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138Inconsistent boundariesSynthese 192 (5): 1267-1294. 2015.Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected . In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of empty p…Read more
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106Real Analysis in Paraconsistent LogicJournal of Philosophical Logic 41 (5): 901-922. 2012.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
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173Transfinite numbers in paraconsistent set theoryReview of Symbolic Logic 3 (1): 71-92. 2010.This paper begins an axiomatic development of naive set theoryin a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal …Read more
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13Piotr Łukowski , Paradoxes , tr. Marek Gensler. Reviewed byPhilosophy in Review 32 (4): 307-309. 2012.
Dunedin, Otago, New Zealand
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |