Frege and the birth of modern logic
This page delivers no verdict; it presents claims and evidence with their sources. No theory in science is absolute. Method
For everyone
With the Begriffsschrift ("concept script") of 1879 Frege rebuilt a logic that had changed little since Aristotle. He treated quantifiers such as "every" and "some" within a complete system for the first time. His aim was to show that arithmetic can be derived from pure logic. In 1902 Russell found a contradiction in the system and the programme could not continue in that form, but the logic he developed became a basic tool of today's mathematics and computer science.
For specialists
The Begriffsschrift defines predicate logic, quantification and rules of inference in a two-dimensional notation. In the Grundgesetze der Arithmetik (1893, 1903) Frege defined numbers as extensions of concepts. Basic Law V, which rests on unrestricted comprehension, allows an object such as "the set of all sets that do not contain themselves" and so gives rise to Russell's paradox. The distinction between sense (Sinn) and reference (Bedeutung) is a foundational concept of the philosophy of language.
Claims
Evidence
Supporting
—
Challenging
In a letter to Frege in 1902, Russell showed that a contradiction about the set of all sets that do not contain themselves can be derived in Frege's system.[2]
Positions
- Neo-logicists (neo-Fregeanism)
- If Hume's principle replaces Basic Law V, arithmetic can be derived consistently, so a version of Frege's programme is still defensible.[3]
Connections
Sources
- Book (1879). Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Louis Nebert, Halle
- Book (1967). From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Harvard University Press
- EncyclopediaGottlob Frege. Stanford Encyclopedia of Philosophyplato.stanford.eduarchive
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Cite this page
Athena contributors. (2026). Frege and the birth of modern logic. Athena: The tree of human knowledge. Retrieved November 1, 2026, from https://latifkedi.github.io/athena/en/d/frege/
@misc{athena_frege,
title = {Frege and the birth of modern logic},
author = {{Athena contributors}},
year = {2026},
howpublished = {\url{https://latifkedi.github.io/athena/en/d/frege/}},
note = {Athena: The tree of human knowledge. Accessed: 2026-11-01}
}Added: September 28, 2026 · Last changed: September 28, 2026 · Page history