Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for bilateral proof rules has (...) a reasonable claim to inferentially articulating the core meaning of all of the classical connectives. I propose this schema in the context of a bilateral sequent calculus in which each connective is given exactly two rules: a rule for affirmation and a rule for denial. Positive and negative rules for all of the classical connectives are given by a single rule schema, harmony between these positive and negative rules is established at the schematic level by a pair of elimination theorems, and the truth-conditions for all of the classical connectives are read off at once from the schema itself. (shrink)

Why must incompatibility be symmetric? An odd question, but recent work in the semantics of non-classical logic, which appeals to the notion of incompatibility as a primitive and defines negation in terms of it, has brought this question to the fore. Francesco Berto proposes such a semantics for negation argues that, since incompatibility must be symmetric, double negation introduction must be a law of negation. However, he offers no argument for the claim that incompatibility really must be symmetric. Here, I (...) provide such an argument, showing that, insofar as we think of incompatibility in normative pragmatic terms, it can play its basic pragmatic function only if it is symmetric. The upshot is that we can vindicate Berto’s claim about the symmetry of incompatibility but only if we, pace Berto, think about incompatibility, in the first instance, as a pragmatic relation between acts rather than a semantic relation between contents. (shrink)

I motivate and develop a use-based semantic theory in opposition to the dominant paradigm in philosophical and linguistic semantics. Drawing inspiration from Wilfrid Sellars, I argue that contemporary semantic theories are faced with a basic problem of explanatory circularity. These theories universally presuppose that worldly knowledge of such things as properties or sets of possible worlds precedes and underlies knowledge of meaning. However, I argue that it is only through learning a language--mastering the rules governing the use of the expressions (...) belonging to that language--that speakers can possibly have knowledge of the worldly entities appealed to by semanticists at the base level of their semantic theories. In response to this fundamental problem, I develop a formal semantic framework in which the meaning of a sentence is understood directly in terms of its role in discourse. In contrast to existing semantic frameworks, this framework does not presuppose speakers' worldly knowledge, and so is actually able to explain it. The result is not just a new kind of semantic theory, but a new conception of the relation between meaning and the world. (shrink)

An “inferentialist” semantic theory for some language L aims to account for the meanings of the sentences of L solely in terms of the inferential rules governing their use. A “hyper-inferentialist” theory admits into the semantics only “narrowly inferential” rules that normatively relate sentences of L to other sentences of L. A “strong inferentialist” theory also admits into the semantics “broadly inferential” rules that normatively relate perceptual states to sentences of L or sentences of L to intentional actions. It is (...) widely thought that only the latter of these two sorts of semantic theories is at all viable. I argue here that the opposite is so. Negatively, strong inferentialism is viciously circular: including rules into the semantic theory that relate perceptual states to sentences of the language requires us to appeal, in individuating those perceptual states, to the very meanings for which we are supposed to be inferentially accounting. Hyper-inferentialism does not face this problem because it does not appeal to any nonlinguistic states. Positively, though hyper-inferentialism is widely thought to be a theoretical non-starter, I argue here that it is a genuine theoretical possibility insofar as it essentially includes cross-perspectival inferences, inferences along the lines of the one from the sentences “The ball is in front of n,” “The ball is red,” and “The lighting is good” to the sentence “n sees that the ball is red.” I make the further exegetical claim that Robert Brandom, though unanimously taken to be a strong inferentialist, is in fact a hyper-inferentialist. (shrink)

Wilfrid Sellars is widely known for two positions that he calls “nominalism.” On the one hand, there is his “psychological nominalism,” according to which any awareness one might have of abstract entities—be they properties, relations, or facts—is a thoroughly linguistic affair, and so cannot be presupposed in thinking about the process of learning a (first) language. On the other hand, there is his ontological nominalism, according to which the world, as it is in itself, is fundamentally a world of concrete (...) particulars and so does not ultimately contain such things as properties, relations, or propositionally-structured facts. Sellars clearly takes these two sorts of “nominalism” to go together. However, one of the most influential inheritors of Sellars's philosophy, Robert Brandom, thinks that they do not. Brandom endorses the former, but denies that the latter “is in the end so much as intelligible.” In this paper, I articulate the connection between Sellars's psychological and ontological nominalism and draw on Brandom's own development of Sellars's functional role semantics to argue, against Brandom, that Sellars's ontological nominalism not only harmonizes with the rest of his philosophical commitments, but is actually made fully intelligible by the very aspect of Sellars's theory that Brandom himself develops. (shrink)

According to existing accounts of indicative conditionals, any argument of the following form is valid: ϕ → ψ, ( ϕ ∧ ψ ) → χ ∴ ϕ → χ. Here, I present a set of counterexamples to show that there exist invalid arguments of this form. I argue that this data poses serious problems to variably strict accounts of conditionals, as such accounts are structurally unable to accommodate it. Dynamic strict accounts, however, are a different story. While existing dynamic strict (...) accounts do not accommodate the data, they are in principle able to, and I propose a modified dynamic strict account, drawing from von Fintel, that does. The key modification is this: whereas existing dynamic strict accounts take into account only the effects of conditional antecedents in changing the semantic context, the data shows that we must also take into account the effects of conditional consequents in changing the semantic context. (shrink)

In recent work, Robert Brandom has articulated important connections between the deontic normative statuses of entitlement and commitment and the alethic modal statuses of possibility and necessity. In this paper, I articulate an until now unexplored connection between Brandom’s core normative statuses of entitlement and commitment and the agentive modal statuses of ability and compulsion. These modals have application not only in action, but also in perception and inference, and, in both of these cases, there is a direct mapping between (...) the normative statuses that one bears towards various claims, articulated from the perspective of the attributor of commitments and entitlements, and the agentive modal statuses that one bears towards various judgments, articulated from the perspective of the undertaker of commitments. I will highlight this correspondence, focusing on the case of perception, and show how it sheds light on the account of mindedness that emerges from Brandom’s theory of discursive practice. (shrink)