Non-triviality Done Proof-Theoretically

French, Rohan; Standefer, Shawn

doi:10.1007/978-3-662-55665-8_30

Rohan French¹⁶ &
Shawn Standefer¹⁷

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10455))

Included in the following conference series:

International Workshop on Logic, Rationality and Interaction

1029 Accesses

Abstract

It is well known that naive theories of truth based on the three-valued schemes K3 and LP are non-trivial.

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

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 39.99; Price excludes VAT (USA)

Softcover Book: USD 54.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

1.
See Gupta (1982), Kremer (1988), or Ripley (2012).
2.
These two rules are based on those from Kremer (1988) and from Negri and von Plato (2001).
3.
The appropriate [Cl] axiom for LP would be .
4.
This problem was pointed out by Kremer (1988).
5.
Negri and von Plato (2001, 32).
6.
Note that we are assuming there are no function symbols in the language.
7.
See Bimbó (2015, 36-51) for details.
8.
Syntax consistency says, roughly, that the set of equalities on the left and negations of equalities on the right can be extended to an annotation set.

References

Bimbó, K.: Proof Theory: Sequent Calculi and Related Formalisms. CRC Press, Boca Raton (2015)
MATH Google Scholar
Gupta, A.: Truth and paradox. J. Philos. Logic 11(1), 1–60 (1982)
Article MathSciNet MATH Google Scholar
Kremer, M.: Kripke and the logic of truth. J. Philos. Logic 17, 225–278 (1988)
Article MathSciNet MATH Google Scholar
Kripke, S.: Outline of a theory of truth. J. Philos. 72, 690–716 (1975)
Article MATH Google Scholar
Negri, S., von Plato, J.: Structural Proof Theory. Cambridge University Press, Cambridge (2001)
Book MATH Google Scholar
Ripley, D.: Conservatively extending classical logic with transparent truth. Rev. Symb. Logic 5(2), 354–378 (2012)
Article MathSciNet MATH Google Scholar

Download references

Acknowledgments

We would like to thank the members of audiences at the Otago Logic Seminar and the Australasian Association for Logic Conference 2016 for feedback on this material. Shawn Standefer’s research was supported by the Australian Research Council, Discovery Grant DP150103801.

Author information

Authors and Affiliations

Monash Unversity, Melbourne, Australia
Rohan French
University of Melbourne, Melbourne, Australia
Shawn Standefer

Authors

Rohan French
View author publications
You can also search for this author in PubMed Google Scholar
Shawn Standefer
View author publications
You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shawn Standefer .

Editor information

Editors and Affiliations

Institute for Logic, Language and Computation, University of Amsterdam , Amsterdam, Noord-Holland, The Netherlands
Alexandru Baltag
Department of Philosophy, The University of Auckland, Auckland, Auckland, New Zealand
Jeremy Seligman
Graduate School of Letters, Hokkaido University , Sapporo, Japan
Tomoyuki Yamada

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

French, R., Standefer, S. (2017). Non-triviality Done Proof-Theoretically. In: Baltag, A., Seligman, J., Yamada, T. (eds) Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science(), vol 10455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55665-8_30

Download citation

DOI: https://doi.org/10.1007/978-3-662-55665-8_30
Published: 24 August 2017
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-55664-1
Online ISBN: 978-3-662-55665-8
eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships

the Association of Logic, Language and Information. (opens in a new tab)