25 Years In Contradiction
(University of Glasgow, 7-9/12/2012)
It has been 25 years since Graham Priest initiated a revolution in logic (and philosophy) and published a book called In Contradiction – A Study of the Transconsistent. The book provides a comprehensive defense of a philosophical stance dubbed dialetheism. Although still controversial, it is now considered as one of the most important philosophical works in these days. Due to its influence on logicians and philosophers all over the world, partisans of dialetheism decided to celebrate its quarter-of-a-century existence by organizing a conference that would reflect the actual status of the debate. The conference – named 25 years In Contradiction – took place at the University of Glasgow in December, 7-9.
It was clear at the beginning that the list of speakers was about to guarantee a unique philosophical experience. The first keynote called ‘Rejection, Denial: A Negative Appraisal of Dialetheism’ was given by Alan Weir (Glasgow). Quite humorously, though, the talk outlined the most discussed points of Priest’s book, including the principal impossibility to refuse dialetheism, the problems concerning the classical recapture, reasoning from classical situations, falsity preservation in dialetheism or the entailment as such. Ben Burgis (Miami) presented a paper (co-authored with Otavio Bueno) called ‘Liars with Curry: Why Dialetheists Violate the Principle of Uniform Solution’. As Burgis argued, given the dissimilarity between the Curry Paradox and the Liar Paradox, dialetheists face a dilemma: either the so-called Inclosure Schema – basically, a pattern common to all paradoxes - describes the structure of Curry Paradox, or not. If it does, so much the worse for Priest’s reliance on the Inclosure Schema. If it does not, Burgis concludes, so much the worse for the schema as a universal tool to paradoxes. The last Friday’s talk was given by Gareth Young (Glasgow). In his ‘Dialetheism and Expressive Limitations’, Young outlined two putative limitations of dialetheism (originally presented in Steward Shapiro’s Simple Truth, Contradiction and Consistency). By means of difference between just false, false and not true sentences, he considered analogical distinction between just invalid, invalid and not valid inferences in order to avoid certain unwanted consequences. He stayed, however, rather skeptical on the issue.
The Saturday’s session commenced with Sebastiano Moruzzi’s (Bologna) presentation of the paper entitled ‘Relativism in Contradiction’ (co-authored with Annalisa Coliva). His contribution concerned the question whether relativism can be a descriptive project. Since disputes in the subjective domains appear to involve judgments with incompatible contents, he claimed, dialetheist relativism is worth of considering. Can Baskent’s (Paris 1) ‘Dialetheism and a Game Theory Paradox’ discussed two approaches to Brandenburger –Keisler Paradox, namely Non-well-funded set theoretic approach and paraconsistent approach. The morning session concluded the second keynote by JC Beall (Connecticut) with his ‘Free of Detachment: Logic, Rationality, and Gluts’. Since glut theory involves the invalidity of modus ponens and modus ponens is central to our theoretical reasoning, the theory seems to be implausible. However, as Beall (very interestingly) tried to show, we still can successfully pursue rational theorizing despite the invalidity of modus ponens. Karin Verelst (Vrije Universiteit Brussel) in her ‘Zeno’s Paradoxes. A Cardinal Problem’ demonstrated that Zeno’s Paradoxes of Motion and Paradoxes of Plurality come down to the same and whatever it was that Zeno’s opponents refuted was certainly not Zeno. Franz Berto’s (Aberdeen) ‘Exclusion vs. Explosion: Going Predicative?’ explores a ‘foothold on undisputed ground’ that we can rely on when we accept true contradictions. One way of getting such a foothold is, for Berto, to consider exclusion as primitive, meaning that exclusion should not be defined at all. The third keynote ‘Inconsistency and Incompleteness, Revised’ by Steward Shapiro (Ohio State) was partly a reminder of his previous paper ‘Incompleteness and Inconsistency’ in which he discusses reliance on an informal provability argument, partly a quite original contribution to the logic of inconsistency.
The last day of the conference began with Aaron Cotnoir’s (St. Andrews) (co-authored with Zach Weber) ‘Inconsistent Boundaries of Ordinary Objects: Toward a Paraconsistent Mereotopology’. As Cotnoir pointed out, the existence of boundaries of everyday objects is problematic, as in classical mereotopology three conditions - boundaries exist, space is topologically connected and discrete entities can be in contact – are mutually inconsistent. However, as he concluded, the problem can be met with a paraconsistent mereotopology. The paper ‘Remarks on Naïve Set Theory Based on LP’ by Hitoshi Omori (Kobe/CUNY) showed, that although systems of paraconsistent logic with classical negation were thought to be quite problematic, there are several possibilities in formulating theories if we have both paraconsistent negation and classical negation. The penultimate talk, by Diego Tajer, (Buenos Aires) was called ‘Dialetheism and the Curry-Validity Paradox’. As Tajer maintained, Validity-Curry paradox shows that if validity is contractive, it is hard to represent it in a dialetheic framework. Thus, the inconsistency of validity is a better explanation for Curry-Validity Paradox in the framework.
Finally, Graham Priest (CUNY/Melbourne). At the very beginning of his talk, Priest confessed that the book was rejected by ten major publishers before one accepted it, and thus if somebody had told him about the 25 anniversary of the book, he would not have believed. Also, he acknowledged that the debate on dialetheism has increasingly improved over the years and expressed deep acknowledgement to all those authors who had contributed to the conference. Although Priest’s talk was called ‘Contradiction, Language and the World’, he spent the whole his time addressing several objections and suggestions being raised during the conference. Given the notes he was making thorough every talk, Priest precisely responded to all the presented papers. He stressed several details that either had been overlooked, or underestimated and thus provoked an exciting discussion. It was especially interesting to see how detailed and delicate any philosophical debate must be in order to avoid potential confusions and misunderstandings.
To conclude, I dare to say that the conference met the highest criteria for philosophical conferences and we can only hope that such conferences will be more frequent in the near future.
Friday, December 7th
13.00 – 14.30 Registration (Common room, ground floor, 67 Oakfield Avenue)
14.30 – 15.30 Keynote: Alan Weir (Glasgow) 'Rejection, Denial, Falsity: A negative appraisal of dialetheism'
15.30 – 16.00 Coffee Break
16.00 – 17.00 Ben Burgis (Miami) 'Liars with Curry: Why Dialetheists Violate the Principle of Uniform Solution'
17.05 – 18.05 Gareth Young (Glasgow) 'Dialetheism and Expressive Limitations'
Saturday, December 8th
09.30 – 10.30 Sebastiano Moruzzi (Bologna) 'Relativism in Contradiction?'
10.30 – 10.55 Coffee Break
10.55 – 11.55 Can Baskent (IHΦST, Paris 1) 'Dialetheism and a Game Theoretical Paradox'
12.00 – 13.00 Keynote: JC Beall (Connecticut) 'Free of detachment: logic, rationality, and gluts'
14.45 – 15.45 Karin Verelst (Vrije Universiteit Brussel) 'Zeno’s Paradoxes. A Cardinal Problem'
16.10 – 17.10 Franz Berto (Aberdeen) 'Exclusion vs. Explosion: Going Predicative?'
17.15 – 18.15 Keynote: Stewart Shapiro (Ohio State) 'Inconsistency and Incompleteness, revisited'
Sunday, December 9th
09.30 – 10.30 Aaron Cotnoir (St Andrews) 'Inconsistent Boundaries of Ordinary Objects: Towards a Paraconsistent Mereotopology’
10.55 – 11.55 Hitoshi Omori (Kobe/CUNY) 'Remarks on Naïve Set Theory Based on LP'
12.00 – 13.00 Kevin DeLapp (Converse) 'Deontic Dialetheism'
14.30 – 15.30 Diego Tajer (Buenos Aires) 'Dialetheism and the Curry-Validity Paradox'
15.35 – 16.35 Keynote: Graham Priest (CUNY/Melbourne) 'Contradiction, Language and the World'
The organizers are grateful to the Scots Philosophical Association and the Analysis Trust for their support.