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Impredicativity and Paradox

Gabriel Uzquiano

Thought: A Journal of Philosophy 8 (3):209-221 (2019)

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Operands and Instances.Peter Fritz - 2023 - Review of Symbolic Logic 16 (1):188-209.details Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but (...) Download Export citation Bookmark 2 citations
19th Brazilian Logic Conference: Book of Abstracts.Cezar A. Mortari & Ricardo Silvestre (eds.) - 2019 - João Pessoa, PB, Brasil: EDUFCG.details This is the book of abstracts of the 19th Brazilian Logic Conferences. The Brazilian Logic Conferences (EBL) is one of the most traditional logic conferences in South America. Organized by the Brazilian Logic Society (SBL), its main goal is to promote the dissemination of research in logic in a broad sense. It has been occurring since 1979, congregating logicians of different fields — mostly philosophy, mathematics and computer science — and with different backgrounds — from undergraduate students to senior researchers. (...) Download Export citation Bookmark
The Many and the One: A Philosophical Study of Plural Logic.Salvatore Florio & Øystein Linnebo - 2021 - Oxford, England: Oxford University Press.details Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) Download Export citation Bookmark 16 citations
Russell’s Paradox and Free Zig Zag Solutions.Ludovica Conti - 2020 - Foundations of Science 28 (1):185-203.details I present the traditional debate about the so called explanation of Russell’s paradox and propose a new way to solve the contradiction that arises in Frege’s system. I briefly examine two alternative explanatory proposals—the Predicativist explanation and the Cantorian one—presupposed by almost all the proposed solutions of Russell’s Paradox. From the discussion about these proposals a controversial conclusion emerges. Then, I examine some particular zig zag solutions and I propose a third explanation, presupposed by them, in which I emphasise the (...) Download Export citation Bookmark
Ground and Grain.Peter Fritz - 2021 - Philosophy and Phenomenological Research 105 (2):299-330.details Current views of metaphysical ground suggest that a true conjunction is immediately grounded in its conjuncts, and only its conjuncts. Similar principles are suggested for disjunction and universal quantification. Here, it is shown that these principles are jointly inconsistent: They require that there is a distinct truth for any plurality of truths. By a variant of Cantor’s Theorem, such a fine-grained individuation of truths is inconsistent. This shows that the notion of grounding is either not in good standing, or that (...) Download Export citation Bookmark 12 citations

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