Are there true contradictions? A critical discussion of Graham Priest's, beyond the limits of thought
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal for General Philosophy of Science 29 (2):289-299 (1998)
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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Citations of this work BETA
Zach Weber (2010). Explanation And Solution In The Inclosure Argument. Australasian Journal of Philosophy 88 (2):353-357.
Gregory Landini (2009). Russell's Schema, Not Priest's Inclosure. History and Philosophy of Logic 30 (2):105-139.
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