Real Analysis in Paraconsistent Logic
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- McKubre-Jordens, M. & Weber, Z. J Philos Logic (2012) 41: 901. doi:10.1007/s10992-011-9210-6
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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.