Tag Archives: formalism

Frege, Thomae, and Formalism / Review of work on Wittgenstein and Russell

Volume 11.2 of The Journal for the History of Analytical Philosophy (JHAP) has now been published online, with full open-access:


It features an article by Richard Lawrence, entitled “Frege, Thomae, and Formalism: Shifting Perspectives” Here is the abstract:

Mathematical formalism is the the view that numbers are “signs” and that arithmetic is like a game played with such signs. Frege’s colleague Thomae defended formalism using an analogy with chess, and Frege’s critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that for Thomae, the formal standpoint is an algebraic perspective on a domain of objects, and a “sign” is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae’s chess analogy is intended to provide a model for such shifts in perspective.

The volume also contains a review of Wittgenstein’s Critique of Russell’s Multiple Relation Theory of Judgement, by James Connelly (Anthem Press 2021), written by Samuel Lebens.

JHAP is a free, open-access, peer-reviewed journal. It is available at https://jhaponline.org/. Submissions welcome!