Abstract
In (D’Agostino M, Floridi L, Synthese 167:271–315, 2009) the authors face the so-called “scandal of deduction” (Hintikka J, Logic, language games and information. Kantian themes in the philosophy of logic. Clarendon Press, Oxford, 1973). This lies in the fact that the Bar-Hillel and Carnap theory of semantic information implies that tautologies carry no information. Given that any mathematical demonstration and more in general every logical inference in a first-order language can be reduced to a tautology; this would imply, that demonstrations bring no fresh information at all.
Addressing this question (D’Agostino M, Floridi L, Synthese 167:271–315, 2009) offers both: (i) a logical model for a strictly analytical reasoning, where the conclusions depend just on the information explicitly present in the premises; and (ii) a proposal for the ranking of the informativeness of deductions according to their increasing recourse to so called “virtual information”, namely information that is temporarily assumed but not contained in the premises.
In this paper I will focus on the status of virtual information in its connection with the Kantian philosophical spirit. Exploiting the standard Kantian difference between theoretical and practical reason, my aim is to show that the access to virtual information is due to what Kant calls practical reason rather then to the theoretical one, even though the effects of its deployment are purely theoretical, i.e. don’t lead an agent to any moral action but just to acquiring new information.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Hempel 1945: “Since all mathematical proofs rest exclusively on logical deduction from certain postulates, it follows that a mathematical theorem, such as the Pythagorean theorem in Geometry, asserts nothing that is objectively or theoretically new as compared with the postulates from which it is derived, although its content may well be psychologically new in the sense that we were not aware of its being implicitly contained in the postulates” (my emphasis).mathematical theorem, such as the Pythagorean theorem in Geometry, asserts nothing that is objectively or theoretically new as compared with the postulates from which it is derived, although its content may well be psychologically new in the sense that we were not aware of its being implicitly contained in the postulates” (Hempel 1945, my emphasis).
- 2.
Hintikka 1973, p. 22.
- 3.
See Sect. 12.2 below.
- 4.
See from the Critique of the pure reason (Kant 1787: 33): “Analytical judgements (affirmative) are therefore those in which the connection of the predicate with the subject is cogitated through identity: those in which this connection is cogitated without identity, are called synthetical judgements. The former may be called explicative, the letter augmentative judgements; because the former add in the predicate nothing to the conception of the subject, but only analyse it into its constituents conceptions, which were thought already in the subject, although in a confused manner; the latter add to our conceptions of the subject a predicate which was not contained in it, and which no analysis could ever have discovered therein.” (my translation).
- 5.
My emphasis.
- 6.
References
Abbott, Edwin A. 1884. Flatland: A romance of many dimensions. London: Seeley & Co.
Carnap, R., and Y. Bar-Hillel. 1953. An outline of a theory of semantic information. In Language and information: Selected essays on their theory and application, ed. Y. Bar-Hillel, 221–274. Reading: Addison-Wesley.
D’Agostino, Marcello. 2010. Tractable depth-bounded logics and the problem of logical omniscience. In Probability, uncertainty and rationality, ed. F. Montagna and H. Hosni, 245–275. Springer.
D’Agostino, Marcello. 2013. Semantic information and the trivialization of logic: Floridi on the scandal of deduction. In Information 2013, vol. 4, 33–59.
———. 2014. Analytic inference and the informational meaning of the logical operators. Logique et Analyse 227: 407–437.
D’Agostino, Marcello, and Luciano Floridi. 2009. The enduring scandal of deduction. Is propositionally logic really uninformative? Synthese 167: 271–315.
Floridi, Luciano. 2011. The philosophy of information. Oxford: Oxford University Press.
Hempel, Carl Gustav. 1945. Geometry and empirical science. American Mathematical Monthly 52: 7–17.
Hintikka, Jaakko. 1973. Logic, language games and information. Kantian themes in the philosophy of logic. Oxford: Clarendon Press.
Kant, Immanuel. 1785. Groundwork for the metaphysic of the moral. Ed. and Trans. Allen W. Wood. New Haven/London: Yale University Press, 2002.
———. 1787. Kritik der reinen Vernunft, in: Kant’s Gesammelte Schriften „Akademieausgabe“, Königlich Preußische Akademie der Wissenschaften, Berlin 1900ff, III Band, 1904, 1911.
———. 1789. Kritik der praktischen Vernunft, in: Kant’s Gesammelte Schriften „Akademieausgabe“, Königlich Preußische Akademie der Wissenschaften, Berlin 1900ff, V Band, 1913.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
d’Alfonso, M.V. (2019). Virtual Information in the Light of Kant’s Practical Reason. In: Berkich, D., d'Alfonso, M. (eds) On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Philosophical Studies Series, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-030-01800-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-01800-9_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01799-6
Online ISBN: 978-3-030-01800-9
eBook Packages: Computer ScienceComputer Science (R0)