Paradox and Paraconsistency: Conflict Resolution in the Abstract SciencesIn a world plagued by disagreement and conflict one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact these disciplines are rife with internal divisions between different, often incompatible, systems. Do these disagreements admit of resolution? Can such resolution be achieved without disturbing assumptions that the theorems of logic and mathematics state objective truths about the real world? In this original and historically rich book John Woods explores apparently intractable disagreements in logic and the foundations of mathematics and sets out conflict resolution strategies that evade or disarm these stalemates. An important sub-theme of the book is the extent to which pluralism in logic and the philosophy of mathematics undermines realist assumptions. This book makes an important contribution to such areas of philosophy as logic, philosophy of language and argumentation theory. It will also be of interest to mathematicians and computer scientists. |
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Paradox and Paraconsistency: Conflict Resolution in the Abstract Sciences John Woods No preview available - 2002 |
Common terms and phrases
abstract sciences ad hominem analysis analytic intuitions Anderson and Belnap argument assert axioms belief Chapter classical logic cognitive dissonance Cohen committed concede concept of set conceptual truths conflict resolution consequence consistent contradiction counterexample counterintuitive deductive derived diagonal dialectical dialethic dialethist disagreement Disjunctive Syllogism disquotational Dixon empirical English entailment epistemology ex falso ex falso quodlibet fact fallacy false fiction Frege Frege's Sorrow Holmes hominem idea ideal model implication inconsistency inference intuitive concept laws Liar Paradox linguistic intuitions logicians mathematics matter methodology modal modal logic naive set theory natural language negation normative objects paraconsistent logic paraconsistentist parties philosophical possible predicate premises principles problem proof proposition Quine Quine's rational realist stance reasoning reductio refers reflective equilibrium refutation relevant logic relevantist rule Russell paradox Russell's say-so semantics sense sentence set theory statement stipulation strategy Suppose synonymy Tarski theoretical theorist theory's things tion true valid