Por José Mestre (Stirling/St Andrews and LanCog - CFUL).

In Begriffsschrift, Frege set out to formulate a language powerful enough to express every mathematical thought. Central to this undertaking was his introduction of the notion of a function. It was this notion that underpinned not only his invention of the quantifier-variable notation but also a kind of synthesis of earlier traditions in logic. Calling it a ‘synthesis’, however, may be misleading. In this talk, I argue that an adequate understanding of the role functions had to play for Frege shows that, in one relevant sense of ‘property’, the values of higher-order variables cannot be properties in his system.

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