Re-engineering commonsense

How is it possible to begin crafting counter-hegemonic knowledge that fosters changed consciousness when agents find themselves to be embedded in, and to further embed, forms of power that disenable them from exactly that? Neither discursive explicitation and reasoning, nor understanding commonsense as an unanalyzable set of practices, would seem to do the job. So, what sort of capacities would be required to craft counter-hegemonic strategies

Conditionals in interaction

There are several issues with the standard approach to the relationship between conditionals and assertions, particularly when the antecedent of a conditional is (or may be) 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 (sometimes) 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

Structuring co-constructive logic for proofs and refutations

This paper considers a topos-theoretic structure for the interpretation of co-constructive logic for proofs and refutations following. It is notoriously tricky to define a proof-theoretic semantics for logics that adequately represent constructivity over proofs and refutations. By developing abstractions of elementary topoi, we consider an elementary topos as structure for proofs, and complement topos as structure for refutation. In doing so, it is possible to consider a dialogue structure between these topoi, and also control their relation such that classical logic (interpreted in a Boolean topos) is simulated where proofs and refutations are conclusive

Co-constructive logics for proofs and refutations

This paper considers logics which are formally dual to intuition- istic logic in order to investigate a co-constructive logic for proofs and refu- tations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and its relation to falsity. It is well known both that intuitionism can not deal constructively with negative information, and that defining falsity by means of intuitionistic negation leads, under widely- held assumptions, to a justification of bivalence. For example, we do not want to equate falsity with the non-existence of a proof since this would render a statement such as “pi is transcendental” false prior to 1882. In addition, the intuitionist account of negation as shorthand for the derivation of absurdity is inadequate, particularly outside of purely mathematical contexts. To deal with these issues, I investigate the dual of intuitionistic logic, co-intuitionistic logic, as a logic of refutation, alongside intuitionistic logic of proofs. Direct proof and refutation are dual to each other, and are constructive, whilst there also exist syntactic, weak, negations within both logics. In this respect, the logic of refutation is weakly paraconsistent in the sense that it allows for state- ments for which, neither they, nor their negation, are refuted. I provide a proof theory for the co-constructive logic, a formal dualizing map between the logics, and a Kripke-style semantics. This is given an intuitive philosophical rendering in a re-interpretation of Kolmogorov’s logic of problems

Reconstructing intersubjective norms

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

An inferentialist approach to paraconsistency

This paper develops and motivates a paraconsistent approach to semantic paradox from within a modest inferentialist framework. I begin from the bilateralist theory developed by Greg Restall, which uses constraints on assertions and denials to motivate a multiple-conclusion sequent calculus for classical logic, and, via which, classical semantics can be determined. I then use the addition of a transparent truth-predicate to motivate an intermediate speech-act. On this approach, a liar-like sentence should be "weakly asserted", involving a commitment to the sentence and its negation, without rejecting the sentence. From this, I develop a proof-theory, which both determines a typical paraconsistent model theory, and also gives us a nice way to understand classical recapture

Duality and inferential semantics

It is well known that classical inferentialist semantics runs into problems regarding abnormal valuations [3, 6, 10]. 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 Greg Restall [13], with the guiding interpretation that the valid sequent Γ \vdash ∆ says that the simultaneous assertion of all of Γ with the denial of all of ∆ is incoherent. However, such structures face significant interpretive challenges [14, 19, 20], 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

Things are not what they seem: the transcendentalism of appearances in the refutation of reductive naturalism

This peer-reviewed paper investigates the dominant underlying approach to aesthetic experience and conscious experience more generally – that is, a neo-Kantian phenomenological approach. In essence, I argue that such approaches are based on a petitio principii in relation to what I call the 'principle of appearing qua appearing' – a principle that, I suggest, underlies the dominant approach to aesthetic perception. So, the ramifications of this argument are that we ought to question the dominance of the phenomenological approach to experience, and reassess our concepts of the aesthetic mode of perception in this light. The paper makes a specific contribution to knowledge in this field in that it identifies a weakness in the dominant arguments relevant to our understanding of conscious experience, and clears the path for views of conscious experience that emerge in cognitive science. The paper has been delivered at a number of major conferences, and is used as a course text at the American University of Berlin

An interactive approach to proof-theoretic semantics

In truth-functional semantics for propositional logics, categoricity and compositionality are unproblematic. This is not the case for proof-theoretic semantics, where failures of both occur for the semantics determined by monological entailment structures for classical and intuitionistic logic. This is problematic for inferentialists, where the meaning of logical constants is supposed to be determined by their rules. Recent attempts to overcome these issues have primarily considered symmetric entailment structures, but these are tricky to interpret. Here, I instead consider an entailment structure that combines provability with the dual notion of disproof (or refutation). This is interpreted as a dialogue structure between the roles of prover and denier, where an assertion of a statement involves a commitment to its defence, and a denial of the statement involves a commitment to its challenge. The interaction between the two is constitutive of a proof-theoretic semantics capable of dealing with the above issues

Expanding the Universe of Universal Logic

In (Béziau 2001), 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 (without invoking the role of classical negation in the completeness proof). However, the reduction to bivaluation may be a side effect 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