Abstract
Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain partial order on non-ontic semantic values as its value. The ordering in question is a told-true order. Analogously, a formula A is logically false just in case no matter what is told about what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain told-false order as its value. Here, truth and falsity are pari passu, and it is the treatment of truth and falsity as independent of each other that leads to an informational interpretation of these notions in terms of a certain kind of higher-level information.
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Notes
The assumption of an algebraic understanding of the logical operations is no more problematic than the various inferentialist interpretations of the connectives. From the algebraic perspective, conjunction, for example, is canonically interpreted as lattice meet, whereas from the inferentialist perspective, a canonical proof of a conjunction is given by a pair consisting of canonical proofs of the conjuncts.
A detailed treatment of trilattice logics has been given by Shramko and Wansing (2011).
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Acknowledgements
I would like to thank an anonymous referee, Andreas Pietz, Yaroslav Shramko, Luca Tranchini, the participants of the Siena Workshop “Anti-realistic Notions of Truth”, September 2010, and audiences at the universities of California at Irvine and St Andrews for useful comments on earlier versions of this paper.
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Wansing, H. A Non-Inferentialist, Anti-Realistic Conception of Logical Truth and Falsity. Topoi 31, 93–100 (2012). https://doi.org/10.1007/s11245-011-9111-x
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DOI: https://doi.org/10.1007/s11245-011-9111-x