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. (shrink)

In a previous issue of this journal, Michael Hicks challenges my critique of Wilfrid Sellars’s arguments against the given and against the foundationalist epistemology that relies on the idea of a sensory given. I had argued that Sellars’s well-known claim that the given is a myth does not succeed because at a critical juncture he misconstrued sense-datum theorists such as Bertrand Russell and H. H. Price. In his response to my argument, Hicks makes the striking claim that Sellars was not (...) targeting foundationalism at all in his discussion of the myth of the given. Hicks reconstructs a key argument in “Empiricism and the Philosophy of Mind” (EPM) in a way intended both to avoid any reference to foundationalism and to do a more effective job than does Sellars’s original argument in uncovering a dilemma for traditional empiricism. The present paper challenges Hicks on two fronts. First, it argues that Hicks’s reconstruction is not more successful than Sellars’s original argument. Second, a review of relevant passages in makes clear that the critique of foundationalism is a prominent aspect of Sellars’s multi-faceted attack on the given. The conclusion reasserts the significance of Sellars’s place in the history of twentieth-century analytic philosophy. (shrink)