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Zalta's intensional logic

C. Anthony Anderson

Philosophical Studies 69 (2-3):221 - 229 (1993)

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On the Methodological Restriction of the Principle of Characterization.Maciej Sendłak - 2020 - Erkenntnis 87 (2):807-825.details The subject of this article is the Principle of Characterization—the most controversial principle of Alexius Meinong’s Theory of Objects. The aim of this text is twofold. First of all, to show that Bertrand Russell’s well-known objection to the Principle of Characterization can be reformulated against contemporary unrestricted interpretations of it. Second, to propose an alternative formulation of this principle. This refers to the methodology of metaphysics and is based on the distinction between pre-theoretical and theoretical languages. The proposed formulation fits (...) Download Export citation Bookmark 2 citations
Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege"s Grundgesetze in Object Theory.Edward N. Zalta - 1999 - Journal of Philosophical Logic 28 (6):619-660.details In this paper, the author derives the Dedekind-Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege's Grundgesetze. The proofs of the theorems reconstruct Frege's derivations, with the exception of the claim that every number has a successor, which is derived from a modal axiom that (...) Download Export citation Bookmark 30 citations
Relations vs functions at the foundations of logic: type-theoretic considerations.Paul Oppenheimer & Edward N. Zalta - 2011 - Journal of Logic and Computation 21:351-374.details Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell's reduction of functions to relations over Frege's reduction of relations to functions. There is an interesting (...) Download Export citation Bookmark 9 citations

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