Did Frege Believe Frege's Principle?

"The Priority Principle from Kant to Frege" [[To appear in Noûs, 201?]]

In a famous passage (A68/B93), Kant writes that "the understanding can make no other use of [...] concepts than that of judging by means of them." Kant's thought is often called the thesis of the priority of judgments over concepts. We find a similar sounding priority thesis in Frege: "it is one of the most important differences between my mode of interpretation and the Boolean mode [...] that ...

Ghost World: A Context for Frege's Context Principle

If Logic, Definitions and the Vicious Circle Principle

In a definition (x)((xr)D[x]) of the set r, the definiens D[x]must not depend on the definiendum r. This implies that all quantifiers in D[x] are independent of r and of (x). This cannot be implemented in the traditional first-order logic, but can be expressed in IF logic. Violations of such independence requirements are what created the typical paradoxes of set theory. Poincaré's Vicious Circl...

Frege's Mathematical Setting

Note: This essay was commissioned and written circa 1997 for The Cambridge Companion to Frege, which has not yet appeared. Although quite a bit of good work on Frege and Dedekind’s mathematical antecedents has since appeared (by Jeremy Avigad, Jamie Tappenden and others), I think this essay still provides the student with a useful introduction to many of the central issues. I have since refined...

Frege and Hilbert on Consistency1

Frege's work in logic and the foundations of mathematics centers on claims of logical entailment; most important amongst these is the claim that arithmetical truths are entailed by purely logical principles. Occupying a less central but nonetheless important role in Frege's work are claims about failures of entailment. Here the clearest examples are his theses that the truths of geometry are no...