26-27 January 2018, University of Salzburg
The topic of the workshop is deflationism about truth: the thought that ‘true’ is a device of generalization whose presence in the language is justified for exclusively expressive purposes. The view can be traced back to Ramsey, and has been the object of much recent debate. We are interested in questions such as: What is the use of ‘true’ in natural languages? Must a deflationary theory of truth be nonconservative? Must deflationary truth be nonclassical? Is a deflationary account of truth compatible with a truth-conditional account of meaning?
- Marianna Antonutti Marfori (MCMP, LMU Munich)
- Bradley Armour-Garb (University at Albany-SUNY)
- Cezary Cieśliński (University of Warsaw)
- Andreas Fjellstad (University of Bergen)
- Henri Galinon (Université Clermont Auvergne)
- Michał T. Godziszewski (University of Warsaw)
- Leon Horsten (University of Bristol)
- Mark Jago (University of Nottingham)
- Carlo Nicolai (University of Utrecht)
- Lavinia Picollo (MCMP, LMU Munich)
- Casper Storm Hansen (The Polonski Academy, Jerusalem)
- James Woodbridge (University of Nevada)
- Churfürststraße 1, 5020, Salzburg, AT
- Room HS 202 (stairway n. 5, ground floor)
Marianna Antonutti Marfori, An Epistemic Route to Justifying Reflection
In this talk, I will present a new way of justifying proof theoretic reflection principles on the basis of epistemic considerations. First, I will discuss three different kinds of philosophical strategies to motivate the addition of proof theoretic reflection principles to formal theories of arithmetic: (i) syntactically, by motivating a certain amount of transfinite induction; (ii) semantically, by committing to a certain notion of truth for arithmetic; or (iii) epistemically, by committing to a notion of (informal or absolute) provability for arithmetic. I will argue that reflection principles can be motivated by implicit commitment to a notion of provability in principle or informal provability in arithmetic. On the basis of our acceptance of the axioms and rules of inference of PA as correctly formalising (at least some of) our arithmetical reasoning, we can take the provability of a given sentence in PA as a warrant for asserting its informal provability. I will show that this is sufficient to formally imply the local and uniform reflection scheme. This gives a precise sense in which accepting formal provability in PA as providing (or demonstrating the existence of) informal proofs entails more arithmetical consequences than the mere use of PA.
Bradley Armour-Garb and James Woodbridge, Defending Deflationism against a Forceful Objection
Abstract: Our talk presents a full picture of deflationism about truth, by explaining the proper way to understand the interrelations between (what Bar-On and Simmons (2007) call) conceptual, linguistic and metaphysical deflationism. We then defend deflationism against Bar-On and Simmons (2007)’s objection that conceptual deflationism is incompatible with the explanatory role the concept of truth plays in an account of assertion or assertoric illocutionary force. We defend deflationism, rather than just conceptual deflationism, because we take Bar-On and Simmons’s stance on their target to involve a mistake. Bar-On and Simmons raise an objection merely to conceptual deflationism, putting the issues involved in metaphysical deflationism and linguistic deflationism to one side. We explain how that cannot really be done because it mistakenly treats the three categories of deflationary views as running independently and as being at the same theoretical level. As we show, in our talk, given the relationships between them, a challenge to conceptual deflationism would flow upward and would amount to a challenge to linguistic deflationism, too, and, thus, to deflationism as a whole. Having defended conceptual deflationism against Bar-On and Simmon’s objection, we conclude that deflationism about truth, understood primarily as a view about truth-talk, but with the other theses that brings with it, remains a viable position to endorse.
Cezary Cieśliński, On the T-schema and implicit commitments
Abstract: One of the basic charges against the disquotationalists is that the T-schema (‘F’ is true if and only if F) does not permit to explain our various implicit commitments – statements which are unprovable in an initial theory of our choice, but such that they should be accepted once we accept the initial theory in question. Thus, it is claimed that accepting Peano arithmetic commits us to accepting that Peano arithmetic is consistent. This consistency statement cannot be derived not only in PA itself, but also in disquotational truth-theoretic extensions of PA, hence (so the argument goes) disquotational truth theories are too weak to explain our hidden commitment to the consistency of Peano arithmetic. In the talk an alternative explanation of implicit commitments will be proposed, one which does not involve proving them in a theory of truth. Moreover, it will be claimed that such an explanation is fully accessible to the disquotationalist. In effect, the disquotationalist has at his disposal sufﬁcient means to account for our implicit commitments and the deflationary standpoint is vindicated.
Andreas Fjellstad, Principles of Validity for the Deflationist
Abstract: It has been proposed in recent literature on substructural logics and logico-semantic paradoxes that a dyadic validity-predicate should satisfy the conditions Validity Proof (VP) and Validity Detachment (VD), conditions that together lead to triviality if we assume that the logic to which they are added is transitive and contractive. This paper argues that, from a deflationist perspective on validity according to which a validity-predicate should adequately capture the logic for which it is defined because its role is to make explicit what is valid according to that logic in order to express generalizations, VD is not required for a validity-predicate. Instead, it suffices to accept a Generalization of the Validity Scheme (GVS), that is, a generalization of VP and its converse which includes meta-inferences such as reductio ad absurdum and transitivity. GVS is, as can be established using revision sequences, consistent with classical logic. After clarifying some issues with expressing meta-inferences involving quantifiers that leads us towards infinitary rules, the paper proceeds to present a sequent calculus in which a validity-predicate is defined for classical logic that satisfies GVS.
Henri Galinon, After deflation
Abstract: I take the deflationist’s central claim to be that truth is an expressive, non-explanatory notion. In this talk I hope to do two things. The first is to show that the thesis that truth is semantically akin to a logical notion is a useful way to articulate and vindicate this basic deflationary claim. The second is to contribute to post-deflationist thinking about truth. Indeed, even if, as the deflationist contends, the notion of truth has no explanatory role to play in the language of an ideally completed natural science, it is still open to think that the notion of truth is a fundamental plank in the language of reason. Thus a number of metacognitive tasks and reflexive stances that are essential to our rational functionings involve the use of the notion of truth, meaning that, while “truth” may have no explanatory force, “having a notion of truth” can still have great explanatory force in accounting for some human cognitive achievements. What are those functionings that involves the concept of truth essentially and make it important to possess such a concept ? I will discuss a few examples drawn from the philosophical and psychological literature and the philosophical picture that emerges.
Michał Tomasz Godziszewski, Local disquotation and semantic (non)conservativeness
Abstract: We analyse the (non)conservativeness properties of the classical locally disquotational theory of typed arithmetic truth TB and investigate its model-theoretic strength w.r.t the class of recursively saturated models of arithmetic. We first strengthen and generalise Cieslinski-Engstrom theorem on semantic (model-theoretic) non-conservativeness of TB over PA to a new result stating that TB is not semantically conservative over any complete extension of PA, including the True Arithmetic TA (= Th(N)). Cieslinski’s and Engstrom’s proof was insufficient to justify the latter and our proof provides a new argument that can be useful in further investigations of properties of axiomatic theories of truth. Further, we transfer the characterization of models of TB over set theories, which has some philosophical implications in the debate on deflationism w.r.t. the concept of mathematical truth. In the second part of the talk we separate the class of models of arithmetic expandable to a model of TB from the class of recursively saturated models, providing a completely new and conceptually simple proof of a result due to Łełyk and Wcisło and contributing to the research in the hierarchy of model-theoretic strength of axiomatic truth theories. The main philosophical meaning of the first result is that it also ultimately strengthens contradiction to the claim purported by Ketland that the phenomenon of conservativeness boils down to adding compositionality principles to a given theory of truth. However, the theorem additionally invites philosophical interpretation contributing to the debate on the conservativeness in the field of deflationary theories of truth — it namely provides a reductio argument against considering semantic conservativeness as an adequate criterion for a truth theory, since the assumption that semantic conservativeness is an adequate criterion for a deflationary theory of truth strongly excludes TB from the class of adequate theories as a too strong one.
Leon Horsten, Type-free truth, reflection, cognitive projects, and (anti-) exceptionalism
Abstract: The global reflection principle for a given theory states that the theory in question proves only true statements. I claim that coherent closeability under repeated global reflection serves as an adequacy condition on axiomatic theories of type-free truth. But if we take this approach, then almost all classical axiomatic theories of type-free truth are classified as inadequate, so that we are forced to withdraw from classical logic in axiomatic type-free truth theories. But then we are faced with McGee’s objection of ‘degradation of method’ against non-classical truth theories (anti-exceptionalism). In my talk I draw on Wright’s theory of cognitive projects (and the accompanying notion of epistemic entitlement) to argue, pace McGee, for a natural non-classical typefree truth theory that can be coherently closed under iterated reflection.
Mark Jago, Deflationism and the identity problem
Abstract: In this paper, I present an argument against Horwich-style deflationism (or minimalism) about truth. I begin by recapping reasons for formulating deflationism in terms of propositions (rather than in terms of sentences or particular utterances). I then argue that the propositions in question should be understood as Russellian or Fregean structured entities, rather than as sets of possible worlds or as pleonastic entities. This sets the stage for an objection I call the identity problem. In short, it is that we cannot x the identity of truth without first fixing the identity of certain propositions, whose identity cannot be fixed without first fixing the identity of truth.
Carlo Nicolai, The four pillars of deflationism and their logic
Abstract: Truth-theoretic defationism can be reasonably characterized by the following influential theses: (1) The meaning of “true” is fixed by the Tarski-biconditionals; (2) The truth predicate enables one to express infinite conjunctions and disjunctions (and (1) is necessary for this task); (3) The truth predicate is fundamentally a device to perform sentential quantification over pronominal variables; (4) Truth does not contribute substantially to philosophical and scientific explanations. In the talk I will question them in the light of recent formal results. More in particular, I will provide examples and results supporting the following claims: if one takes (1) seriously, (2) requires a strong notion of equivalence between an infinite conjunction (disjunction) and the corresponding universally quantified sentence involving truth that, under natural assumptions, cannot hold; there is a precise sense in which the truth predicate is not a quantificational device but a coarser-grained logical tool; an understanding of (4) in terms of the conservativeness of the theory of truth over the base theory is either too narrow or leads to a shift of the hierarchy of explanation towards new notions that are no less mysterious than truth. I will conclude by analyzing the prospects of a view of truth that still hasn’t lost its appeal.
Lavinia Picollo, Deflationism is not an inferentialism
Abstract: It is frequently argued that formal theories of truth that square with the principles of deflationism must be (i) axiomatic and (ii) purely disquotational. As deflationism places truth among other logical devices, it would seem the view is tied to some form of inferentialism. I argue that the adequacy of this claim depends heavily on the purpose deflationists wish the formal theory for. More specifically, I argue that if the goal is to employ the truth predicate provided by the theory in the logical capacity deflationists ascribe to it, not only disquotational but also compositional principles can be deemed both acceptable and useful form a deflationary perspective, along with Tarskian truth definitions and families of models.
Casper Storm Hansen, A Conventionalist Solution to the Liar Paradox
Abstract: I will suggest a solution to the liar paradox, in the sense of an answer to those who believe that the liar is both true and not true, based on the premise that language is conventional. According to David Lewis’s theory of conventions, for a sentence to have truth conditions is for the language community in question to have a convention regarding the circumstances in which the sentence is appropriately assertible (in a certain sense). The power to institute language conventions does not come with the power to make a state of affairs both obtain and not obtain, and therefore the liar is not both conventionally appropriately assertible and not conventionally appropriately assertible. Whether it is one or the other is an empirical question that depends on contingent details about our conventions. I draw on Thomas Nagel’s ideas about a view from nowhere to explain why our language psychology can make it seem that the liar ought to be true if and only if it is not.
- Julien Murzi (Salzburg)
- Lorenzo Rossi (Salzburg)
For questions or any other queries, please contact Julien Murzi (j.murzi AT gmail.com) or Lorenzo Rossi (lorenzo.rossi AT sbg.ac.at).
The workshop is sponsored by the Austrian Science Fund (FWF) and is hosted by the Philosophy Department (KGW) at the University of Salzburg.