Workshop: Semantic Paradox, Context, and Generality

June 26-28, 2019 – University of Salzburg

Speakers

The topics of the workshop are semantic paradox, context, and generality. There are deep relations between semantic paradoxes, such as the Liar, and theories of context shift, generality, and quantification. For instance, in contextualist theories of truth, paradoxical sentences fail to express any proposition in their original context of reasoning, but express a proposition in a richer context, where new propositions are available for expressions. Analogously, in a tradition that goes back at least to Russell and Zermelo, paradoxical reasonings are seen as “diagonal” arguments that expand any given domain of quantification. In this workshop, we will investigate the relations between semantic paradoxes, context relativity, and generality. We are interested in questions such as: Do paradoxical reasonings impose some form of context shift? Does this show that semantic predicates, or expressions involving them more generally, are context dependent in some special way? Do semantic paradoxes force a rejection of absolute generality? 

Venue

Programme

June 26

  • 8:30-9:00: Welcome and coffee
  • 9:00-10:30: Agustín Rayo, ‘A Localist Account of the Liar’
  • 10:30-10:45: Coffee break
  • 10:45-12:15: Gabriel Uzquiano, ‘Impredicativity and Intensionality’
  • 12:15-13:30: Lunch break
  • 13:30-15:00: Salvatore Florio and Nick Jones, ‘Unrestricted Quantification and the Structure of Type Theory’
  • 15:00-15:15: Coffee break
  • 15:15-16:45: Susanne Bobzien, ‘Semantic Agnosticism, Assessment Sensitivity and Indirect Revenge’

19:00 Dinner at Ko.Co (http://koco-salzburg.at/en/)

June 27

  • 9:00-9:30: Welcome and coffee
  • 9:30-11:00: Øystein Linnebo, ‘Generality Explained’
  • 11:00-11:15: Coffee break
  • 11:15-12:45: Lorenzo Rossi, ‘Bicontextualism’
  • 12:45-14:15: Lunch break
  • 14:15-15:45: Friederike Moltmann, ‘Truth Predicates, Truth Bearers, and their Variants’
  • 15:45-16:00: Coffee break
  • 16:00-17:30: James Studd, ‘Hybrid-Relativism and Revenge’

19:00 Dinner at Zwettler’s (https://www.zwettlers.com/startseite/)

June 28

  • 9:00-9:30: Welcome and coffee
  • 9:30-11:00: Michael Glanzberg, ‘Unrestricted Quantification and Extraordinary Context Dependence?’
  • 11:00-11:15: Coffee break
  • 11:15-12:45: Keith Simmons, ‘Paradoxes of Validity’
  • 12:45-14:15: Lunch break
  • 14:15-15:45: Paul Égré, ‘Liars and Half-Truths’
  • 15:45-16:00: Coffee break
  • 16:00-17:30: Christopher Gauker, ‘Paradoxes of Truth-in-Context-X’

19:00 Dinner at Pauli Stubm (https://www.paul-stube.at)

Abstracts

S. Bobzien, ‘Semantic Agnosticism, Assessment Sensitivity and Indirect Revenge’

Semantic agnosticism is a revenge-proof non-hierarchical theory of truth related to Herzberger, though it takes truth operators as primary and truth predicates as derivative; it ‘grounds’ Liar and Truth-teller sentences and marks semantically paradoxical sentences as – malignantly – assessment sensitive; its logical structure is captured by (an extension of) the modal system S4M (= S4 plus the McKinsey axiom); this yields the result that nothing at all can be derived from semantically paradoxical sentences. I sketch the theory, examine a form of indirect revenge and offer a natural first-order extension of S4M that forestalls this.

P. Égré, ‘Liars and Half-Truths’

A half-truth may be defined as a sentence that is true in one sense, but that fails to be true in another sense (viz. Egré and Icard 2018). In this talk I propose to discuss the aspects under which the Liar can be considered a half-truth. Talk of half-truths, like talk of half-full containers, suggests that truth could be gradable. There is ample linguistic evidence that “true” patterns as an absolute gradable adjective (in the sense of Unger 1975, Kennedy and McNally 2005), namely as a closed-scale adjective (see Egré 2018 for brief mention, and Henderson 2019 for a detailed review). In the first part of that talk, I discuss some of that evidence, and conclude that the sense in which “true” is gradable is therefore limited (see Burnett 2017). To say that a sentence is half-true, however, indicates that it fails to be perfectly true. In the second part of the paper, I use this to revisit the strict-tolerant account of the Liar (Ripley 2012, Cobreros et al. 2013). While the strict-tolerant account was initially conceived for vague predicates, its extension to the semantic paradoxes assumes that assertion, but not truth, comes in different degrees. I reconsider this claim, by asking whether one should not think of the Liar as lacking a feature of perfect truth, and what feature that might be.

S. Florio & N. Jones, ‘Unrestricted Quantification and the Structure of Type Theory’

Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantification. However, they also pose a prima facie problem for it: each quantifier ranges over at most one level of the hierarchy and is therefore not unrestricted. It is difficult to evaluate this problem without a principled account of what it is for a quantifier to be unrestricted. Drawing on an insight of Russell’s about the relationship between quantification and the structure of predication, we offer such an account. We use this account to examine the problem in three different type-theoretic settings, which are increasingly permissive with respect to predication. We conclude that unrestricted quantification is available in all but the most permissive kind of type theory.

C. Gauker, ‘Paradoxes of Truth-in-Context-X’

The truth predicate that we utilize in our semantic metalanguage must be a two-place predicate relating sentences to contexts, the truth-in-context-X predicate. In particular, the semantics of sentences containing the one-place truth predicate must be formulated in terms of truth-in-context-X. Consequently, we may conclude that paradoxical sentences containing the one-place truth-predicate are neither true nor false in any context without inviting revenge paradoxes. Still, there are also paradoxical sentences containing the truth-in-context-X predicate. These, however, can be blocked by placing restrictions on the structure of contexts. While contexts must specify a domain of contexts, and what a context denotes relative to a context must be a context in the context domain of that context, no context may belong to its own context domain. A generalization of that restriction blocks all of the paradoxes of truth-in-context-X. This restriction entails that, in a certain sense, we cannot talk about the context we are in. This result will be defended on broadly ontological grounds, and it will be conjectured that our semantic metalanguage can be regarded as semantically closed.

M. Glanzberg, ‘Unrestricted Quantification and Extraordinary Context Dependence?’

One of the responses to a well-known family of paradoxes, including Russell’s paradox and the Liar paradox, is to claim that quantification is never absolutely unrestricted. I have defended a contextualist version of this response, which argues that the lack of absolutely unrestricted quantifiers is an effect of context dependence of quantifiers on the background domain. In earlier work, however, I raised the concern that this sort of context dependence is distinct from the ordinary context dependence we see with quantifier domain restriction. I thus proposed an ‘extraordinary’ form of context dependence. In this paper, I shall reconsider how extraordinary the context dependence required by the contextualist response to the paradox really is. Relying on recent work on the semantics of quantifiers, especially, the ‘distributive-universal’ quantifiers, I shall show that some cases of context dependence of background domain can be assimilated to the ordinary context dependence of quantifier domain restriction. Thus, in a least some cases, the contextualist response to the paradoxes can be seen as an appeal to ordinary context dependence.

Ø. Linnebo, ‘Generality Explained’

What explains a true universal generalization? I distinguish two kinds of explanation. While an instance-based explanation proceeds via each instance of the generalization, a generic explanation is independent of each instance, relying instead on completely general facts about the properties or operations involved in the generalization. This distinction is illuminated by means of a truthmaker semantics, which is also used to show that instance-based explanations support classical logic, while generic explanations support only intuitionistic logic. If time permits, I’ll make some remarks about applications to the liar paradox.

F. Moltmann, ‘Truth Predicates, Truth Bearers, and their Variants’

In this talk I will argue that truth predicates and their variants, predicates of correctness, satisfaction, and validity, do not apply to propositions (not even with that-clauses), but to a range of attitudinal and modal objects. As such natural language reflects a notion of truth that is primarily a normative notion of correctness constitutive of representational objects. I will also argue that true is part of a larger class of satisfaction predicates whose semantic differences are best accounted for in terms of a truthmaker theory along the lines of Fine’s recent truthmaker semantics.

A. Rayo, ‘A Localist Account of the Liar’

I offer an account of the Liar Paradox that is based on the assumption that meanings are constructed in context when speaker and hearer secure the right kind of coordination.

L. Rossi, ‘Bicontextualism’

Contextualist theories of truth have a number of virtues – they offer a uniform, elegant, and fully classical treatment of both ‘standard’ and ‘revenge’ paradoxes. However, standard contextualist theories of truth are incompatible with absolute generality, the view that one can successfully quantify over everything whatsoever. Far from being a minor side effect, this makes it impossible for contextualist theories to correctly interpret arguably absolutely general truths, such as ‘everything is self-identical’. In this paper, I develop a contextualist theory of truth that is compatible with absolute generality, while retaining the virtues of standard contextualism, including its treatment of revenge paradoxes.

K. Simmons, ‘Paradoxes of Validity’

Suppose the following argument is written on the board in room 227:

(P) 1=1

So,

(C) The argument written on the board in room 227 is not valid.

This argument generates a paradox, closely related to paradoxes of denotation and the Liar paradox. I propose a contextual approach to this paradox of validity. There are two main claims. The first is that our semantic expression ‘valid’ is context-sensitive. The second, inspired by a brief, tantalizing remark of Gödel,  is that the validity predicate is significant everywhere except for certain singularities, in analogy with division by zero. I extend the approach to other paradoxes of validity, and explore the connections to Curry-style validity paradoxes.

J. Studd, ‘Hybrid-Relativism and Revenge’

Absolutism about quantifiers is the view that quantifiers sometimes range over an absolutely comprehensive domain. Relativists about quantifiers often oppose this view on the grounds that concepts such as set are ‘indefinitely extensible. To assuage doubts about the coherence of this view, relativism and the argument from indefinite extensibility may be regimented with the help of ‘modalized quantifiers’. But what is the status of these putatively relativist-friendly generalizing devices? Some relativists may be tempted to combine their quantifier-relativism with a species of absolutism about modalized quantifiers. I argue that this hybrid view faces a revenge problem.

G. Uzquiano, ‘Impredicativity and Intensionality’

Russell’s ban on impredicativity underwrites at least two approaches to a broad family of intensional paradoxes, which include Russell’s paradox of propositions, Kripke’s paradox about time and thought, Prior’s paradox, and Kaplan’s modal paradox. One approach allows for unrestricted higher-order quantification but rejects impredicative comprehension. The other approach ramifies higher-order quantification and replaces each quantifier with an open-ended hierarchy of restricted quantifiers of the same type. Both approaches reject certain higher-order generalizations of Cantor’s theorem at the heart of some of the intensional paradoxes. One of the purposes of this talk is to clarify the role of impredicativity in the proof of these and similar results and to suggest that Russell’s ban on impredicativity provides only a partial response to the intensional paradoxes. The other is to explore a link between them and certain semantic paradoxes.