67 research outputs found

    Relational Semantics for the Paraconsistent and Paracomplete 4-valued Logic PŁ4

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    The paraconsistent and paracomplete 4-valued logic PŁ4 is originally interpreted with a two-valued Belnap-Dunn semantics. In the present paper, PŁ4 is endowed with both a ternary Routley-Meyer semantics and a binary Routley semantics together with their respective restriction to the 2 set-up cases

    Truth from comparison

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    Prior and the “Logic of the Word of God”

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    Dispelling the Freudian Specter: A.N. Prior's Discussion of Religion in 1943

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    Letters between Mary and Arthur Prior in 1954: Topics on Metaphysics and Time

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    The Metaphysics of Time:Themes from Prior

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    Arthur Prior and Special Theory of Relativity: Two Standpoints from the Nachlass

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    Metasemantics and fuzzy mathematics

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    The present thesis is an inquiry into the metasemantics of natural languages, with a particular focus on the philosophical motivations for countenancing degreed formal frameworks for both psychosemantics and truth-conditional semantics. Chapter 1 sets out to offer a bird's eye view of our overall research project and the key questions that we set out to address. Chapter 2 provides a self-contained overview of the main empirical findings in the cognitive science of concepts and categorisation. This scientific background is offered in light of the fact that most variants of psychologically-informed semantics see our network of concepts as providing the raw materials on which lexical and sentential meanings supervene. Consequently, the metaphysical study of internalistically-construed meanings and the empirical study of our mental categories are overlapping research projects. Chapter 3 closely investigates a selection of species of conceptual semantics, together with reasons for adopting or disavowing them. We note that our ultimate aim is not to defend these perspectives on the study of meaning, but to argue that the project of making them formally precise naturally invites the adoption of degreed mathematical frameworks (e.g. probabilistic or fuzzy). In Chapter 4, we switch to the orthodox framework of truth-conditional semantics, and we present the limitations of a philosophical position that we call "classicism about vagueness". In the process, we come up with an empirical hypothesis for the psychological pull of the inductive soritical premiss and we make an original objection against the epistemicist position, based on computability theory. Chapter 5 makes a different case for the adoption of degreed semantic frameworks, based on their (quasi-)superior treatments of the paradoxes of vagueness. Hence, the adoption of tools that allow for graded membership are well-motivated under both semantic internalism and semantic externalism. At the end of this chapter, we defend an unexplored view of vagueness that we call "practical fuzzicism". Chapter 6, viz. the final chapter, is a metamathematical enquiry into both the fuzzy model-theoretic semantics and the fuzzy Davidsonian semantics for formal languages of type-free truth in which precise truth-predications can be expressed

    One-Variable Fragments of First-Order Many-Valued Logics

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    In this thesis we study one-variable fragments of first-order logics. Such a one-variable fragment consists of those first-order formulas that contain only unary predicates and a single variable. These fragments can be viewed from a modal perspective by replacing the universal and existential quantifier with a box and diamond modality, respectively, and the unary predicates with corresponding propositional variables. Under this correspondence, the one-variable fragment of first-order classical logic famously corresponds to the modal logic S5. This thesis explores some such correspondences between first-order and modal logics. Firstly, we study first-order intuitionistic logics based on linear intuitionistic Kripke frames. We show that their one-variable fragments correspond to particular modal Gödel logics, defined over many-valued S5-Kripke frames. For a large class of these logics, we prove the validity problem to be decidable, even co-NP-complete. Secondly, we investigate the one-variable fragment of first-order Abelian logic, i.e., the first-order logic based on the ordered additive group of the reals. We provide two completeness results with respect to Hilbert-style axiomatizations: one for the one-variable fragment, and one for the one-variable fragment that does not contain any lattice connectives. Both these fragments are proved to be decidable. Finally, we launch a much broader algebraic investigation into one-variable fragments. We turn to the setting of first-order substructural logics (with the rule of exchange). Inspired by work on, among others, monadic Boolean algebras and monadic Heyting algebras, we define monadic commutative pointed residuated lattices as a first (algebraic) investigation into one-variable fragments of this large class of first-order logics. We prove a number of properties for these newly defined algebras, including a characterization in terms of relatively complete subalgebras as well as a characterization of their congruences

    The theory and pedagody of semantic inconsistency in critical reasoning

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    One aspect of critical reasoning is the analysis and appraisal of claims and arguments. A typical problem, when analysing and appraising arguments, is inconsistent statements. Although several inconsistencies may have deleterious effects on rationality and action, not all of them do. As educators, we also have an obligation to teach this evaluation in a way that does justice to our normal reasoning practices and judgements of inconsistency. Thus, there is a need to determine the acceptable inconsistencies from those that are not, and to impart that information to students. We might ask: What is the best concept of inconsistency for critical reasoning and pedagogy? While the answer might appear obvious to some, the history of philosophy shows that there are many concepts of “inconsistency”, the most common of which comes from classical logic and its reliance on opposing truth-values. The current exemplar of this is the standard truth functional account from propositional logic. Initially, this conception is shown to be problematic, practically, conceptually and pedagogically speaking. Especially challenging from the classical perspective are the concepts of ex contradictione quodlibet and ex falso quodlibet. The concepts may poison the well against any notion of inconsistency, which is not something that should be done unreflectively. Ultimately, the classical account of inconsistency is rejected. In its place, a semantic conception of inconsistency is argued for and demonstrated to handle natural reasoning cases effectively. This novel conception utilises the conceptual antonym theory to explain semantic contrast and gradation, even in the absence of non-canonical antonym pairs. The semantic conception of inconsistency also fits with an interrogative argument model that exploits inconsistency to display semantic contrast in reasons and conclusions. A method for determining substantive inconsistencies follows from this argument model in a 4 straightforward manner. The conceptual fit is then incorporated into the pedagogy of critical reasoning, resulting in a natural approach to reasoning which students can apply to practical matters of everyday life, which include inconsistency. Thus, the best conception of inconsistency for critical reasoning and its pedagogy is the semantic, not the classical.Philosophy Practical and Systematic TheologyD. Phi
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