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A Classical Prejudice?

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Knowledge, Technology & Policy

Abstract

In this paper, I reassess Floridi’s solution to the Bar-Hillel–Carnap paradox (the information yield of inconsistent propositions is maximal) by questioning the orthodox view that contradictions cannot be true. The main part of the paper is devoted to showing that the veridicality thesis (semantic information has to be true) is compatible with dialetheism (there are true contradictions) and that, unless we accept the additional non-falsity thesis (information cannot be false), there is no reason to presuppose that there is no such thing like contradictory information.

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Notes

  1. The original version is based on state descriptions instead of models, but as may be seen from Kemeny (1953), it can be so reformulated.

  2. Basically, my reasons for endorsing the stronger semantic principle is based on the epistemic value of information; see, e.g. Dretske (2009).

  3. Sainsbury (1995, 136), but see also the discussion of Philosophy’s Most Difficult Problem in Woods (2003, 14–6).

  4. A possible reply is that there is a good reason to assume that the solution should be different, namely the fact that information has to be true whereas mere semantic content does not have to. This reply is flawed for two reasons: first, because premises have to be true as well; second, because the reply already presupposes that no contradiction can be true and that we only need to avoid explosion because sometimes we have to reason from a mix of true and false premises.

  5. Alternatively and in analogy with the standard approach to conditional probability, one could say that the content of A, given B, is only defined if B is not necessarily false. I do not further explore this alternative.

  6. Remember: Explosion and the falsity of contradictions come apart in several non-classical logics. Even the law of non-contradiction is not sufficient to validate explosion.

  7. This line of thought is loosely inspired by views of Floridi. I do not recall whether these were expressed in print.

  8. Thus, if an inconsistency involves all premises, the only difference between inconsistency and, say, adhocness is that the former is a syntactic feature whereas the latter is not.

  9. An alternative reply would be that liar sentences do not qualify as information because whatever their truth value, they will have that truth value as a matter of necessity. As a result, if only contingent truths qualify as semantic information, such sentences are easily dismissed. In view of the existence of so-called contingent liars (Field 2008, 24), it is immediately clear that this strategy will not work.

  10. Whether there are no observables based on ill-typed variables or no levels of abstraction based on ill-typed interpreted variables is just a matter of terminology.

  11. By successful construction, I only mean construction according to the specification, i.e. the agreement between intended and actual behaviour. Whether this also involves the successful construction of a (physical) artefact is a separate issue we can refer to as implementability. The latter is undoubtedly relevant but beyond the scope of the present discussion.

  12. Still, if one believes that we can only reason about relations between models and not about relations between the world in itself and our models, one has to conclude that metaphysical dialetheism cannot be defended.

  13. Remark that in this case the move from semantic dialetheism to informational dialetheism does not involve considerations about what we can and/or should believe but only depends on the nature of semantic information itself.

  14. When formulated with a dialetheic negation of the kind favoured by Priest, saying that information must be true and may not be false does not prevent information from being false. What is required is something like ‘true only’ or ‘untruth’ rather than truth and falsity.

  15. Remark that this restricted ability to reject some contradictions is—at least if we deny trivialism and have the means to avoid Curry’s paradox (Beall 2009, Chapt. 2)—all we need to recapture what Floridi (2007) refers to as syntactically erasing information.

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Acknowledgements

A very early version of the material in this paper was presented as “Semantic Information and Logical Orthodoxy” at the 2006 European Computing and Philosophy Conference in Trondheim, Norway. The topic came up in discussions with Luciano Floridi regularly. This is the first published version of ideas from the original presentation and the outcome of the ensuing discussions.

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  1. Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussel, Belgium

    Patrick Allo

  2. IEG, Oxford University, Oxford, UK

    Patrick Allo

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Correspondence to Patrick Allo.

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Postdoctoral Fellow of the Science Foundation (FWO).

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Allo, P. A Classical Prejudice?. Know Techn Pol 23, 25–40 (2010). https://doi.org/10.1007/s12130-010-9098-4

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