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Logical Pluralism: Another Application for Chunk and Permeate

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Abstract

A motivation behind one kind of logical pluralism is the thought that there are different kinds of objects, and that reasoning about situations involving these different kinds requires different kinds of logics. Given this picture, a natural question arises: what kind of logical apparatus is appropriate for situations which concern more than one kind of objects, such as may arise, for example, when considering the interactions between the different kinds? The paper articulates an answer to this question, deploying the methodology of Chunk and Permeate, developed in a different context by Brown and Priest (J Philos Log 33:379–388, 2004).

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Notes

  1. The pluralisms of Batens (1985, 1990), Beall and Restall (2006), Bueno (2002), and da Costa (1997), though very different, can all be seen in this way. I do not suggest that any of them would endorse the following examples.

  2. Priest (2006), ch. 12.

  3. Brown and Priest (2004, 200+).

  4. Brown and Priest (2004), Sect. 5.

  5. A natural assumption is that ρ ij should be identified syntactically, so that it is recursive. All the examples in the paper are of this kind. But in principle anyway, it could be determined in some other way. There is no reason in theory why is should not be a set of arbitrary computational complexity. Of course, if practice, not theory, is important, matters are different.

  6. And obviously, if this output is to be more than just the consequences of A 0, some information had better flow into C 0!

  7. Possibly, other translations might be appropriate. Thus, ‘\(\rightarrow\)’ here might be replaced by ‘\(\supset\)’, where \(A\supset B\) is \(\neg A\vee B.\)

  8. See Priest (1987), ch. 10, and Priest (2002), Sect. 8.

  9. I assume that these are the natural translations. They are, after all, what the restricted quantifiers express in their original classical context. But I could imagine situations where the ‘\(\supset\)’ should be replaced by ‘\(\rightarrow\)’, or even some entirely different conditional, such as that of Beall et al. (2006).

  10. See Priest (1987), ch. 9, and Priest (2002), Sect. 8.

  11. A somewhat different permeability relation could allow through all the consistent consequences of C P (i.e., all those provable α for which \(\lnot\alpha\) cannot also be proved). In general, though, this would make the filter highly non-effective.

  12. Versions of this paper were given in 2008 at a meeting of the Melbourne Logic Group, and at the conference Logical Pluralism in Tartu, Estlonia. I’m grateful for the helpful comments of the members of those audiences. Thanks, too, go to an anonymous referee for this volume.

References

  • Batens, D. (1985). Meaning, acceptance and dialectics. In J. C. Pitt (Eds.), Change and progress in modern science (pp. 333–360). Dordrecht: Reidel.

    Chapter  Google Scholar 

  • Batens, D. (1990). Against global paraconsistency. Studies in Soviet Thought, 39, 209–229.

    Article  Google Scholar 

  • Beall, J. C., Brady, R., Hazen, A., Priest, G., & Restall, G. (2006). Relevant restricted quantification. Journal of Philosophical Logic, 35, 587–98.

    Article  Google Scholar 

  • Beall, J. C., & Restall, G. (2006). Logical pluralism. Oxford: Oxford University Press.

    Google Scholar 

  • Brown, B., & Priest, G. (2004). Chunk and permeate I: The infinitesimal calculus. Journal of Philosophical Logic, 33, 379–88.

    Article  Google Scholar 

  • Brown, B., & Priest, G. (200+). Chunk and permeate II: The Bohr theory of the atom, to appear.

  • Bueno, O. (2002). Can a paraconsistent theorist be a logical monist? Chap. 29. In W. Carnielli, M. Coniglio, I. M. L. D’Ottaviano (Eds.), Paraconsistent logic: The logical way to be inconsistent. New York, NY: Marcel Dekker.

    Google Scholar 

  • da Costa, N. C. A. (1997). Logique Classique et Non-classique: Essai sur les Fondements de la Logique. Paris: Masson.

    Google Scholar 

  • Priest, G. (1987). In contradiction: A study of the transconsistent, Dordrecht: Martinus Nijhoff; (2nd edn), Oxford: Oxford University Press, 2006.

  • Priest G. (2002) Paraconsistent logic, vol. 6. In D. Gabbay, & F. Guenthner (Eds.), Handbook of philosophical logic (2nd edn) (pp. 287–393). Dordrecht: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Priest, G. (2006). Doubt truth to be a liar. Oxford: Oxford University Press.

    Google Scholar 

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Authors and Affiliations

  1. Department of Philosophy, University of Melbourne, Melbourne, Australia

    Graham Priest

  2. Department of Philosophy, University of St Andrews, St Andrews, Scotland, UK

    Graham Priest

  3. The Graduate Center, City University of New York, New York, NY, USA

    Graham Priest

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  1. Graham Priest
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Correspondence to Graham Priest.

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Priest, G. Logical Pluralism: Another Application for Chunk and Permeate. Erkenn 79 (Suppl 2), 331–338 (2014). https://doi.org/10.1007/s10670-013-9472-1

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