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The logic of ‘being informed’ revisited and revised

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Abstract

The logic of ‘being informed’ gives a formal analysis of a cognitive state that does not coincide with either belief, or knowledge. To Floridi, who first proposed the formal analysis, the latter is supported by the fact that unlike knowledge or belief, being informed is a factive, but not a reflective state. This paper takes a closer look at the formal analysis itself, provides a pure and an applied semantics for the logic of being informed, and tries to find out to what extent the formal analysis can contribute to an information-based epistemology.

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Notes

  1. One reason for this is that one can still maintain that knowledge implies belief whereas being informed does not. This move is, at least in principle, available to anyone interested in an information-based epistemology because even if the tri-partite analysis of knowledge is beyond repair, knowledge can still as a matter of fact imply belief.

  2. See Adams (2010) where the logic of being informed is contrasted with the Dretskian program, and Arlo Costa & Parikh (2006) where a neighbourhood semantics is used to model this kind of knowledge. Note also that the rejection of closure under known implication goes back to Dretske (1970) where the notion of information isn’t even mentioned.

  3. By way of comparison, Dunn thinks of information as “what is left from knowledge when you subtract, justification, truth, belief (...) [and] the thinker” (Dunn 2008, 581). Floridi would presumably agree with all but the omission of truth. Still, the contrast is crucial, for on Dunn’s account information is any kind of semantic content (which is fine for a logician), whereas for Floridi it is much less generic (but more useful for doing epistemology).

  4. One should, however, keep in mind that it is not all that obvious that the framework of basic modal logic in which the KTB-analysis is formulated has the necessary resources to establish the stronger result.

  5. This distinction is relevant for and used by formally oriented logicians (see Blackburn et al. 2001, 1.7) as well as more philosophically oriented ones (see Girle 2000, 10.4).

  6. I assume here that the syntactical approach cannot provide the kind of positive characterisation of information versus true belief, and therefore further ignore that aspect and focus on the negative characterisation induced by the lack of introspection.

  7. For otherwise the “margin for error principle” given in Williamson 2000, Chap. 5 and Appendix 2 would, given that it warrants a KTB-analysis of knowledge, perfectly serve our purpose.

  8. Strongly semantic information is standardly defined as true, well-formed and meaningful data. Given the assumption that all basic data are sentences of a suitable formal language, all such data are well-formed and meaningful by definition.

  9. We might expect that objections to this kind of restrictions as a means to avoid Gettier-counterexamples (Feldman 1974) carry over to the present proposal. I shall ignore this issue here, but only remark that the analogy is only partial: Gettier-counterexamples presuppose a fallible account of justification, but being informed is entirely independent from this justificatory aspect.

  10. I.e. \(\Vert \cdot \Vert_{{\mathfrak{M}}}\) is ‘lifted’ from a function from propositional parameters to sets of worlds to a function from (sets of) formulae to sets of worlds.

  11. To see that this duly captures the above description of true beliefs, just note that \((\Vert \Upgamma \Vert_{{\mathfrak{M}}} \cup @) \subseteq \Vert \varphi \Vert_{{\mathfrak{M}}}\) holds iff \(\Vert \Upgamma \Vert_{{\mathfrak{M}}} \subseteq \Vert \varphi \Vert_{{\mathfrak{M}}}\) and \(@ \subseteq \Vert \varphi \Vert_{{\mathfrak{M}}}\) hold separately, which are equivalent to, respectively, \(\Upgamma \models_{{\mathfrak{M}}} \varphi\) (\(\Upgamma\) strictly implies φ in model \(\mathfrak{M}\)) and \(@\,{\Vdash}\,\varphi.\)

  12. Compare with the embedding of intuitionistic logic in the modal logic S4.

  13. The formulation of the second condition does not refer to what is actually true, and thereby also works if s settles an issue that is indeterminate at @. In the remainder of this paper I shall nevertheless stick to the initial condition.

  14. This is just the well-known idea from non-normal modal logics that at non-normal worlds anything is possible; see Priest 2001, pp. 58–59.

  15. Remark that the intermediate step where a sentential reformulation of a’s basic data is given is indispensable, for mere de re data cannot themselves be qualified as true or false.

  16. This might look odd, because it is specified as a constraint on the data one holds. Yet, it does not have to be so, for the actual constraint might still only have an impact on that part of the data which actually constitute information; it simply wasn’t defined that way.

  17. This does not entirely square with the analysis in Floridi (forthcoming), but the relevant issue here is that being informed does not coincide with the usual externalist accounts of knowledge.

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Allo, P. The logic of ‘being informed’ revisited and revised. Philos Stud 153, 417–434 (2011). https://doi.org/10.1007/s11098-010-9516-1

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