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Information closure and the sceptical objection

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Abstract

In this article, I define and then defend the principle of information closure (pic) against a sceptical objection similar to the one discussed by Dretske in relation to the principle of epistemic closure. If I am successful, given that pic is equivalent to the axiom of distribution and that the latter is one of the conditions that discriminate between normal and non-normal modal logics, a main result of such a defence is that one potentially good reason to look for a formalization of the logic of “\(S\) is informed that \(p\)” among the non-normal modal logics, which reject the axiom, is also removed. This is not to argue that the logic of “\(S\) is informed that \(p\)” should be a normal modal logic, but that it could still be insofar as the objection that it could not be, based on the sceptical objection against pic, has been removed. In other word, I shall argue that the sceptical objection against pic fails, so such an objection provides no ground to abandon the normal modal logic B (also known as KTB) as a formalization of “\(S\) is informed that \(p\)”, which remains plausible insofar as this specific obstacle is concerned.

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Notes

  1. For an early overview see Floridi (2004a), on the various meanings and uses of ‘information’ see Floridi (2010a).

  2. At least since Dretske (1981), see now Dretske (1999). For an introduction see Floridi (2009) or (2011b). On relevant semantic information, see Floridi (2008b), on how semantic information may become knowledge, see Floridi (2012).

  3. The statal condition of being informed is that enjoyed by \(S\) once \(S\) has acquired the information (actional state of being informed) that \(p\). It is the sense in which a witness, for example, is informed (holds the information) that the suspect was with her at the time when the crime was committed. The distinction is standard among grammarians, who speak of passive verbal forms or states as “statal” (e.g. “the door was shut (state) when I last checked it”) or “actional” (e.g. “but I don’t know when the door was shut (act)”).

  4. The reader interested in a clear and informative presentation of Dretske’s and Nozick’s positions may wish to consult Luper (2010). On the debate see White (1991), Jäger (2004), Baumann (2006), Luper (2006), Shackel (2006), Dretske (2006). At the time of writing, the most recent contribution is Adams et al. (2011), which defends Dretske’s position. In two recent articles, Genia Schoenbaumsfeld (2012a, b) has defended the principle of epistemic closure from a Wittgensteinian perspective that converges with some of the conclusions reached in the following pages about information closure. I am grateful to her for sharing her research.

  5. The analysis of the logic of being informed in terms of a non-normal modal logic is developed by Allo (2011).

  6. This of course leaves open the possibility that other objections might be more successful, see for example Wheeler (forthcoming). It also does not touch upon a stronger objection in terms of logical omniscience; see the conclusion of this paper for a link to the issue and D’Agostino (2013).

  7. Logics without the axiom of distribution may be obtained by moving to a neighbourhood-semantics and may be used to formalise Nozick’s analysis of knowledge. Logics without strong necessitation, or even without weak necessitation, are obtained by including non-normal worlds in the Kripke-models, see Allo (2011). Logics without uniform substitution can be found in the area of dynamic epistemic logic, where, for instance, the dynamic operator for public announcements is not a normal modal operator even though it distributes over implication and satisfies necessitation. I am grateful to one of the anonymous referees for the specification.

  8. On the connection between logical omniscience and the problem of closure in the context of a philosophy of information see Floridi (2006) and D’Agostino (2010).

  9. The interested reader is referred to the excellent review in Luper (2010). In this article I use K and SP in the way in which they are used in the epistemological literature rather than in modal logic (see below).

  10. It is not necessary, but might be preferable, to adopt a uniformity of interpretation between the two material implications. However, the conclusions reached in this article are independent of the specific interpretation of the second material implication.

  11. See D’Agostino and Floridi (2009) and D’Agostino (2010, 2013) for a full analysis of the issue.

  12. The reader may prefer to analyse this in terms of boundaries offered by the chosen level of abstraction, see Floridi (2008a) for this alternative way of formulating the point.

  13. I am grateful to one of the anonymous referees for having called my attention to this important point.

  14. I specify “metaphorically” because a material implication is resource insensitive, but the suggestion that PIC can be seen as “exchanging a twenty pounds banknote into many one-dollar bills” presupposes an implication that is resource sensitive (like a linear implication), since we cannot exchange a twenty pounds banknote into many one-dollar bills and a twenty pounds banknote, or life would be too simple. I am grateful to one of the anonymous referees for the request to clarify this point.

  15. I have argued against the sceptical challenge in Floridi (1996, 2010b).

  16. Such co-variance principle has been at the core of the philosophy of information at least since its explicit formulation in Dretske (1981). The version provide here is from Floridi (2011a, p. 41), which is a slight modification of the version provided by Barwise and Seligman (1997).

  17. See for example Cocchiarella and Freund (2008) or Hughes and Cresswell (1984). The axiom is also and perhaps better known as the K axiom, but such terminology would be confusing in this paper. A less popular name is deductive cogency axiom.

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Acknowledgments

I discussed previous versions of this article as invited speaker at the European Science Foundation workshop on the Philosophy of Computer Science and AI (Ponta Delgado, Azores, 7–9 September 2011); the international conference on “Philosophy of Information”, Info-Metrics Institute, American University (Washington D.C., USA, 3 October, 2011); and the Philosophy of Information Workshop, Department of Philosophy and Cognitive Science, Lund University (Lund, Sweden, 9–11 May, 2013). I am indebted to Gregory Wheeler and the ESF; to Amos Golan and the Info-Metrics Institute at AU; to Frank Zenker and Lund University; and to the participants in such meetings for the fruitful opportunity to discuss my ideas and to receive so much helpful feedback. Penny Driscoll kindly copyedited the final version. The two anonymous reviewers of the journal provided many insightful comments and suggestions for improvements and saved me from several shortcomings and obscurities. The article is really much better thanks to them.

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Floridi, L. Information closure and the sceptical objection. Synthese 191, 1037–1050 (2014). https://doi.org/10.1007/s11229-013-0306-0

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