Bilateral approaches to meaning
20 – 22 June 2019
University of Amsterdam and Institute for Logic, Language and Computation
Maria Aloni — Weak assertion meets information states: a logic for epistemic modality and quantification
(based on joint work by Aloni, Incurvati and Schlöder)
The article presents the first example of a fully worked out quantified logic for epistemic modality which derives the infelicity of epistemic contradictions (Yalcin, 2007) while solving a number of puzzles arising from the combination of epistemic modals and quantifiers (e.g., Groenendijk et al., 1996 and Ninan, 2018). The proposed logic extends the propositional multilateral proof theory from Incurvati and Schlöder (2018) with quantifiers and provides it with a model theory which uses states (Veltman, 1996) and conceptual covers (Aloni, 2001). The logic, which is sound and complete, is based on a distinction between speech acts and content which is encoded both on the proof-theoretical and the model-theoretical level. Proof-theoretically, formulae are decorated with force markers. Model-theoretically, force markers operate globally as tests on information states while the clauses of the logical constants are recursively given in terms of update potentials. In the discussion we will emphasize the virtue of studying epistemic modality and quantification both from a proof-theoretic and a model-theoretic perspective.
David Beisecker — Bilateralism and its pragmatist roots
While significant and explicit expressions of both bilateralism and rejectivism can be found in the historical record, contemporary bilateralists are generally silent about this history. Here I wish to call particular attention to bilateralism that can be discerned in the work of C.S. Peirce. For in his Monist series of 1905-6, Peirce offers us a strikingly bilateral formulation of the pragmatic maxim, which directs us to the consequences not only of affirming a conception, but also those of denying it. These bilateral formulations of the pragmatic maxim are meant to map onto features of his system of logical notation, which is bilateral in a most literal sense. Peirce’s graphs begin with one side of a piece of paper upon which are inscribed claims represented as affirmed. But that sheet of paper is to be understood as also having a reverse side upon which one inscribes claims to be denied. Peirce then conceives of negation as a device for viewing an inscribed claim from the opposite side. Logical proofs are transformations of graphs (“moving pictures of thought”) according to rules or permissions, which in effect depend upon which side of the sheet of paper (front or reverse) a claim is inscribed. Consequently for Peirce, the inferential significance of a claim has both positive and negative aspects.
In short, then, I will argue that bilateralism finds early expression in Classical Pragmatism, and moreover, that it is deeply embedded in Peirce’s graphical notation for logic. Contemporary bilateralists would thus do well to recognize and draw upon Peirce as a particular source of inspiration.
Leïla Bussière — Dissent and Rejection
In bilateralist projects, a study of rejection has proven fruitful to determine the inferential potential of sentences. However, the speech act of rejection and its norms have yet to be clearly characterized, if we are to treat rejection on par with assertion. Incurvati and Schlöder show that rejection may be weak, i.e. such that from the rejection of p, one cannot infer ¬p. In addition, rejection can bear on the performance of an utterance: for example, an utterance can be deemed incorrect in a conversational context, because it does not respect agreed upon conventions. Therefore, a unified theory of the speech act of rejection needs to account for (i) cases of weak rejection, and (ii) ‘pragmatic’ rejection.
I will examine four contemporary accounts of assertion, and construct from each of them a corresponding possible account of rejection. I propose a distinction within theories of assertion between conditions-based accounts that propose ‘upstream norms’, and effect-based accounts (‘downstream norms’). Condition-based accounts such as theories of assertion such as expression-of-attitude approaches and norm-based approaches to assertion provide us with conditions that need to be fulfilled to perform an assertion or rejection. Their focus on content means that they need to account for pragmatic rejection with a distinct set of conditions, thus failing to give a unified perspective on rejection. On the other hand, effect-based accounts such as the common ground approach and the commitment approach provide a unified picture of the conversational effect of rejection. Therefore, this may warrant treating rejection as a unique speech act, whose set of conditions might be disjunctive.
Peter Hawke and Shane Steinert-Threlkeld — Semantic expressivism for modals, conditionals and quantification
Luca Incurvati and Julian Schlöder — Meta-ethical inferential expressivism
We develop a novel solution to the negation version of the Frege–Geach problem by taking up recent insights from the bilateral programme in logic. Bilateralists derive the meaning of negation from a primitive B-type inconsistency involving the attitudes of assent and dissent. Some may demand an explanation of this inconsistency in simpler terms, but we argue that bilateralism’s assumptions are no less explanatory than those of A-type semantics that only require a single primitive attitude, but must stipulate inconsistency elsewhere. On the basis of these insights, we develop a version of B-type expressivism we call inferential expressivism. This is a novel semantic framework that characterises meanings by inferential roles that define which attitudes one can infer from the use of terms. We apply this framework to normative vocabulary, thereby solving the Frege–Geach problem generally and comprehensively. Our account moreover includes a semantics for epistemic modals, thereby also explaining normative terms under epistemic modals.
Teresa Marques — Illocutionary force and attitude mode in normative disputes
Recently, several articles have addressed the way people communicate and disagree about moral and normative claims. Perez Carballo and Santorio (2016) offer a model of communication for expressivists, and Khoo and Knobe (2016) offer a model for moral disagreements. Their proposals modify the Stalnakerian account of assertion in terms of updates of the context set with normative claims, where people accept that certain actions are mandatory, permissible, or forbidden. Moreover, these updates are offered as answers to QUDs. In this talk, I’ll raise four problems that non-cooperative speakers (engaged in lying, misleading, bullshitting, denigrating or insulting) pose to these models of normative communication. First, some answers to a QUD that are correct (on the modified Stalnakerian models) are rightfully rejected as misleading, or bullshitting, because of their illocutionary force, a fact the Stalnakerian models can’t explain properly. Second, the representation of what norms are common ground can’t be made just in terms of a speaker’s acceptance that her interlocutor accepts that an action is permissible (required, etc.), since that can happen without it becoming common ground or taken for granted that the action is permissible. Some examples from derogatory or insulting language make this clear. Third, there are QUDs which violate the condition that all speakers intend to engage in inquiry to settle whether Q, e.g., non-cooperative speakers will not want to settle all questions. Hence, what makes a question a QUD can’t be that all speakers intent to engage in inquiry to settle it. Finally, even in cases where speakers agree which is the QUD about what is to be done, and where they prima facie disagree, it doesn’t follow from their incompatible context update proposals about what to do that (a) no norm is in force in that situation, and it doesn’t follow that (b) their proposals are neither true nor false, as some examples will make clear. I suggest that more needs to be said about the normative requirements involved with the illocutionary force of different speech acts, and that more needs to be said about the ‘modes’ of the acceptance states that allow norms or values to become common ground.
Greg Restall — Assertions, Denials, Questions, Answers and the Common Ground
In this talk, I examine some of the interconnections between norms governing assertion, denial, questions and answers, and the common ground of a discourse. When we pay attention to the structure of norms governing polar (yes/no) questions, we can clarify the distinction between strong and weak denials, together with the parallel distinction between strong and weak assertion, and the way that these speech acts interact with the common ground.
With those connections established, I respond to two criticisms of the program sketched out in my 2005 paper “Multiple Conclusions”. First, that understanding the upshot of a valid sequent X ⊢ Y as enjoining us to not assert each member of X and deny each member of Y is altogether too weak to explain the inferential force of logical validity. Deriving X ⊢ A should tell us, after all, something about justifying A on the basis of X, rather than merely prohibiting A’s denial. Where is the force to actually conclude the conclusion of a proof? A second, related criticism is that the format of multiple conclusion sequents seems unsatisfactory, in that it has no place for distinguishing a single conclusion, and proofs, after all, seem to be proofs of individual claims.
I will argue that both of these concerns can be assuaged if we pay closer attention to the norms connecting assertions and denials along with justification requests — questions aiming at eliciting reasons for assertions or denials. Once we understand the connection between justification requests, definitions and the common ground, we will see not only that the these two concerns can be met. A derivation of a sequent X ⊢ A,Y gives us an answer to a justification request “why A?” in any available context where each member of X has been ruled in and each member of Y has been ruled out, and a derivation of a sequent X, B ⊢ Y, similarly gives us an answer to the justification request “why not B?” in any such context. The picture that results utilises the full multiple premise, multiple conclusion sequent calculus of classical logic, and does due justice to the idea that a proof (or a refutation) proves (or refutes) one thing relative to background assumptions or premises. In addition, when we consider the connection between justification requests and the norms governing definitions, we can see more clearly what could be involved in taking the connective/quantifier rules of a logical system to define the concepts they introduce.
David Ripley — Position-theoretic semantics, disagreement, and entailment
The purpose of this talk is to present and partially articulate an alternative to both model-theoretic and proof-theoretic semantics: position-theoretic semantics. On this approach, both proofs and models are mere technical auxiliaries, without any direct connection to meaning. Neither reference nor inference comes first; both are derivative. Meaning is in the first place located in positions (collections of assertions and denials) and the notion of disagreement between positions.
A position-theoretic semantics, like any other semantics, owes (among other things) an account of entailment. But while disagreement is a matter of ruling out, entailment seems to be a matter of guaranteeing or ruling in. So it’s not immediately obvious how to use this position-theoretic framework to understand entailment. Indeed, there is some reason to think that it cannot be done, stemming from an objection by Florian Steinberger to Greg Restall’s work. This talk, however, shows how to develop a position-theoretic account of entailment, by developing a notion of equivalence between positions, and using this to understand when assertions and denials can be implicit in a position.
Lucas Rosenblatt — Invalidities
There are many ways of understanding what it is for an argument to be valid. Although we usually identify the concept of validity with (classical, first-order) logical validity and, in turn, we typically take this to capture the notion of necessary preservation of truth in virtue of logical form, this is just one way in which validity can be explained. A different understanding of the notion of validity that has received some attention recently is based on the idea that an argument is valid if and only if accepting its premises is (materially) incoherent with rejecting its conclusion. The main claim of the talk will be that, under this understanding of the notion of validity, all the usual reasons to privilege a treatment of validities over a treatment of invalidities loose much of their force. Validity and invalidity are on a par, which means that there is no reason to treat validities primitively and to define invalidities in terms of them.
Sebastian Speitel — Meaning and logicality in bilateralist frameworks