Robert Brandom has described “implication space” semantics, first put forward in Daniel Kaplan’s dissertation, as the “holy grail” of inferentialist semantics. However, when one tries to work through the details of the semantic framework, it is very hard to make intuitive sense of what the semantic clauses actually say. In this paper, I articulate a novel interpretation of implication space semantics as a bilateral successor to Brandom’s earlier “incompatibility semantics.” On this interpretation of the framework, semantic values are assigned, in the first instance, to “positions” consisting in assertions and denials, and the semantic value of such a position is the set of positions that are incompatible with it. I show how this interpretation renders otherwise obscure features of this semantic framework intuitively intelligible in terms of notions previously articulated by Brandom, most notably, that of incompatibility entailment.

According to an act-based conception of propositions, propositions are types of cognitive or linguistic acts. Such accounts are advertised as having major metaphysical and epistemological advantages over traditional platonic accounts. However, existing versions of such accounts appeal to platonic properties and relations in order to account for the contents expressed by predicates, reintroducing many of the problems they aim to solve. Characterizing both that a is F and that it's F as different types of ``assertibles'' (the former can be asserted full-stop and the latter can be asserted of things), the issue can be seen as a limitation of existing act-based approaches: they apply only to a restricted class of assertibles. In this paper, I show how adopting a normative functionalist approach to linguistic meaning enables one to generalize the act-based approach to all assertibles such that no appeal to extrinsic properties and relations is needed. I show, further, how this radicalized act-based account provides the resources for a satisfactory account of our knowledge of objective states of affairs, properties, and relations (which I dub ``instantiables'') in terms of our mastery of linguistic norms.

Recent work in bilateral logic has concerned itself with whether and to what extent strong negation, which "toggles" between assertion and denial, is definable in bilateral systems that lack it. This paper presents a number of results about the definability of strong negation in bilateral systems. First, I show that a constructive Nelson-style Sheffer stroke defines the strong negation of A as (A|(A|A))|A. The same stroke defines the constructive Nelson implication, thus providing a single-connective basis for the strong-negation-and-implication fragment of N4. Second, I provide an exhaustive characterization of the eight combinations of a single "aggregative" connective and a single Nelson-style connective that suffice to jointly define strong negation, with neither defining it individually. One such combination is the material conditional together with constructive co-implication. Third, I show that a constructive and connexive Wansing-style Sheffer stroke (recently referred to as "connexive exclusion") likewise defines the strong negation of A as (A|(A| A))|A and also defines connexive implication. Fourth, I show that, unlike with the Nelson-style connectives, there are no combinations of Wansing-style and aggregative connectives that jointly define strong negation if neither connective defines it individually.

In a recent paper, Nils Kürbis argues that bilateral natural deduction systems in which assertions and denials figure as hypothetical assumptions are unintelligible. In this paper, I respond to this claim on two counts. First, I argue that, if we think of bilateralism as a tool for articulating discursive norms, then supposition of assertions and denials in the context of bilateral natural deduction systems is perfectly intelligible. Second, I show that, by transposing such systems into sequent notation, one can make perfect sense of them without talking about supposition at all, just talking in terms of relations of committive consequence. I conclude by providing some motivation for adopting this normative interpretation of bilateralism on which this response to Kürbis’s argument is based.

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.

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.

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 sentences “The ball is in front of n ,” “The ball is red,” and “The lighting is good” to sentence “ n sees that the ball is red.” I make the further exegetical claim that Brandom ( Making it explicit , Harvard University Press, Cambridge, 1994 ), though unanimously taken to be a strong inferentialist, is in fact a hyper-inferentialist.

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.

According to existing accounts of indicative conditionals, any argument of the following form is valid: 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 (Lewis 1973; Stalnaker 1968), as such accounts are structurally unable to accommodate it. Dynamic strict accounts (von Fintel 2001; Gillies, 2007; Willer 2017), 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 (2001), 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.

Semantic theorists often wish to be metaphysically non-committal. When faced with the question of whether to follow David Lewis (1973, 1986) in thinking of the possible worlds that figure into their semantic theories are just as real as the actual world, most theorists are likely to follow Robert Stalnaker (1984) in thinking of possible worlds as in some way identified with or constructed out of properties and relations belonging to the actual world.1 Yet, when it comes to such things as properties and relations themselves, contemporary semantic theorizing almost always proceeds on platonist grounds, unapologetically appealing to properties and relations as the semantic contents of predicates. The reason why is quite clear: properties and relations seem to be just the sorts of things that are needed at the base level of the semantic theory, providing the basic contents that can be combined in various semantically significant ways to form the meanings of complex expressions. To do semantics without appeal to properties and relations would be to do semantics without contents, and surely, one would think, such a thing cannot be done. I argue here that this is not so—we can do semantics without contents, thinking of the meanings of predicates entirely in terms of what one does in uttering them without any appeal to any things that one says of things in doing so. Moreover, what doing semantics in this way reveals is not only that it’s possible to do semantics without appeal to properties and relations, but that it’s necessary in order to arrive at the correct account of what these entities are: “shadows” See, for instance, Partee (1988, 102) and Cheirchia and McConnell-Ginnett (1990, 207-208).

Recent literature on propositions has claimed that the traditional conception of propositions, inherited from Frege and Russell, is untenable (King 2008; King, Speaks, and Soames 2014; Hanks 2015). Broadly characterized, the traditional conception of propositions holds (1) that there are propositions, (2) that propositions are the basic bearers of truth and falsity, and (3) that they are the basic bearers of truth and falsity in virtue of being the basic entities that represent things as being certain ways. The primary target of recent critical work on propositions has been the third tenet of this traditional conception. Here, I poinpoint the core problem of the traditional conception. , considering first how it arises in Mark Johnston’s (2006) recent attempt to explain how propositions, traditionally conceived, represent and showing then how it still arises in Jeff King’s (2009, 2015) non-traditional attempt to explain how propositions represent. The problem, which I’ll call “the relation relocation problem,” is that the relation needed to bind together the constituents of a proposition so as to explain how it represents things as being a certain way, has to be relocated from acts of thinking subjects to objective entities, and the intelligibility of this relation does not survive the attempted relocation. After

Sellars has carried out Kant’s transcendental idealism farther than any other philosopher of the 20th century. Indeed, Science and Metaphysics, which can be regarded as a summation of Sellars’s work though his most productive period, is nothing other than an attempt to articulate a Kantian transcendental idealist picture, fitting his career’s work into that picture. What is perhaps most notable about this picture from the perspective of contemporary Kant scholarship is that it falls squarely in the traditional “two worlds” reading of Kant (Strawson 1966, Guyer 1979, Van Cleve 1999, Juarning 2021), rather than one of the various sorts of “two aspect” readings that have been dominant for the past four decades (Prauss 1974, Allison 1983, Langton 1998, Allais 2004, 2015). For Sellars, the Kantian distinction between appearances and things in themselves really does demarcate two distinct worlds—the world of everyday experience, which Sellars regards as “existing only as the contents of actual and obtainable conceptual representings” (SM, 173), and the real world, which contains the happenings that account for the existence of the conceptual contents that constitute the world of everyday experience. Crucially, fundamentally distinct sorts of entities constitute these respective worlds—conceptual contents, on the one hand, and non-conceptual material happenings, on the other—and there is no one-to-one mapping between the constituents of one world and the constituents of the other. Apart from

Abstract In recent work, Robert Brandom (2008. Between Saying and Doing. Oxford: Oxford University Press; 2019. A Spirit of Trust. Cambridge, MA: Harvard University Press) 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.

1This includes accounts of truth-conditional varieties (Lewis 1973; Stalnaker 1968), including even McGee’s (1985) semantics that invalidates modus ponens, suppositional varieties (Adams 1966, 1975; Edgington 1995, 2001), and dynamic varieties (von Fintel 2001; Gillies 2004, 2007, 2009; Willer 2017). Some of these accounts, such as Lewis (1973), von Fintel (2001), and Gilles (2007), are proposed for counterfactuals, but they can be straightforwardly carried over as accounts of indicatives. In what follows, I will talk as if they are simply proposed as accounts of indicatives. Following Rothschild (2020), I do not take Kratzer’s (1981, 1986) restrictor view to be a view of conditionals competing with these other views, but, rather, a view of the meaning of “if” that is compatible with multiple views of the meanings of full “If . . . then . . .” sentences, but, in any case, it should be clear that it validates arguments of this form in much the same way the Lewis/Stalnaker account does. I should note from the outset that I do not explicitly consider suppositional views here, but it should be clear from the discussion of the variably strict view that there is a structurally analogous problem here. Just to be clear that such views fall within that target range, note that Adams (1975) describes this inference pattern as “universally probabilistically sound in that the uncertainty of the conclusion can never exceed the sum of the uncertainty of the premises,” (22).