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James Trafford
University For The Creative Arts
  1. Co-Constructive Logic for Proofs and Refutations.James Trafford - 2014 - Studia Humana 3 (4):22-40.
    This paper considers logics which are formally dual to intuitionistic logic in order to investigate a co-constructive logic for proofs and refutations. 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 (...)
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  2. Inference and Rational Commitment.James Trafford - 2013 - Prolegomena 12 (1):5-20.
    This peer-reviewed paper intervenes in debates relating to overarching themes that impact upon mass media studies, communication theory and theories of cognition more generally. In particular, the paper discusses issues involving how our ordinary psychological thinking relates to norms of rationality (and how these latter are conceived). In essence, I argue against a dominant approach taken by Christopher Peacocke, that rationality can be grounded in the possession of certain concepts. The article makes a new contribution to the field by arguing (...)
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  3. Compositionality and Modest Inferentialism.James Trafford - 2014 - Teorema: International Journal of Philosophy (1):39-56.
    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 (...)
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    Expanding the Universe of Universal Logic.James Trafford - 2014 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 29 (3):325-343.
    In [5], Béziau provides a means by which Gentzen’s sequent calculus can be combined with the general semantic theory of bivaluations. In doing 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. (...)
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    Is ‘No’ a Force-Indicator? Yes, Sooner or Later!Fabien Schang & James Trafford - 2017 - Logica Universalis 11 (2):225-251.
    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.
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