Gottlob Frege
Father of modern logic — quantification, sense and reference, the foundations of arithmetic.
Overview
A German mathematician and logician who revolutionized logic for the first time since Aristotle and founded analytic philosophy. His Begriffsschrift introduced modern quantificational logic; he sought to derive arithmetic from logic alone (logicism), and his distinction between 'sense' and 'reference' reshaped the philosophy of language. Little recognized in his lifetime, his work became the foundation of 20th-century logic and analytic philosophy through Russell and Wittgenstein.
What they supported — and why
Modern (quantificational) logic
SupportedA new logical notation captures generality and relations with quantifiers and variables, far surpassing Aristotle's syllogistic.
WhyOrdinary and Aristotelian logic could not express the reasoning of mathematics; a rigorous formal language was needed to make inference exact.
Logicism
SupportedThe truths of arithmetic are ultimately truths of logic, derivable from purely logical laws and definitions.
WhyIf numbers and arithmetic can be defined in logical terms, mathematics gains a secure, non-empirical foundation.
Sense and reference
SupportedAn expression has both a reference (what it stands for) and a sense (the mode of presentation); 'the morning star' and 'the evening star' share a reference but differ in sense.
WhyOnly distinguishing sense from reference explains how identity statements can be informative and how meaning works — founding modern philosophy of language.
Causes championed
- Rigor and precision in logic
- Secure foundations for mathematics
- A scientific philosophy of language
Issues wrestled with
- What is the correct logic?
- What are numbers, and what grounds arithmetic?
- How does language mean?
Hurdles faced
- Russell's paradox, which shattered the foundations of his life's work
- Near-total neglect in his own lifetime
Works & books
2 catalogued. Status shows how much survives to today.
Begriffsschrift (Concept-Script)
SurvivesThe founding work of modern formal logic.
The Foundations of Arithmetic; 'On Sense and Reference'
SurvivesHis logicist philosophy of mathematics and his theory of meaning.
Read the texts free
Their works online — Open Library catalogues 95 works & editions, 4 of them free to read in full.
The influence network
See Gottlob Frege in the map →Influenced
In their words
“Every good mathematician is at least half a philosopher, and every good philosopher at least half a mathematician.”
— attributed
Legacy
He refounded logic and launched analytic philosophy; modern logic, the philosophy of language, and the foundations of mathematics all begin with him.
Follow their questions
This thinker is a stop on these paths through philosophy.
Further reading
Cross-checked against these authoritative references.