logicism

Without this device, the project of logicism would have been doubtful or impossible.

The axiomatic method, brought to the extreme, results in logicism.

Few mathematicians are typically concerned on a daily, working basis over logicism, formalism or any other philosophical position.

The Grundlagen also helped to motivate Frege's later works in logicism.

Russell's philosophy of mathematics was not formalist, however; it is usually considered a form of logicism.

- A critical survey of the ongoing rehabilitation of Frege's logicism.

The starting point of the ongoing sympathetic reexamination of Frege's logicism.

That aim is known as logicism.

However, the basic spirit of logicism remains valid, as that theorem is proved with logic just like other theorems.

Origin of the name "logicism"

Gottlob Frege was the founder of logicism.

Opposing the completely deductive character of logicism, intuitionism emphasizes the construction of ideas in the mind.

It borrows Russell's logicism and extends it to a computational set of ideas and knowledge.

Gödel in his 1944 bores down to the exact place where Russell's logicism fails and offers a few suggestions to rectify the problems.

Since he treated the subject of primitive notions in geometry and set theory, this text is a watershed in the development of logicism.

As perhaps its core tenet, logicism forbids any "intuition" of number to sneak in either as an axiom or by accident.

Kurt Gödel's incompleteness theorem is sometimes alleged to undermine logicism because it shows that no particular axiomatization of mathematics can decide all statements.

"Language-planning" and syntactical techniques derived from these developments were used to defend logicism in the philosophy of mathematics and various reductionist theses.

At the beginning of the 20th century, 3 schools of philosophy of mathematics were opposing each other: Formalism, Intuitionism and Logicism.

Evidence of the assertion of logicism was collected by Russell and Whitehead in their Principia Mathematica.

In the foundations of mathematics, this project is variously understood as logicism or as part of the formalist program of David Hilbert.

In general the logicism of Dedekind-Frege is similar to that of Russell, but with significant (and critical) differences in the particulars (see Criticisms, below).

Dedekind's path to logicism had a turning point when he was able to reduce the theory of real numbers to the rational number system by means of set theory.

Hilbert dismissed logicism as a "false path": "Some tried to define the numbers purely logically; others simply took the usual number-theoretic modes of inference to be self-evident.

Carnap, Heyting, and von Neumann delivered one-hour addresses on the mathematical philosophies of logicism, intuitionism, and formalism, respectively (Dawson 1996, p. 69).