Quotes About Frege

Decidability is impossible. We are back in the land of paradox, with Epimenides declaring that he is a liar and Bertrand Russell upsetting Frege's applecart

Frege has the merit of ... finding a third assertion by recognising the world of logic which is neither mental nor physical.

In order to avoid these errors, we must employ a symbolism which excludes them, by not applying the same sign in different symbols and by not applying signs in the same way which signify in different ways. A symbolism, that is to say, which obeys the rules of logical grammar—of logical syntax. (The logical symbolism of Frege and Russell is such a language, which, however, does still not exclude all errors.)

Frege's work it followed that arithmetic, and pure mathematics generally, is nothing but a prolongation of deductive logic. This disproved Kant's theory that arithmetical propositions are 'synthetic' and involve a reference to time. The development of pure mathematics from logic was set forth in detail in Principia Mathematica, by Whitehead and myself.

What are numbers? What is the nature of arithmetical truth?

Gwen went up to Cambridge and read Moral Sciences and started on a Ph.D. thesis on Frege.

Russell's point is that if the set is a member of itself, then by definition it can't be a member of itself. But if it is not a member of itself, then it is a member of itself. So it is both a member of itself and not a member of itself. And that is a contradiction. This glaring mistake, allegedly, left Frege a broken man.

Where both [Frege and Husserl] failed was in demarcating logical notions too strictly from psychological ones… These failings have left philosophy open to a renewed incursion from psychology, under the banner of 'cognitive science'. The strategies of defence employed by Husserl and Frege will no longer serve: the invaders can be repelled only by correcting the failings of the positive theories of those two pioneers.