Are there true contradictions? A critical discussion of Graham Priest's, beyond the limits of thought

The present article critically examines three aspects of Graham Priest's dialetheic analysis of very important kinds of limitations (the limit of what can be expressed, described, conceived, known, or the limit of some operation or other). First, it is shown that Priest's considerations focusing on Hegel's account of the infinite cannot be sustained, mainly because Priest seems to rely on a too restrictive notion of object. Second, we discuss Priest's treatment of the paradoxes in Cantorian set-theory. It is shown that Priest does not address the issue in full generality; rather, he relies on a reading of Cantor which implicitly attributes a very strong principle concerning quantification over arbitrary domains to Cantor. Third, the main piece of Priest's work, the so-called “inclosure schema”, is investigated. This schema is supposed to formalize the core of many well-known paradoxes. We claim, however, that formally the schema is not sound.
Keywords dialetheism  paraconsistent logic  paradox  infinity  quantification  domain principle  Priest  Hegel  Cantor  Cartwright
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DOI 10.1023/A:1008230118573
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Explanation And Solution In The Inclosure Argument.Zach Weber - 2010 - Australasian Journal of Philosophy 88 (2):353-357.
Russell's Schema, Not Priest's Inclosure.Gregory Landini - 2009 - History and Philosophy of Logic 30 (2):105-139.

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