziau & A. Costa-Leite (Eds.), Dimensions of logical concepts (Vol. 55, pp. 11–33). Campinas, Brazil: Coleção CLE.
Lakemeyer, G. (1986). Steps towards a first-order logic of explicit and implict belief. In: J. Y. Halpern (Ed.), Proceedings of the first conference on theoretical aspects of reasoning about knowledge (pp. 325–340). San Francisco, California: Morgan Kaufmann.
Lakemeyer, G. (1987). Tractable metareasoning in propositional logic of belief. In: Proceedings of the tenth international joint conference on artificial intelligence (pp. 401–408).
Lakemeyer, G. (1990). A computationally attractive first-order logic of belief. In: Proceedings of JELIA 90 (pp. 333–347). Heidelberg: Springer.
Levesque, H. J. (1984) A logic of implicit and explicit belief. In: Proceedings of the fourth national conference on artificial intelligence (pp. 198–202).
Lewis, D. (1975) Language and languages. In: K. Gunderson (Ed.), Language, mind and knowledge (pp. 3–35). University of Minnesota Press.
Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell.
Peirce, C. S. (1992). Reasoning and the logic of things: the cambridge conferences lectures of 1898. Cambridge Mass.: Harvard University Press.
Priest, G. (1987). In contradiction: a study of the transconsistent. Dordrecht: Martinus Nijhoff.
Priest, G. (2008). An introduction to non-classical logic. Cambridge: Cambridge University Press.
Rantala, V. (1975). Urn models. Journal of Philosophical Logic, 4, 455–474.
Sequoiah-Grayson, S. (2008). The scandal of deduction. Journal of Philosophical Logic, 37(1), 67–94.
Stalnaker, R. (1976). Propositions. In: A. MacKay & D. Merrill (Eds.), Issues in the philosophy of language (pp. 79–91). New Haven: Yale University Press.
Stalnaker, R. (1984) Inquiry. Cambridge, MA: MIT Press.
van Benthem, J. (2011). Logical dynamics of information and interaction. Cambridge: Cambridge University Press.
van Benthem, J., & Martinez, M. (2008). The stories of logic and information. In: J. van Benthem & P. Adriaans (Eds.), Handbook of the philosophy of information (pp. 217–280). Amsterdam: Elsevier.
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Jago, M. The Content of Deduction. J Philos Logic 42, 317–334 (2013). https://doi.org/10.1007/s10992-011-9222-2
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DOI: https://doi.org/10.1007/s10992-011-9222-2