Abstract
This paper begins by arguing that a truth conditional approach to the semantics for relevant logic is unnatural. Rather, we should adopt an informational semantics. On this view, the indices in the model theory are not possible or impossible worlds, but are situations. A statement is not true or false at a situation; rather a situation can be said either to contain or fail to contain certain pieces of information. Valid inference, then, is seen as information preservation, not truth preservation. The distinction between truth and information gives us some freedom in our treatment of logic. For example, we may have a very classical theory of truth but a very non-classical theory of information. On the other hand, we may accept very non-classical theories of truth (such as dialetheism) together with an informational treatment of logic.
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.
Well, this isn’t strictly speaking true. Some relevant logicians, especially Meyer and Restall, include the so-called Church constant T in their language. This constant is true at every index in every model.
- 2.
See Barwise and Perry (1983). The suggestion of the link between relevant logic and situation semantics was first made by John Perry (in Barwise and Perry 1985 and in conversation with me in 1992) and Barwise (1993). Their ideas have been developed in Restall (1996), Beall and Restall (2006) and Mares (1996, 2004).
- 3.
Quoted in Seligman and Moss (1997, p. 288).
- 4.
- 5.
I have developed a position since I wrote this paper. See Mares (2010).
- 6.
- 7.
I am grateful to Mark Colyvan for pressing me on this point.
- 8.
This is a simplification of William James’ view.
- 9.
I am grateful to Greg Restall for forcefully arguing that we need not interpret the little grey men classically even if we adopt a classical theory of truth.
- 10.
He made a similar reply in conversation. I’m not sure I have his reply exactly right, so I do not attribute it to him.
- 11.
Of course this is not an argument against Priest since he does not subscribe to an informational reading of his semantics. My point is only that on the informational approach to semantics it is not clear that we have to accept the T-scheme even if we have a naive theory of truth.
- 12.
Using ‘second order’ in the sense in which it is used in the vagueness literature, i.e. as in ’second order vagueness’.
- 13.
References
Barwise, J. 1993. Constraints, channels, and the flow of information. In Situation theory and its applications, vol 3, ed. P. Aczel, Y. Katagiri, and S. Peters. Stanford: CSLI.
Barwise, J., and J. Perry. 1983. Situations and attitudes. Cambridge: MIT Press.
Barwise, J., and J. Perry. 1985. Shifting situations and shaken attitudes. Linguisitics and Philosophy 8: 105–161.
Beall, J.C., and G. Restall. 2006. Logical pluralism. Oxford: Oxford University Press.
Dunn, J.M. 1993. Star and perp: Two treatments of negation. Philosophical Perspectives 7: 331–357.
Floridi, L. 2004. Information. In The blackwell guide to philosophy of computing and information, ed. L. Floridi. Oxford: Blackwell.
Goldblatt, R. 1974. Semantical analysis of orthologic. Journal of Philosophical Logic 3: 19–35.
Mares, E.D. 1996. Relevant logic and the theory of information. Synthese 109: 345–360.
Mares, E.D. 2004. Relevant logic: A philosophical interpretation. Cambridge: Cambridge University Press.
Mares, E.D. 2009. General information in relevant logic. Synthese 167: 343–362.
Mares, E.D. 2010. The nature of information: A relevant approach. Synthese 175 Supplement, 1: 111–132.
Mares, E.D. 2012. Relevance and conjunction. Journal of Logic and Computation, 22: 7–21.
Priest, G. 1992. What is a non-normal world? Logique et analyse 35: 291–302.
Priest, G. 2000. Motivations for paraconsistency: The slippery slope from classical logic to dialetheism. In Frontiers of paraconsistent logic, ed. D. Batens, C. Mortensen, G. Priest, and J.-P. van Bendigem. Baldock: Research Studies Press.
Priest, G. 2008. Introduction to non-classical logic: From ifs to is. Cambridge: Cambridge University Press.
Restall, G. 1995. Four-valued semantics for relevant logics (and some of their Rivals). Journal of Philosophical Logic 24: 139–160.
Restall, G. 1996. Information flow and relevant logic. In Logic, language, and computation, vol 1, ed. J. Seligman and D. Westerståhl. Stanford: CSLI.
Seligman, J., and L.S. Moss. 1997. Situation theory. In Handbook of logic and language, ed. J. van Benthem and A. ter Meulen. Amsterdam: Elsevier Science.
Shapiro, S. 2006. Vagueness in context. Cambridge: Cambridge University Press.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht.
About this chapter
Cite this chapter
Mares, E.D. (2013). Information, Negation, and Paraconsistency. In: Tanaka, K., Berto, F., Mares, E., Paoli, F. (eds) Paraconsistency: Logic and Applications. Logic, Epistemology, and the Unity of Science, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4438-7_4
Download citation
DOI: https://doi.org/10.1007/978-94-007-4438-7_4
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-4437-0
Online ISBN: 978-94-007-4438-7
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)