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Basic laws of arithmetic

In Basic Laws of Arithmetic. Oxford, U.K.: Oxford University Press (1893)

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  1. Frege’s Theory of Real Numbers: A Consistent Rendering.Francesca Boccuni & Marco Panza - forthcoming - Review of Symbolic Logic:1-44.
    Frege's definition of the real numbers, as envisaged in the second volume of Grundgesetze der Arithmetik, is fatally flawed by the inconsistency of Frege's ill-fated Basic Law V. We restate Frege's definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege's own indications is possible at all.
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  • Notational Differences.Francesco Bellucci & Ahti-Veikko Pietarinen - 2020 - Acta Analytica 35 (2):289-314.
    Expressively equivalent logical languages can enunciate logical notions in notationally diversified ways. Frege’s Begriffsschrift, Peirce’s Existential Graphs, and the notations presented by Wittgenstein in the Tractatus all express the sentential fragment of classical logic, each in its own way. In what sense do expressively equivalent notations differ? According to recent interpretations, Begriffsschrift and Existential Graphs differ from other logical notations because they are capable of “multiple readings.” We refute this interpretation by showing that there are at least three different kinds (...)
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  • Identity and intensionality in Univalent Foundations and philosophy.Staffan Angere - 2017 - Synthese 198 (Suppl 5):1-41.
    The Univalent Foundations project constitutes what is arguably the most serious challenge to set-theoretic foundations of mathematics since intuitionism. Like intuitionism, it differs both in its philosophical motivations and its mathematical-logical apparatus. In this paper we will focus on one such difference: Univalent Foundations’ reliance on an intensional rather than extensional logic, through its use of intensional Martin-Löf type theory. To this, UF adds what may be regarded as certain extensionality principles, although it is not immediately clear how these principles (...)
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  • Rastrgan između obrisa logike.Abbas Ahsan & Marzuqa Karima - 2022 - European Journal of Analytic Philosophy 18 (2):10-41.
    Zapadna suvremena logika korištena je za unapređenje islamske filozofske teologije, koja je povijesno koristila aristotelovsko-avicenovsku logiku, na temelju toga što se logika shvaćala kao inherentno normativna. To je usprkos kontroverzama o statusu logike u islamskoj teološkoj tradiciji. Normativni autoritet logike znači da ona utječe na sadržaj onoga u što bismo trebali vjerovati i na to kako bismo trebali revidirati ta uvjerenja. Ovaj rad nastoji pokazati da je, bez obzira na nekompatibilne razlike između dvaju sustava, temeljna značajka zapadne suvremene logike i (...)
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