A vindication of logicism

Peter Roeper*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    Frege regarded Hume's Principle as insufficient for a logicist account of arithmetic, as it does not identify the numbers; it does not tell us which objects the numbers are. His solution, generally regarded as a failure, was to propose certain sets as the referents of numerical terms. I suggest instead that numbers are properties of pluralities, where these properties are treated as objects. Given this identification, the truth-conditions of the statements of arithmetic can be obtained from logical principles with the help of definitions, just as the logicist thesis maintains.

    Original languageEnglish
    Article numbernkv026
    Pages (from-to)360-378
    Number of pages19
    JournalPhilosophia Mathematica
    Volume24
    Issue number3
    DOIs
    Publication statusPublished - 1 Oct 2016

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