On the Impredicativity and Circularity of Frege’s Ancestral

João Vitor Schmidt


Among Frege’s major contributions to the philosophy of mathematics lies his famous definition for the Ancestral relation. Presented first in the 1879 Begriffsschrift, it has an important role in Frege’s logicism, given that it provides the conditions for transforming the predecessor relation into a linear-ordered series. One of the objec-tions for Frege’s definition comes from its impredicativity and the circularity thus yielded. Such objection was pointed by Benno Kerry in 1887, and more recently by Ignacio Angelelli in 2012. In this article, I argue from a Fregean perspective that Frege’s Ancestral is not circular, although its inevitably impredicative character.


Gottlob Frege. Ancestral Relation. Impredicativity. Logicism.

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Direitos autorais 2020 João Vitor Schmidt