Recent experiments have shown that naive speakers find borderline contradictions involving vague predicates acceptable. In Cobreros et al. we proposed a pragmatic explanation of the acceptability of borderline contradictions, building on a three-valued semantics. In a reply, Alxatib et al. show, however, that the pragmatic account predicts the wrong interpretations for some examples involving disjunction, and propose as a remedy a semantic analysis instead, based on fuzzy logic. In this paper we provide an explicit global pragmatic interpretation rule, based on (...) a somewhat richer semantics, and show that with its help the problem can be overcome in pragmatics after all. Furthermore, we use this pragmatic interpretation rule to define a new consequence-relation and discuss some of its properties. (shrink)
The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific (...) consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic. (shrink)
DaveRipley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction—whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to (...) a closure operator in the expected way, then it necessarily contracts. We counter Ripley’s objection by presenting an approach to multiset consequence that escapes this trap. This approach is multiple-conclusioned in a heterodox way, for multiple succedents are given a conjunctive, rather than a disjunctive reading. Finally, we address a further objection by French and Ripley to the effect that the informational interpretation of sequents in linear logic does not motivate cut. (shrink)
While participating in a symposium on DaveRipley’s forthcoming book Uncut, I had proposed that employing a strict-tolerant interpretation of the weak Kleene matrices provided a content-theoretical conception of the bounds of conversational norms that enjoyed advantages over Ripley’s use of the strong Kleene matrices. During discussion, I used the case of sentences that are taken to be out-of-bounds for being secrets as an example of a case in which the setting of conversational bounds in practice diverged (...) from the account championed by Ripley. In this paper, I consider an objection that my treatment of quantifiers was mistaken insofar as the confidentiality of a sentence ϕ may not lift to the sentence ∃xϕ and draw from this objection that neither the strong nor the weak Kleene interpretation of quantifiers suﬃces, but that a novel interpretation may do so. (shrink)
This introduction to a special issue of Topoi introduces and summarises the relationship between three main varieties of 'enactivist' theorising about the mind: 'autopoietic', 'sensorimotor', and 'radical' enactivism. It includes a brief discussion of the philosophical and cognitive scientific precursors to enactivist theories, and the relationship of enactivism to other trends in embodied cognitive science and philosophy of mind.
This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends classical (...) logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)
Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.
This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but the (...) other does not.). (shrink)
A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections.
ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.
We present a specific elaboration and partial defense of the claims that cognition is enactive, embodied, embedded, affective and (potentially) extended. According to the view we will defend, the enactivist claim that perception and cognition essentially depend upon the cognizer’s interactions with their environment is fundamental. If a particular instance of this kind of dependence obtains, we will argue, then it follows that cognition is essentially embodied and embedded, that the underpinnings of cognition are inextricable from those of affect, that (...) the phenomenon of cognition itself is essentially bound up with affect, and that the possibility of cognitive extension depends upon the instantiation of a specific mode of skillful interrelation between cognizer and environment. Thus, if cognition is enactive then it is also embodied, embedded, affective and potentially extended. (shrink)
For some reason, participants hold agents more responsible for their actions when a situation is described concretely than when the situation is described abstractly. We present examples of this phenomenon, and survey some attempts to explain it. We divide these attempts into two classes: affective theories and cognitive theories. After criticizing both types of theories we advance our novel hypothesis: that people believe that whenever a norm is violated, someone is responsible for it. This belief, along with the familiar workings (...) of cognitive dissonance theory, is enough to not only explain all of the abstract/concrete paradoxes, but also explains seemingly unrelated effects, like the anthropomorphization of malfunctioning inanimate objects. (shrink)
Some of Dave Chappelle’s uses of storytelling about seemingly mundane events, like his experiences with his “white friend Chip” and the police, are examples of what W.E.B. Du Bois calls “Positive Propaganda.” This is in contrast to “Demagoguery,” the sort of propaganda described by Jason Stanley that obstructs empathic recognition of others, and undermines reasonable debate among citizens regarding policies that matter: the justice system, welfare, inequality, and race, for example. Some of Chappelle’s humor, especially in his most recent (...) Netflix specials, but also in his earlier standup performances and his series The Chappelle Show, is akin to art that appeals to emotion in the ways suggested by Du Bois in “Criteria of Negro Art” (1926). Beauty is essential to art, but, “I do not care a damn for any art that is not used for propaganda. But I do care when propaganda is confined to one side while the other is stripped and silent” (p. 22). The “one side” is that which appears to extoll American ideals, but in reality undermines them, perpetuating the subordinate status of “the other”--black citizens. Replace “beauty” with “humor” or “funny”, and we see striking parallels between Chappelle’s socio-political performances and Du Bois’ call for positive propaganda, each of which constitute “civic rhetoric” broadly construed. We no longer live in Du Bois’ America of explicit denial of rights. In many ways our situation is worse, as the mechanisms of exclusion are implicit, difficult to dislodge, because they are invisible. Chappelles’ humor draws attention to subtle undermining-propaganda in our liberal democracy, transforming it through his counter-propaganda into the spectacle that it should be; ubiquitous democracy-denying propaganda should be as obvious to whites as it is to minorities. In his words, we should all see that “that shit is fucking incredible” (Killin’ Them Softly). (shrink)
In this richly argued and provocative book, David Davies elaborates and defends a broad conceptual framework for thinking about the arts that reveals important continuities and discontinuities between traditional and modern art, and between different artistic disciplines. Elaborates and defends a broad conceptual framework for thinking about the arts. Offers a provocative view about the kinds of things that artworks are and how they are to be understood. Reveals important continuities and discontinuities between traditional and modern art. Highlights core topics (...) in aesthetics and art theory, including traditional theories about the nature of art, aesthetic appreciation, artistic intentions, performance, and artistic meaning. (shrink)
Social and linguistic perceptions are linked. On one hand, talker identity affects speech perception. On the other hand, speech itself provides information about a talker's identity. Here, we propose that the same probabilistic knowledge might underlie both socially conditioned linguistic inferences and linguistically conditioned social inferences. Our computational–level approach—the ideal adapter—starts from the idea that listeners use probabilistic knowledge of covariation between social, linguistic, and acoustic cues in order to infer the most likely explanation of the speech signals they hear. (...) As a first step toward understanding social inferences in this framework, we use a simple ideal observer model to show that it would be possible to infer aspects of a talker's identity using cue distributions based on actual speech production data. This suggests the possibility of a single formal framework for social and linguistic inferences and the interactions between them. (shrink)
The purpose of this essay is to shed some light on a certain type of sentence, which I call a borderline contradiction. A borderline contradiction is a sentence of the form F a ∧ ¬F a, for some vague predicate F and some borderline case a of F , or a sentence equivalent to such a sentence. For example, if Jackie is a borderline case of ‘rich’, then ‘Jackie is rich and Jackie isn’t rich’ is a borderline contradiction. Many theories (...) of vague language have entailments about borderline contradictions; correctly describing the behavior of borderline contradictions is one of the many tasks facing anyone offering a theory of vague language. Here, I first briefly review claims made by various theorists about these borderline contradictions, attempting to draw out some predictions about the behavior of ordinary speakers. Second, I present an experiment intended to gather relevant data about the behavior of ordinary speakers. Finally, I discuss the experimental results in light of several different theories of vagueness, to see what explanations are available. My conclusions are necessarily tentative; I do not attempt to use the present experiment to demonstrate that any single theory is incontrovertibly true. Rather, I try to sketch the auxiliary hypotheses that would need to be conjoined to several extant theories of vague language to predict the present result, and offer some considerations regarding the plausibility of these various hypotheses. In the end, I conclude that two of the theories I consider are better-positioned to account for the observed data than are the others. But the field of logically-informed research on people’s actual responses to vague predicates is young; surely as more data come in we will learn a great deal more about which (if any) of these theories best accounts for the behavior of ordinary speakers. (shrink)
Three leading philosopher-logicians present a clear and concise overview of formal theories of truth, explaining key logical techniques. Truth is as central topic in philosophy: formal theories study the connections between truth and logic, including the intriguing challenges presented by paradoxes like the Liar.
In this essay, I engage with the work of the mid-twentieth-century US suspense novelist Patricia Highsmith in order to open up the question of queerness as a historically locatable theory and practice of antinormativity in the post-identitarian, post-new-social-movement United States. I argue that Highsmith's Ripley novels offer a discomfitingly intimate counter-fantasy to the politically radical ambitions of both gay liberation and queer studies, one that reminds us of the constitutive power of commodification in the making of social fantasies of (...) gendered and sexual subversion in the United States in the second half of the twentieth century. In offering her readers scenes that become situations in their reliance on repetition in order to create and then alleviate tension, Highsmith's Ripley novels enact a relation of attachment indicative of the momentary and addictive pleasures of consumer capitalism. Through this formal signature, I argue, Highsmith's work offers us access to a different affective history of queerness in the United States, one that illuminates the power and appeal of norms and their constitutive presence in the production of queer subjects and worlds. (shrink)
This paper consider Prior's connective Tonk from a particular bilateralist perspective. I show that there is a natural perspective from which we can see Tonk and its ilk as perfectly well-defined pieces of vocabulary; there is no need for restrictions to bar things like Tonk.
The problem of structure and agency has been the subject of intense debate in the social sciences for over 100 years. This book offers a solution. Using a critical realist version of the theory of emergence, Dave Elder-Vass argues that, instead of ascribing causal significance to an abstract notion of social structure or a monolithic concept of society, we must recognise that it is specific groups of people that have social structural power. Some of these groups are entities with (...) emergent causal powers, distinct from those of human individuals. Yet these powers also depend on the contributions of human individuals, and this book examines the mechanisms through which interactions between human individuals generate the causal powers of some types of social structures. The Causal Power of Social Structures makes particularly important contributions to the theory of human agency and to our understanding of normative institutions. (shrink)
How do questions concerning consciousness and phenomenal experience relate to, or interface with, questions concerning plans, knowledge and intentions? At least in the case of visual experience the relation, we shall argue, is tight. Visual perceptual experience, we shall argue, is fixed by an agent’s direct unmediated knowledge concerning her poise (or apparent poise) over a currently enabled action space. An action space, in this specific sense, is to be understood not as a fine-grained matrix of possibilities for bodily movement, (...) but as a matrix of possibilities for pursuing and accomplishing one’s intentional actions, goals and projects. If this is correct, the links between planning, intention and perceptual experience are tight, while (contrary to some recent accounts invoking the notion of ‘sensorimotor expectations’) the links between embodied activity and perceptual experience, though real, are indirect. What matters is not bodily activity itself, but our practical knowledge (which need not be verbalized or in any way explicit) of our own possibilities for action. Such knowledge, selected, shaped and filtered by the grid of plans, goals, and intentions, plays, we argue, a constitutive role in explaining the content and character of visual perceptual experience. (shrink)
This paper discusses two distinct strategies that have been adopted to provide fine-grained propositions; that is, propositions individuated more finely than sets of possible worlds. One strategy takes propositions to have internal structure, while the other looks beyond possible worlds, and takes propositions to be sets of circumstances, where possible worlds do not exhaust the circumstances. The usual arguments for these positions turn on fineness-of-grain issues: just how finely should propositions be individuated? Here, I compare the two strategies with an (...) eye to the fineness-of-grain question, arguing that when a wide enough range of data is considered, we can see that a circumstance-based approach, properly spelled out, outperforms a structure-based approach in answering the question. (Part of this argument involves spelling out what I take to be a reasonable circumstance-based approach.) An argument to the contrary, due to Soames, is also considered. (shrink)
In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, (...) which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. (shrink)
I maintain that George Ripley (1802-1880) is among the most philosophically searching New England transcendentalists. In this essay I argue that Ripley’s denial that God’s miracles are the sole evidence of Christian truth clarifies the issues and debate that divide empiricists who seek evidence for truth through external verification and intuitionists who maintain that religious truth is manifest only within the minds, hearts, and special senses of true believers.
Substructural theories of truth are theories based on logics that do not include the full complement of usual structural rules. Existing substructural approaches fall into two main families: noncontractive approaches and nontransitive approaches. This paper provides a sketch of these families, and argues for two claims: first, that substructural theories are better-positioned than other theories to grapple with the truth-theoretic paradoxes, and second—more tentatively—that nontransitive approaches are in turn better-positioned than noncontractive approaches.
This paper presents and defends a way to add a transparent truth predicate to classical logic, such that and A are everywhere intersubstitutable, where all T-biconditionals hold, and where truth can be made compositional. A key feature of our framework, called STTT (for Strict-Tolerant Transparent Truth), is that it supports a non-transitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STTT allows for arise in paradoxical cases.
Supervaluational theories of vagueness have achieved considerable popularity in the past decades, as seen in eg , . This popularity is only natural; supervaluations let us retain much of the power and simplicity of classical logic, while avoiding the commitment to strict bivalence that strikes many as implausible. Like many nonclassical logics, the supervaluationist system SP has a natural dual, the subvaluationist system SB, explored in eg , .1 As is usual for such dual systems, the classical features of SP (...) (typically viewed as benefits) appear in SB in ‘mirror-image’ form, and the nonclassical features of SP (typically viewed as costs) also appear in SB in ‘mirror-image’ form. Given this circumstance, it can be difficult to decide which of two dual systems is better suited for an approach to vagueness.2 The present paper starts from a consideration of these two approaches— the supervaluational and the subvaluational—and argues that neither of them is well-positioned to give a sensible logic for vague language. §2 presents the systems SP and SB and argues against their usefulness. Even if we suppose that the general picture of vague language they are often taken to embody is accurate, we ought not arrive at systems like SP and SB. Instead, such a picture should lead us to truth-functional systems like strong Kleene logic (K3) or its dual LP. §3 presents these systems, and argues that supervaluationist and subvaluationist understandings of language are better captured there; in particular, that a dialetheic approach to vagueness based on the logic LP is a more sensible approach. §4 goes on to consider the phenomenon of higher-order vagueness within an LP-based approach, and §5 closes with a consideration of the sorites argument itself. (shrink)
Some theorists have developed formal approaches to truth that depend on counterexamples to the structural rules of contraction. Here, we study such approaches, with an eye to helping them respond to a certain kind of objection. We define a contractive relative of each noncontractive relation, for use in responding to the objection in question, and we explore one example: the contractive relative of multiplicative-additive affine logic with transparent truth, or MAALT. -/- .
This paper provides a defense of the full strength of classical logic, in a certain form, against those who would appeal to semantic paradox or vagueness in an argument for a weaker logic. I will not argue that these paradoxes are based on mistaken principles; the approach I recommend will extend a familiar formulation of classical logic by including a fully transparent truth predicate and fully tolerant vague predicates. It has been claimed that these principles are not compatible with classical (...) logic; I will argue, by both drawing on previous work and presenting new work in the same vein, that this is not so. We can combine classical logic with these intuitive principles, so long as we allow the result to be nontransitive. In the end, I hope the paper will help us to handle familiar paradoxes within classical logic; along the way, I hope to shed some light on what classical logic might be for. (shrink)
We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with classical logic.
At least since [Frege, 1960] and [Geach, 1965], there has been some consensus about the relation between negation, the speech act of denial, and the attitude of rejection: a denial, the consensus has had it, is the assertion of a negation, and a rejection is a belief in a negation. Recently, though, there have been notable deviations from this orthodox view. Rejectivists have maintained that negation is to be explained in terms of denial or rejection, rather than vice versa. Some (...) other theorists have maintained that negation is a separate phenomenon from denial, and that neither is to be explained in terms of the other. In this paper, I present and consider these heterodox theories of the relation between negation, denial, and rejection. (shrink)
The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole ST-based hierarchy, of which ST itself is only the first step, that seems to become more (...) and more classical at each level. I think this seeming is misleading: for certain purposes, anyhow, metainferential hierarchies give us no reason to move on from ST. ST is indeed only the first step on a grand metainferential adventure; but one step is enough. This paper aims to explain and defend that claim. Along the way, I take the opportunity also to develop some formal tools and results for thinking about metainferential logics more generally. (shrink)
Skepticism about the limits of online learning is as old as online learning itself. As with other technologically-driven innovations in pedagogy, there are deep-seated worries that important educational goods might be effaced or obscured by the ways of teaching and learning that online methods allow. One family of such worries is inspired by reflections on the bodily basis of an important kind of understanding, and skepticism over whether this bodily basis can be inculcated in the absence of actual, flesh-and-blood, classroom (...) interactions. This paper focuses on the ways in which such worries arise in the influential work of Hubert Dreyfus. The negative conclusion for which I argue is that endorsing Dreyfus's Merleau-Pontian picture of the relationship between bodily skill and understanding does not commit us to his general pessimism concerning online learning—bodily, emotional, and interactive dimensions might be essential to learning, but we lack reasons to think that online learning necessarily lacks these dimensions. The negative argument motivates a positive claim: rather than giving up on online learning we should focus on designing courses and pedagogies that scaffold the bodily, affective and interactive dynamics constitutive of understanding in a particular domain. (shrink)
This chapter attempts to give a brief overview of nonclassical (-logic) theories of truth. Due to space limitations, we follow a victory-through-sacrifice policy: sacrifice details in exchange for clarity of big-picture ideas. This policy results in our giving all-too-brief treatment to certain topics that have dominated discussion in the non-classical-logic area of truth studies. (This is particularly so of the ‘suitable conditoinal’ issue: §4.3.) Still, we present enough representative ideas that one may fruitfully turn from this essay to the more-detailed (...) cited works for further study. Throughout – again, due to space – we focus only on the most central motivation for standard non-classical-logic-based truth theories: namely, truth-theoretic paradox (specifically, due to space, the liar paradox). (shrink)
I consider the phenomenon of conflation—treating distinct things as one—and develop logical tools for modeling it. These tools involve a purely consequence-theoretic treatment, independent of any proof or model theory, as well as a four-valued valuational treatment.
Suppose Alice asserts p, and the Caterpillar wants to disagree. If the Caterpillar accepts classical logic, he has an easy way to indicate this disagreement: he can simply assert ¬p. Sometimes, though, things are not so easy. For example, suppose the Cheshire Cat is a paracompletist who thinks that p ∨ ¬p fails (in familiar (if possibly misleading) language, the Cheshire Cat thinks p is a gap). Then he surely disagrees with Alice's assertion of p, but should himself be unwilling (...) to assert ¬p. So he cannot simply use the classical solution. Dually, suppose the Mad Hatter is a dialetheist who thinks that p ∧ ¬p holds (that is, he thinks p is a glut). Then he may assert ¬p, but it should not be taken to indicate that he disagrees with Alice; he doesn't. So he too can't use the classical solution. The Cheshire Cat and the Mad Hatter, then, have a common problem, and philosophers with opinions like theirs have adopted a common solution to this problem: appeal to denial. Denial, these philosophers suppose, is a speech act like assertion, but it is not to be understood as in any way reducing to assertion. Importantly, denial is something different from the assertion of a negation; this is what allows it to work even in cases where assertion of negation does not. Just as importantly, denial must express disagreement, since this is the job it's being enlisted to do. (shrink)
This article conducts a dialogue and creates a new synthesis between two of the most influential ontological discourses in the field of sociology: assemblage theory and critical realism. The former proposes a focus on difference, fluidity, and process, the latter a focus on stability and structure. Drawing on and assessing the work of Deleuze, DeLanda, and Bhaskar, we argue that social ontology must overcome the tendency to bifurcate between these two poles and instead develop an ontology more suited to explaining (...) complex social phenomena by accommodating elements of both traditions. Going beyond DeLanda’s recent work, we argue that a concept of causal types must be used alongside a typology of structures to give us an ontology that can sustain sociology’s need for both formation stories and causation stories. We illustrate the necessity and value of our proposed synthesis by discussing MacKenzie’s recent empirical analysis of a high-frequency trading firm. (shrink)
This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.