Real Analysis in Paraconsistent Logic

Journal of Philosophical Logic 41 (5):901-922 (2012)
Abstract
This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open
Keywords Paraconsistent logic  Non-classical mathematics  Compactness theorems
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References found in this work BETA
Ross T. Brady (1989). The Non-Triviality of Dialectical Set Theory. In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. 437--470.

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