Skip to main content
SpringerLink
Log in
Book cover

Paraconsistency: Logic and Applications pp 123–139Cite as

Consequence as Preservation: Some Refinements

  • Chapter
  • First Online:

  • 1007 Accesses

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 26))

Abstract

Preservationism generalises the idea of consequence beyond the standard focus on ‘preservation of truth’ or, syntactically, preservation of consistency. Instead, we preservationists suggest that other properties of premise sets can also worthy of preservation by a consequence relation. This paper presents a broader view of the properties that consequence relations can preserve, focusing on symmetrical treatments of consequence relations in multiple-conclusion logics that preserve variations on proof-theoretic consistent deniability from right to left as well as consistent assertability from left to right. The paper closes with remarks on another approach to producing preservationist logics, viz. the preservation of a ‘base’ consequence relation across a range of images of premise and conclusion sets, rather than preservation of properties of premise and conclusion sets. Further formal definitions and results appear in two appendices.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    We speak of extensions in two senses here: strictly speaking, a set Σ is an extension of a set Γ if and only if Σ is a superset of Γ, Σ ⊃ Γ. But we also sometimes describe a sentence α as an extension of a set Γ. What we mean in that case is the set that results from adding α to Γ, Γ ∪{ α}.

  2. 2.

    Conversation with Graham Priest.

  3. 3.

    In effect, ambiguity allows us to capture the results of using ‘both’ and ‘neither’ as (respectively) designated and non-designated fixed points for negation, while insisting that the two sets of ambiguously-treated letters be disjoint ensures that we never treat the same sentence letter in both these ways.

  4. 4.

    As a comment by Pol Nicholson suggested.

References

  • Apostoli, P., and B. Brown. 1995. A solution to the completeness problem for weakly aggregative modal logics. Journal of Symbolic Logic 60(3): 832–842.

    Article  Google Scholar 

  • Brown, B. 1999. Yes, Virginia, there really are paraconsistent logics. Journal of Philosophical Logic 28: 489–500.

    Article  Google Scholar 

  • Brown, B. 2001. LP, FDE and ambiguity. In IC-AI 2001 volume II: Proceedings of the 2001 meetings of the international conference on artificial intelligence, ed. H. Arabnia. CSREA publications. Las Vegas, Nevada.

    Google Scholar 

  • Brown, B., and P.K. Schotch. 1999. Logic and aggregation. Journal of Philosophical Logic 28: 265–287.

    Article  Google Scholar 

  • Jennings, R.E., and P.K. Schotch. 1981. Some remarks on (weakly) weak modal logics. Notre Dame Journal of Formal Logic 22: 309–314.

    Article  Google Scholar 

  • Jennings, R.E., and D.K. Johnston. 1983. Paradox-tolerant logic. Logique et Analyse 26: 291–308.

    Google Scholar 

  • Jennings, R.E., and P.K. Schotch. 1984. The preservation of coherence. Studia Logica 43: 89–106.

    Article  Google Scholar 

  • Jennings, R.E., P.K. Schotch, and D.K. Johnston. 1980. Universal first order definability in modal logic. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 26: 327–330.

    Article  Google Scholar 

  • Jennings, R.E., P.K. Schotch, and D.K. Johnston. 1981. The n-adic first order undefinability of the Geach formula. Notre Dame Journal of Formal Logic 22: 375–378.

    Article  Google Scholar 

  • Johnston, D.K. 1978. A generalized relational semantics for modal logic. M.A. thesis, Department of Philosophy, Simon Fraser University, Barnaby.

    Google Scholar 

  • MacLeod, M.C., and P.K. Schotch. 2000. Remarks on the modal logic of Henry Bradford Smith. The Journal of Philosophical Logic 29: 603–615.

    Article  Google Scholar 

  • Priest, G. 1979. The logic of paradox. Journal of Philosophical Logic 8: 219–241.

    Article  Google Scholar 

  • Schotch, P.K. 2000. Skepticism and epistemic logic. Studia Logica 65: 187–198.

    Article  Google Scholar 

  • Schotch, P.K., and R.E. Jennings. 1980a. Inference and necessity. Journal of Philosophical Logic 9: 327–340.

    Article  Google Scholar 

  • Schotch, P.K., and R.E. Jennings. 1980b. Modal logic and the theory of modal aggregation. Philosophia 9: 265–278.

    Article  Google Scholar 

  • Schotch, P.K., and R.E. Jennings. 1989. On detonating. In Paraconsistent logic, G. Priest, R. Routley, and J. Norman, 306–327. Munich: Philosophia Verlag.

    Google Scholar 

  • Thorn, P. 2000. Paraconsistency and the image of science. In Logical Consequences, ed. J. Woods and B. Brown. London: Hermes.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, University of Lethbridge, Lethbridge, Alberta, Canada

    Bryson Brown

Authors
  1. Bryson Brown
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bryson Brown .

Editor information

Editors and Affiliations

  1. , Department of Philosophy, University of Auckland, Arts 2, 18 Symonds Street, Auckland, 1142, New Zealand

    Koji Tanaka

  2. , Department of Philosophy, University of Aberdeen, King's College, High Street, Aberdeen, AB24 3UB, United Kingdom

    Francesco Berto

  3. , Department of Philosophy, Victoria University of Wellington, Murphy 518, Kelburn Parade, Wellington, New Zealand

    Edwin Mares

  4. , Department of Education, University of Cagliari, Via Is Mirrionis 1, Cagliari, 09123, Italy

    Francesco Paoli

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht.

About this chapter

Cite this chapter

Brown, B. (2013). Consequence as Preservation: Some Refinements. 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_8

Download citation

Publish with us

Policies and ethics

Search

Navigation