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Gottlob Frege and modern logic
1848–1925· Philosopher· Knowledge, logic & science
Well documentedSolid records, texts or physical evidence.
German mathematician who invented modern logic in 1879 and launched analytic philosophy by analyzing meaning and the foundations of arithmetic.
See it on the Philosophy map →The idea
The idea: arithmetic is pure logic, and both can be written in a precise symbolic language. His Begriffsschrift (1879) introduced quantifiers, 'for all' and 'there exists,' handling statements like 'every number has a successor' that Aristotle's syllogisms could not. In 'On Sense and Reference' (1892) he noted that 'the Morning Star' and 'the Evening Star' name the same planet, Venus, yet differ in meaning. Main objection: Russell's 1902 paradox showed his system inconsistent.
Why it matters
His logic underlies modern mathematics, computer science and linguistics, and his analysis of language through logic launched analytic philosophy via Russell and Wittgenstein.
Legacy and sources
His books and papers, written over 44 years teaching at Jena, were little read until Russell championed them; a 1924 diary later revealed antisemitic views.
Still debated
Whether his program can be partly rescued; 'neo-logicists' since the 1980s argue arithmetic follows from logic plus one simple principle about counting.
Connections (4)
▸Aristotle's logic and the syllogism was superseded by the logic of Gottlob Frege and modern logicWell documented
The connection
For two thousand years Aristotle's syllogism ('all men are mortal; Socrates is a man...') was treated as complete; Kant said logic had not advanced a step. Frege's quantifiers handled relations and nested statements, like 'everyone loves someone,' that syllogisms could not, making the old logic a small special case of the new.
When and how
Jena, Germany, 1879, in Frege's 88-page booklet Begriffsschrift ('concept-script'), which almost no one understood at the time.
How we know
The Begriffsschrift itself; historians of logic such as William and Martha Kneale date modern logic from it, and logic textbooks now teach its methods.
Debates and open questions
Credit is shared with Boole's algebra of logic (1847) and Peirce's quantifiers (1885); and 'superseded' may overstate it, since valid syllogisms remain valid.
▸Gottlob Frege and modern logic founded Analytic philosophyMostly agreed
The connection
Frege invented modern logic, with symbols for 'all' and 'some' (quantifiers) that could analyze arguments far beyond Aristotle's syllogisms. He also showed how to study meaning precisely, distinguishing a word's sense from what it refers to. These tools, taken up by Russell and Wittgenstein, became the core method of analytic philosophy.
When and how
In Jena, Germany: Begriffsschrift ('Concept-Script', 1879), The Foundations of Arithmetic (1884) and 'On Sense and Reference' (1892).
How sure are we?
Russell and Wittgenstein credited him directly; Michael Dummett's Frege: Philosophy of Language (1973) made the case that he founded the tradition.
Debates and open questions
Calling him the founder is partly hindsight: he was little read in his lifetime, and Moore and Russell's revolt at Cambridge owed little to him at first.
▸Bertrand Russell exposed a paradox in the work of Gottlob Frege and modern logicWell documented
The connection
As Frege's Basic Laws of Arithmetic, volume 2, was going to press, Russell wrote to him about a contradiction: the set of all sets that do not contain themselves both does and does not contain itself. Frege's system allowed such sets, so it was inconsistent. Frege added a hasty appendix admitting his foundation had been shaken.
When and how
Russell found the paradox in 1901 and wrote to Frege in Jena on 16 June 1902; volume 2 appeared in 1903 with Frege's appendix.
How we know
Both letters survive; Frege's reply of 22 June 1902 describes his 'consternation' that the basis of arithmetic had been shaken.
Debates and open questions
How best to fix the paradox is still debated: Russell's theory of types and modern set theory avoid it, but no fix is universally seen as natural.
▸Gottlob Frege and modern logic influenced Ludwig WittgensteinWell documented
The connection
Wittgenstein, an engineering student gripped by the foundations of mathematics, visited Frege, who advised him to study with Russell at Cambridge. Frege's logic, and his principle that words have meaning only in the context of a sentence, shaped the Tractatus, whose preface credits 'Frege's great works'.
When and how
Wittgenstein visited Frege in Jena in 1911 and several times later; they corresponded until 1920.
How we know
The Tractatus preface credits Frege and Russell; surviving letters show Frege, sent the manuscript, said he could not make out its meaning.
Debates and open questions
Scholars debate whether Frege or Russell influenced the Tractatus more; recent scholarship often stresses Frege's larger role.