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  1. The Power of Predication and Quantification.Edward N. Zalta -2025 -Open Philosophy 8 (1):1-16.
    In this article, I show how two modes of predication and quantification in a modal context allow one to (a) define what it is for an individual or relation to exist, (b) define identity conditions for properties and relations conceived hyperintensionally, (c) define identity conditions for individuals and prove the necessity of identity for both individuals and relations, (d) derive the central definition of free logic as a theorem, (e) define the essential properties of abstract objects and provide a framework (...) for defining the essential properties of ordinary objects, and (f) derive a theory of truth. I also describe my indebtedness to the work of Terence Parsons and take the opportunity to advance the discussion in connection with an objection raised to the theory of essential properties. (shrink)
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  • On Jan Łukasiewicz's ‘The Principle of Contradiction and Symbolic Logic’.Adam Trybus &Bernard Linsky -2020 -History and Philosophy of Logic 41 (2):183-190.
    This is a companion article to the translation of ‘Zasada sprzeczności a logika symboliczna’, the appendix on symbolic logic of Jan Łukasiewicz's 1910 book O zasadzie sprzeczności u Arytotelesa (On the Principle of Contradiction in Aristotle). While the appendix closely follows Couturat's 1905 book L'algebra de la logique (The Algebra of Logic), footnotes show that Łukasiewicz was aware of the work of Peirce, Huntington and Russell (before Principia Mathematica). This appendix was influential in the development of the Polish school of (...) logic, directly inspiring Stanisław Leśniewski and Leon Chwistek and more widely by serving as a text of the new symbolic logic. This appendix was an important source of the dominant algebraic logic in Poland, but also indicates that Łukasiewicz appreciated Russell's axiomatic approach to logic. (shrink)
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