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TRANSMISSION OF VERIFICATION

Part of: Proof theory and constructive mathematics General logic

Published online by Cambridge University Press:  21 July 2020

ETHAN BRAUER  and
NEIL TENNANT
ETHAN BRAUER
Affiliation:
DEPARTMENT OF PHILOSOPHY THE OHIO STATE UNIVERSITYCOLUMBUS, OH43210, USAE-mail:brauer.28@osu.eduE-mail:tennant.9@osu.edu
NEIL TENNANT
Affiliation:
DEPARTMENT OF PHILOSOPHY THE OHIO STATE UNIVERSITYCOLUMBUS, OH43210, USAE-mail:brauer.28@osu.eduE-mail:tennant.9@osu.edu
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Abstract

This paper clarifies, revises, and extends the account of the transmission of truthmakers by core proofs that was set out in chap. 9 of Tennant (2017). Brauer provided two kinds of example making clear the need for this. Unlike Brouwer’s counterexamples to excluded middle, the examples of Brauer that we are dealing with here establish the need for appeals to excluded middle when applying, to the problem of truthmaker-transmission, the already classical metalinguistic theory of model-relative evaluations.

Keywords

Core Logiccore proofverificationtruthmakerfalsificationfalsitymakerevaluationlogical consequencetruthmaker-transmission

MSC classification

Primary: 03F03: Proof theory, general
Secondary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) 03B20: Subsystems of classical logic (including intuitionistic logic)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 4 , December 2021 , pp. 866 - 881
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Copyright
© Association for Symbolic Logic, 2020

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References

BIBLIOGRAPHY

Tennant, N. (2010). Inferential semantics. In Lear, J., & Oliver, A., editors. The Force of Argument: Essays in Honor of Timothy Smiley. London: Routledge, pp. 223–257.Google Scholar
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Tennant, N. (2015a). Cut for classical core logic. Review of Symbolic Logic, 8(2), 236–256.CrossRefGoogle Scholar
Tennant, N. (2015b). The relevance of premises to conclusions of core proofs. Review of Symbolic Logic, 8(4), 743–784.CrossRefGoogle Scholar
Tennant, N. (2017). Core Logic. Oxford: Oxford University Press.CrossRefGoogle Scholar
Tennant, N. (2018). A logical theory of truthmakers and falsitymakers. In Glanzberg, M., editor. Handbook on Truth. Oxford: Oxford University Press, pp. 355–393.Google Scholar