I don't know about you, dear reader, but I very much enjoy reading reports of conferences I would have liked to attend but did not. This month there were two great conferences with closely related themes (with just a weekend in between): Paradoxes of Truth and Denotation in Barcelona, and Truth at Work in Paris. It was a real marathon for truth-seekers and paradox-avengers! Having missed the conferences myself, I thought of asking Shawn Standefer, one of the brave people having attended both, for a short report for M-Phi. As you see, we are expanding our line of business here at this blog, now also having live coverage of recent events :) Anyway, lame jokes aside, here's Shawn's very thorough and informative report.

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I recently had the pleasure of attending two conferences on truth. The first was the Seventh Barcelona Workshop on Issues in the Theory of Reference, held in Barcelona , and the second was Truth at Work, held in Paris . Both were well run, multi-day conferences jammed full of interesting talks, and the organizers of both should be commended. I will highlight a few things that cropped up at both conferences and some talks that stood out to me. I do not have good notes for, or clear memories of, all the talks, so the summary will be unfortunately uneven.

There were several presentations motivating substructural logics in response to the paradoxes. Julien Murzi presented some criticisms of Field's recent work based on its inability to contain an adequate validity predicate. This was, I think, based on joint work with JC Beall. Murzi used this to motivate rejecting the structural rule of contraction in addition to the rule of contraction for the conditional. Elia Zardini motivated a contraction-free logic based on paradoxes that arise from adding predicates for naive logical properties, such consistency and inconsistency, that obey simple inference rules. Zardini has obtained some interesting metatheoretic results concerning the validity relation for his logic using a non-classical metalanguage. One point that was pushed in discussion was that there are difficulties of making philosophical and semantic sense of the failure of structural contraction.

Joint work by Pablo Cobreros, Paul Egre, David Ripley, and Robert van Rooij was presented at both conferences. They used work on vagueness to motivate a non-transitive logic that can be given a surprisingly clean, surprisingly classical proof theory. TheirBarcelona presentation focused on semantic paradoxes and proof theory and their Paris presentation focused on paradoxes of vagueness, model theory, and conditionals. In discussion, one point that came out was that there is a sense in which their logic is classical and a sense in which it is not. As pointed out in questions, getting clearer on the notion or notions of classicality at issue here will be useful in understanding and evaluating some of the competing theories of truth.

There was more good work on proof theory presented inParis by Volker Halbach and Leon Horsten. Halbach presented a talk on disquotational theories of truth, full of technical results demonstrating that disquotational theories, ones that add T-sentences and no general principles as axioms to PA, can be rather powerful and complex, depending on which set of T-sentences is added to PA. He said that many of the results can be found in his 2009 RSL paper and his new book. Horsten closed out the Paris conference with a talk, based on joint work with Welch and someone whose name I did not write down, about axioms for different revision theories of truth. He began by pointing out that revision theories based on a single Herzberger sequence can define a notion of determinateness just as powerful as the one found in Field's work. The results he presented were, to me, surprising. He went on to discuss difficulties in axiomatizing the stable and nearly stable truth sets in such sequences.

There was a talk at each conference responding to Leitgeb's work on the paradoxes. InBarcelona , Rafal Urbaniak argued that Leitgeb's analysis of Yablo's paradox and circularity was inadequate and proposed a semantic approach that categorized sentences better than Leitgeb's notion. In Paris , Denis Bonnay presented joint work with someone (my apologies for missing the name) on developing Leitgeb's analysis of groundedness. They showed how there were several parameters involved in the inductive definition of the set of grounded sentences in Leitgeb's sense, and how varying these can bring them into line with Cantini's supervaluationist scheme. Both Urbaniak's and Bonnay's work pointed to fruitful directions in formal work on aboutness and groundedness.

Both conferences featured discussion of Stephen Read's work on Bradwardine's theory of truth. InBarcelona , Graham Priest gave a talk on difficulties that Bradwardine's theory faces in dealing with the paradoxes of denotation when extended to terms in the way one would expect. This was the only talk on paradoxes of denotation at the conference. Stephen Read was in the audience and gave an extended response indicating points in the argument he would resist. In Paris , Stephen Read went over which of the compositional or commutativity principles were compatible with Bradwardine's theory. On the Read-Bradwardine view, truth commutes with conjunction and disjunction but not with the conditional and negation.

Michael Glanzberg gave interesting talks at both conferences on two different approaches to truth: the complex and the simple. The former sees truth as substantive and embraces hierarchies of truth but no substantive notions of determinateness. The latter takes a deflationary view of truth and embraces notions of determinateness but rejects hierarchies of truth. Glanzberg presented some technical results concerning iteration and reflection, including some analysis of the complexity involved in long iterations found in different approaches.

Anil Gupta presented talks at both conferences on the role of the T-sentences in theories of truth, focusing on what sort of conditional should be used in them. Gupta initially motivated the analysis of the T-sentences by framing a logical problem, the sorting of good arguments from bad. He used this to motivate a new conditional for the revision theory and showed how it can be used to address some of the initial problems he raised.

InBarcelona , Hartry Field presented some of his work on restricted quantification and the difficulties faced by his paracomplete approach. This was worked into a criticism of paraconsistent theories, because Field thinks that the prospects for an adequate treatment of restricted quantification is more promising in paracomplete approaches than in paraconsistent ones. Some of the discussion focused on how we were supposed to adjudicate between the different sets of principles that the two approaches preserved. I did not, however, get notes on the responses.

InBarcelona , James Woodbridge and Bradley Armour-Garb gave a talk on how their deflationary view of truth as pretense deals with semantic defect. In Paris , Woodbridge gave a talk on developments of his truth as pretense view, focusing on responses to several objections that it has faced.

InParis , there were two talks on the role of the word `true' in natural language. Friederike Moltmann presented some distributional data concerning different truth-like constructions and argued they were non-equivalent. Dora Achourioti motivated and defended a project of looking at the use of the truth predicate in communication. While not about natural language, there was a talk on truth in formal semantics. James Shaw argued that assigning an extension to the truth predicate causes problems for the compositionality of semantics. He used this to motivate a procedural interpretation of the truth predicate. Unfortunately, I am not sure what happened to my notes for these talks.

Riccardo Bruni gave a great talk on a sequent calculus presentation for the calculus for finite definitions from the Revision Theory book. He introduced a special conditional, and he sketched how to prove an elimination theorem for the calculus with the definitional rules, classical logic on indexed formulas, and his new conditional. Stefan Wintein argued that Philip Kremer's formalization of the Gupta-Belnap criterion of vicious circularity did not adequately respect the original intuitions of the informal idea. Wintein then proposed a new version that focused on T-sentences. Wintein's version was, I believe, slightly weaker than Kremer's, as the two come apart in the case of Wintein's generalized strong Kleene schemes.

Graham Leach-Krouse gave an excellent talk on the surprise examination paradox. Leach-Krouse showed how to formalize the reasoning involved in the paradox and then presented a generalization of it. The generalized version leads to Solovay's theorem connecting provability logic and its arithmetic interpretation. Leach-Krouse used this fact to argue against Ramsey's famous distinction between the logical and the linguistic paradoxes. Great stuff.

There were a few other talks at the conferences, but I either cannot find my notes for them or do not have good notes for them. InBarcelona , Christopher Gauker argued for a well-foundedness principle about contexts in formal semantics. Andre Billon presented a relativist solution to the paradoxes. David Liggins argued for alethic nihilism. Colin Johnston presented an analysis of the paradoxes in terms of conflicting rules. Alexis Burgess presented and adjudicated a dispute between Scharp and Eklund about the inconsistency theory of truth and revising the truth predicate.

InParis , Henri Galinon talked about what is involved in accepting a theory and drew consequences of his analysis for deflationism. Pascal Engel argued that the normative role of the truth predicate poses a problem for deflationism. Philippe de Rouilhan talked about abstraction in relation to Frege's distinction between concept and object. Gila Sher sketched a correspondence account of truth. Luca Tranchini talked about validity in the Dummett-Prawitz tradition of proof-theoretic semantics and the problems it poses for that project.

There were several presentations motivating substructural logics in response to the paradoxes. Julien Murzi presented some criticisms of Field's recent work based on its inability to contain an adequate validity predicate. This was, I think, based on joint work with JC Beall. Murzi used this to motivate rejecting the structural rule of contraction in addition to the rule of contraction for the conditional. Elia Zardini motivated a contraction-free logic based on paradoxes that arise from adding predicates for naive logical properties, such consistency and inconsistency, that obey simple inference rules. Zardini has obtained some interesting metatheoretic results concerning the validity relation for his logic using a non-classical metalanguage. One point that was pushed in discussion was that there are difficulties of making philosophical and semantic sense of the failure of structural contraction.

Joint work by Pablo Cobreros, Paul Egre, David Ripley, and Robert van Rooij was presented at both conferences. They used work on vagueness to motivate a non-transitive logic that can be given a surprisingly clean, surprisingly classical proof theory. Their

There was more good work on proof theory presented in

There was a talk at each conference responding to Leitgeb's work on the paradoxes. In

Both conferences featured discussion of Stephen Read's work on Bradwardine's theory of truth. In

Michael Glanzberg gave interesting talks at both conferences on two different approaches to truth: the complex and the simple. The former sees truth as substantive and embraces hierarchies of truth but no substantive notions of determinateness. The latter takes a deflationary view of truth and embraces notions of determinateness but rejects hierarchies of truth. Glanzberg presented some technical results concerning iteration and reflection, including some analysis of the complexity involved in long iterations found in different approaches.

Anil Gupta presented talks at both conferences on the role of the T-sentences in theories of truth, focusing on what sort of conditional should be used in them. Gupta initially motivated the analysis of the T-sentences by framing a logical problem, the sorting of good arguments from bad. He used this to motivate a new conditional for the revision theory and showed how it can be used to address some of the initial problems he raised.

In

In

In

Riccardo Bruni gave a great talk on a sequent calculus presentation for the calculus for finite definitions from the Revision Theory book. He introduced a special conditional, and he sketched how to prove an elimination theorem for the calculus with the definitional rules, classical logic on indexed formulas, and his new conditional. Stefan Wintein argued that Philip Kremer's formalization of the Gupta-Belnap criterion of vicious circularity did not adequately respect the original intuitions of the informal idea. Wintein then proposed a new version that focused on T-sentences. Wintein's version was, I believe, slightly weaker than Kremer's, as the two come apart in the case of Wintein's generalized strong Kleene schemes.

Graham Leach-Krouse gave an excellent talk on the surprise examination paradox. Leach-Krouse showed how to formalize the reasoning involved in the paradox and then presented a generalization of it. The generalized version leads to Solovay's theorem connecting provability logic and its arithmetic interpretation. Leach-Krouse used this fact to argue against Ramsey's famous distinction between the logical and the linguistic paradoxes. Great stuff.

There were a few other talks at the conferences, but I either cannot find my notes for them or do not have good notes for them. In

In

Doug Patterson gave a talk about Tarski's views on definition and language, which was, I believe, similar to a talk he gave at Munich that is now available in iTunes. Finally, Julien Boyer presented some negative results concerning Hintikka's idea that Dummett's ideas about proof and verification are best cashed out in terms of recursive winning strategies in game theoretic semantics.

I will close by mentioning two things that came up in discussion in different talks that I want to highlight. The first is the complexity of theories of truth. This was mentioned by several people. There are some nice results about the complexity of different approaches, even of straightforward disquotational theories. Some people took these results as strong reasons against adopting different theories. What should we make of these arguments?

The second thing has to do with the philosophy of logic. There seemed to be some important questions about how we are supposed to think of logic in the context of truth. There was a divide over whether classical logic should be privileged, what this means, and if it should be privileged, why. This may, however, just be a recasting of old debates about the status of non-classical logic. The wealth of material in the area of theories of truth seems promising as a way of shedding new light on those debates.

I will close by mentioning two things that came up in discussion in different talks that I want to highlight. The first is the complexity of theories of truth. This was mentioned by several people. There are some nice results about the complexity of different approaches, even of straightforward disquotational theories. Some people took these results as strong reasons against adopting different theories. What should we make of these arguments?

The second thing has to do with the philosophy of logic. There seemed to be some important questions about how we are supposed to think of logic in the context of truth. There was a divide over whether classical logic should be privileged, what this means, and if it should be privileged, why. This may, however, just be a recasting of old debates about the status of non-classical logic. The wealth of material in the area of theories of truth seems promising as a way of shedding new light on those debates.

To paraphrase something I believe Stu Shapiro once said (If not him, then I said it and he agreed - the memory is fuzzy!)

ReplyDelete"In the face of the paradoxes, classical logic must be earned, not assumed."

The context was a discussion of Williamson's argument for epistemicism, where Williamson points out the theoretical usefulness of classical logic and suggests that giving up classical logic has more drawbacks than keeping it and adopting epistemicism (the argument is of course more complicated than that - see his book).

This seems right to me. On one understanding, classical logic codifies all sorts of assumptions about the determinacy of the subject matter of one's theory that might be true (even if not logically true) of classical mathematics, but are at least in doubt when talking about semantics, vague predicates, etc.

I should have clarified - it is Stu's (my?) comment that seems right, not Williamson's come-what-may adherence to classical logic!

ReplyDeleteNice post Shawn, and nice Stu-quote Roy!

ReplyDeleteI think the third author involved in the joint project with Leon H and Philip W on axiomatizations of revision theories is our very own Dr Dr Prof Hannes Leitgeb!

Hi Roy,

ReplyDeleteI would have thought that if we can show (1) classical logic is more theoretically useful than (some) non-classical logic and (2) giving it up has more drawbacks than keeping it, we just have made a lot of progress towards `earning' it and not simply assuming it. Am I missing something?

Best,

Sam

Sam,

ReplyDeleteI agree with your point in general. What I worry about, however, is how various advantages and disadvantages are weighed. Williamson seems (and this is certainly a bit of a caricature, but this is the Internet after all) to take the computational simplicity and past successes of classical logic to be a VERY strong point in its favor. I would agree that, all else being equal, the simplicity of classical logic is good reason to choose it over other logics. But if the options are, for example, to keep classical logic and accept epistemicism (which is, at least to me, crazily counterintuitive and artificial) versus giving up classical logic for some alternative non-classical account of vagueness, it just seems like the issue of simpilicity and past success just don't seem like very strong considerations in favor of classical logic.

Note: I don't by any stretch mean to suggest that this is the only argument Williamson gives for classical logic and epistemicism, or even the best. But he does argue along these lines in such a way as to suggest that he takes this line of thinking to be relatively compelling.

Second note: In the "theoretical usefulness" comment, I meant something like: The usefulness and fruitfulness that classical logic has displayed in past applications provides (defeasible, but nevertheless very strong) reasons for retaining it, if possible, in future applications.

Hi Roy,

ReplyDeleteThanks for the clarification, that was really helpful!

Best,

Sam

That is a good quotation from Shapiro. I think my phrasing of my question may have been misleading. The question I was wondering about wasn't whether we should keep classical logic. Rather, I was wondering about what was being claimed when someone claims their theory of truth is classical. One of the phrases that was thrown around at the conferences was "classical logic, the kind that has cut". This was said, partly in jest, in reference to the Ripley-Egre-Rooij-Cobreros theory of truth, which loses cut when the truth predicate is around. There is a sense in which that system is classical and at least one in which it is not. Lots of people claim to maintain classical logic, and it seems like in the area of theories of truth, there are a few things one could mean by this. I'm not sure where to look for a discussion of this.

ReplyDeleteJulien,

I had thought it as someone besides Leitgeb or perhaps in addition to him. Whoops.