James Trafford

Robert Brandom famously attempts to provide an account of norms that are grounded in intersubjective practices, so dealing with problems raised by Wittgenstein’s regress arguments. This relies upon providing an explanation of the correctness of those practices in terms of our dispositions to treat each other’s practices as correct or incorrect. The view faces a number of hurdles, however, particularly when it comes to providing a non-circular account of the norms of practice, from within those practices themselves. This essay argues that Brandom’s attempt to ground norms in intersubjective practices is circular, and requires communal stability. I go on to suggest that, by taking practices of interaction as foundational, we can ground norms in action coordination. Norms, on this view, become sedimented through our interactions, and explicit normative talk is required to keep our interactions coherent with each other.

It is well known that classical inferentialist semantics runs into problems regarding abnormal valuations (Carnap in Formalization of logic. Harvard University Press, Cambridge, 1943; Hjortland in Notre Dame J Formal Logic 55(4):445–467, 2014; Peregrin in J Philos Logic 39(3):255–274, 2010). It is equally well known that the issues can be resolved if we construct the inference relation in a multiple-conclusion sequent calculus. The latter has been prominently developed in recent work by Restall (Logic, methodology and philosophy of science: proceedings of the twelfth international congress. Kings College Publications, pp 189–205, 2005), with the guiding interpretation that the valid sequent says that the simultaneous assertion of all of Γ with the denial of all of Δ is incoherent. However, such structures face significant interpretive challenges (Rumfitt in Grazer Philos Stud 77(1):61–84, 2008; Steinberger in J Philos Logic 40(3):333–355, 2011; Tennant in The taming of the true. Oxford University Press, Oxford, 1997), and they do not provide an adequate grasp on the machinery of the duality of assertions and denials that could (a) provide an abstract account of inferential semantics; (b) show why the dual treatment is semantically superior. This paper explores a slightly different tack by considering a dual-calculus framework consisting of two, single-conclusion, inference relations dealing with the preservation of assertion and the preservation of denial, respectively. In this context, I develop an abstract inferentialist semantics, before going on to show that the framework is equivalent to Restall’s, whilst providing a better grasp on the underlying proof-structure.

This chapter returns to some of the foundational issues discussed in the introduction and first chapter, particularly regarding the justification of logical rules. In Chaps. 1 and 2, I argued that standard inferentialist accounts do not suffice to provide justification of basic logical rules. In response, an analysis of logical inference as acts taking place in dialogical situations is provided, by taking interactions to be structured around moves that may be defined as coherent under certain circumstances. This is used to underpin a novel account of the proof-theoretic notion of harmony as a way of balancing moves. I show that this leads to a constructive logic over both proofs and refutations, where logical rules are justfied internally, at the termination of dialogue. This means that, rather than start with logical rules a priori, the rules themselves are derivative of dialogical balance, so we can reconstruct certain logical rules subsequent to interaction. I finish by discussing the relationships between the formal structure presented here, and related structures.

In this chapter, I first consider mode standard constructive semantic approaches to the formal propositional logics for proofs and refutations. Whilst these illuminate aspects of the structure of interactive logic, they also highlight the shortcomings of standard semantics, even in dualised form. Nonetheless, the way in which these structures “objectify” propositions is useful for considering propositions as stable objects subsequent to their construction in interaction. These ideas are made more precise through the notion of bisimulation equivalence, and closure under bisimulation. To finish, I provide a number of examples, using these to highlight a slightly more liberal conception of the coherence of interactions.

In this chapter, I shed light on the issues raised in the above chapter by providing an overview of the concepts of proof and assertion, both of which are central to inferentialist approaches to semantics. In so doing, I shall argue that, in contrast to the prescriptive and monological approach to logic that underlies the problems discussed in the previous chapter, we should think of both proof and assertion in a much more liberal way. In brief, the suggestion is that, to take seriously the dictum that “meaning is determined by use” requires us to provide an account of the processes of our proving activities, which take place in the context of assertion games.

A perennial question in consideration of logic concerns where the rules of logic come from? This question is overflowing with sub-questions regarding, for example, what is meant by the rules of logic; whether or not we are concerned with the justification of rules, or the meaningfulness of certain rules, or both (these are often run together); how do we understand the relationship between logical rules and truth; what is the normative role of logical rules? In this chapter, I provide a brief overview of inferentialism in Sect. 2, before going on to identify a number of concerns frequently made against it.

In this chapter, I provide an overview and argument to the effect that reasoning, including scientific and mathematical inquiry, is inherently both dialogical and dynamic. That is to say, reasoning is social and interactive, and requires an account of history that is not captured by an absolutist and monological account of proofs. I begin by considering the role of dialogue in logic, beginning first with a short analysis of Brandom’s account of dialogue, before discussing the history of logic, and recent approaches to logical games in the work of Jaako Hintikka and Lorenzen. There, I argue that a distinct approach is required where assertion and denial, dialogical response and testing, are central to the dynamics of reasoning and the creation of new knowledge. It is in this light that I go on to discuss the specific role of dialogue in mathematical proofs, with particular attention to the work of Imre Lakatos. Lakatos’ [1] approach to inquiry is understood to operate as a kind of dialogue between “prover” and “refuter”, where a conjecture is considered by means of proof attempts and tests in the form of refutation attempts, disproofs and counter-examples. Such “proofs that do not prove” are part and parcel with the development of inquiry, until a conclusive proof or refutation of the conjecture is reached. I go on to provide a discussion of the broader approach to dialogues, with particular reference to the interactional work of Ginzburg (e.g. [2]). I will discuss a number of constraints over dialogues taking interaction, rather than rules, to be a priori, such that co-operative interactions may be understood to form the basis of the kinds of approaches to inquiry previously discussed. I will also briefly turn to considering how this approach fares in relation to providing a way of accounting for “reasons”, which does not fall into the trap of important criticisms in feminist and post-colonialist theory. I show that the dialogical approach being advocated here is capable of providing a way of moving beyond such criticisms, with particular attention to the role of emotion in interactive reasoning processes as allowing responses to be “framed” adequately. I finish by drawing together the discussion, arguing that interactions may subsequently give rise to propositional meaning under constraints of coherence, convergence, and symmetry.

This chapter suggests that the approach suggested to this point provides a novel approach to understanding logical paradoxes. In particular, I argue that what is typically thought to be captured by paraconsistency and paracompleteness is best understood as a form of epistemological instability that can be dealt with in the context of the dialogical dynamics of reasoning. This is used to motivate an approach called paracoherence, which can deal with strengthened versions of paradox, and is compatible with a bivalent approach to local truth and falsity. This will be clarified by first considering logic and paradox in relation to standard arguments regarding logical revision. Arguments for and against logical revisionism share assumptions regarding logical rules that have been argued against in previous chapters. As such, I suggest that the interactive approach provides not a revision of logic, but an attempt to rethink logic from the ground up.

This peer-reviewed essay is an intervention into the emerging field of 'Speculative Realism', which has links to the field of Speculative Aesthetics. The work is essentially an attempt to develop a theory of perception that is not at odds with the scientific worldview. In this respect, the dominant views of aesthetic perception are critiqued in favour of neurophilosophical views stemming from Thomas Metzinger. In order to position myself, I go on to analyse the fiction of Thomas Ligotti to develop the idea of a non-human-centric phenomenal experience. This work operates within several philosophical contexts: one is the debate between phenomenology and scientific realism, of which the developing field of Speculative Realism is a part, and upon which the journal Collapse has been incredibly influential; a further context is that of transcendental materialism; another is that of the relationship between literature and philosophy. The article marks a departure within these fields by suggesting that recent developments in cognitive science can be understood not through a naïve scientism or a kind of brute materialism, but only through understanding the transcendental ramifications to the phenomenal experience of the human.

This paper tackles foundational issues regarding the justification of logical rules. It is argued that standard accounts from both proof-theoretical and semantical points of view do not su ffi ce to account for the justification of basic logical rules. By way of response, an analysis of logical inference as acts taking place in dialogical situations is provided. In turn, this makes way for an internal justification of logical rules at the termination of dialogue, that can be formalized in terms of co-constructive logic for proof and refutation [author reference omitted].

This article considers neoliberalism through the “peaceful violence” of its social spaces that are stratified and ordered around raciality whilst abjuring the explicit presence of racialised power. Many dominant analyses of neoliberalism in the social science have figured racial injustices as ideological fossils to be swept away by a fundamentally neutral political economy that has shaped all human activity according to market principles. As such, racial injustices are understood as material deviations from conditions of economic power on the one hand, and cultural deviations in hegemonic common sense on the other. Against the grain of these approaches, I argue that racialised power is better understood as a productive technology fundamental to the structuring of our worlds, their neoliberal organisation just one iteration of ongoing coloniality. Contrary to popular analysis and this account of neoliberalism, contemporary racialised violence and nationalist discourse are, therefore, not only consistent with the power of neoliberal classes but also result from weaknesses in their hegemonic power.

This article considers neoliberalism through the “peaceful violence” of its social spaces that are stratified and ordered around raciality whilst abjuring the explicit presence of racialised power. Many dominant analyses of neoliberalism in the social science have figured racial injustices as ideological fossils to be swept away by a fundamentally neutral political economy that has shaped all human activity according to market principles. As such, racial injustices are understood as material deviations from conditions of economic power on the one hand, and cultural deviations in hegemonic common sense on the other. Against the grain of these approaches, I argue that racialised power is better understood as a productive technology fundamental to the structuring of our worlds, their neoliberal organisation just one iteration of ongoing coloniality. Contrary to popular analysis and this account of neoliberalism, contemporary racialised violence and nationalist discourse are, therefore, not only consistent with the power of neoliberal classes but also result from weaknesses in their hegemonic power.

One of the central issues facing contemporary political theory is the problem of difference. This problem is perhaps clearest in disagreements regarding the role of pluralism between advocates of deliberative, and agonistic, approaches to democracy. According to agonists, deliberative democracy has only paid lip-service to pluralism, emphasising agreement, consensus, and universalism. Instead, agonists argue that we should accommodate incommensurable difference as central to political organisation. But this shift threatens to emphasise particularity at the expense of commonality, so preventing the transformation of social positions. These debates turn largely around the ways in which power is conceived in relation to democratic interaction, with deliberativists emphasising ideals of free and equal discourse, and agonists, the irreducible role of power. I begin by outlining a structural approach to social power, to show how we are all structurally implicated in power relationships. I go on to show how emphasising structural implication shifts us beyond debates that revolve around difference, drawing attention to the more foundational problem of how agents may come to understand these structures and each other, in ways that surpass or transcend the specific constraints acting upon them. Considering this, I develop a complex account of structural implication that emphasises the relationships between social norms, reasoning, and objective power relationships. This approach illuminates lacunae in similar approaches, particularly regarding the way in which structural power disenables us from often seeing structural imbalances of power, and clarifies the ways in which collective political transformation is possible.

In, Béziau provides a means by which Gentzen’s sequent calculus can be combined with the general semantic theory of bivaluations. In do- ing so, according to Béziau, it is possible to construe the abstract “core” of logics in general, where logical syntax and semantics are “two sides of the same coin”. The central suggestion there is that, by way of a modification of the notion of maximal consistency, it is possible to prove the soundness and completeness for any normal logic. However, the reduction to bivaluation may be a side e ff ect of the architecture of ordinary sequents, which is both overly restrictive, and entails certain expressive restrictions over the language. This paper provides an expansion of Béziau’s completeness results for logics, by showing that there is a natural extension of that line of thinking to n -sided sequent constructions. Through analogical techniques to Béziau’s construction, it is possible, in this setting, to construct abstract soundness and completeness results for n -valued logics.

There are several issues with the standard approach to the relationship between conditionals and assertions, particularly when the antecedent of a conditional is false. One prominent alternative is to say that conditionals do not express propositions, but rather make conditional assertions that may generate categorical assertions of the consequent in certain circumstances. However, this view has consequences that jar with standard interpretations of the relationship between proofs and assertion. Here, I analyse this relationship, and say that, on at least one understanding of proof, conditional assertions may reflect the dynamics of proving, which generate categorical assertions. In particular, when we think about the relationship between assertion and proof as rooted in a dialogical approach to both, the distinction between conditional and categorical assertions is quite natural.

This book argues for a view in which processes of dialogue and interaction are taken to be foundational to reasoning, logic, and meaning. This is both a continuation, and a substantial modification, of an inferentialist approach to logic. As such, the book not only provides a critical introduction to the inferentialist view, but it also provides an argument that this shift in perspective has deep and foundational consequences for how we understand the nature of logic and its relationship with meaning and reasoning. This has been upheld by several technical results, including, for example a novel approach to logical paradox and logical revision, and an account of the internal justification of logical rules. The book shows that inferentialism is greatly strengthened, such that it can answer the most stringent criticisms of the view. This leads to a view of logic that emphasizes the dynamics of reasoning, provides a novel account of the justification and normativity of logical rules, thus leading to a new, attractive approach to the foundations of logic. The book addresses readers interested in philosophy of language, philosophical and mathematical logic, theories of reasoning, and also those who actively engage in current debates involving, for example, logical revision, and the relationship between logic and reasoning, from advanced undergraduates, to professional philosophers, mathematicians, and linguists.

This paper discusses the philosophical and logical motivations for rejectivism, primarily by considering a dialogical approach to logic, which is formalized in a Question–Answer Semantics. We develop a generalized account of rejectivism through close consideration of Mark Textor's arguments against rejectivism that the negative expression ‘No’ is never used as an act of rejection and is equivalent with a negative sentence. In doing so, we also shed light upon well-known issues regarding the supposed non-embeddability and non-iterability of force indicators.

Phenomenal Concepts and Phenomenal Knowledge is an edited volume of new essays relating to the debates around phenomenal experience in philosophy of mind. Alter and Walter provide an excellent introduction to the volume, producing a well edited collection of papers that represent some of the most interesting and cutting edge work in the field, and together provide a subtle and complex overview of the contemporary theoretical landscape. In addition, as many of the papers refer to others within the volume, they provide an excellent opportunity for in depth and complex debate between some of the leading theorists at work today. This review concentrates on ways in which papers in the volume further debates around the construal of phenomenal consciousness as physical or non-physical, and also on new responses to the infamous knowledge argument

This paper provides both a solution and a problem for the account of compositionality in Christopher Peacocke’s modest inferentialism. The immediate issue facing Peacocke’s account is that it looks as if compositionality can only be understood at the level of semantics, which is difficult to reconcile with inferentialism. Here, following up a brief suggestion by Peacocke, I provide a formal framework wherein compositionality occurs the level of the determining relation between inference and semantics. This, in turn provides a “test” for compositionality, which, problematically, Peacocke’s natural deduction framework for classical logic can not meet. To finish, I briefly outline an alternative, bilateralist, framework for modest inferentialism, for which compositionality holds.

This peer-reviewed essay is an intervention into the emerging field of 'Speculative Realism', which has links to the field of Speculative Aesthetics. The work is essentially an attempt to develop a theory of perception (and more broadly consciousness) that is not at odds with the scientific worldview. In this respect, the dominant views of aesthetic perception (Kantian / neo-Kantian phenomenology) are critiqued in favour of neurophilosophical views stemming from Thomas Metzinger. In order to position myself, I go on to analyse the fiction of Thomas Ligotti to develop the idea of a non-human-centric phenomenal experience. This work operates within several philosophical contexts: one is the debate between phenomenology and scientific realism, of which the developing field of Speculative Realism is a part, and upon which the journal Collapse has been incredibly influential; a further context is that of transcendental materialism; another is that of the relationship between literature and philosophy. The article marks a departure within these fields by suggesting that recent developments in cognitive science can be understood not through a naïve scientism or a kind of brute materialism, but only through understanding the transcendental ramifications to the phenomenal experience of the human