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Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
‘Zach Weber’s Paradoxes and Inconsistent Mathematics is easily one of the most important books in inconsistent mathematics - and contradiction-involving theories in general - since the pioneering books of Chris Mortensen (1995), Graham Priest (1987) and Richard Sylvan (formerly Routley) (1980) … Not since said pioneering works have I encountered a more important book on would-be true contradictory theories than Weber’s … The development of such inconsistent maths from the pioneering ideas … to Weber’s latest work is as significant as the development from chiseling stone tablets to recent smart phones.’
Jc Beall Source: Notre Dame Philosophical Reviews
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