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Thinkers

Gottlob Frege

Analytic · Europe · 1848 to 1925

German logician who built modern logic. He argued that meaning and number are real and shared, not just in our heads.

What it is

Gottlob Frege (1848 to 1925) was a German mathematician and philosopher who invented modern logic with quantifiers, tried to derive arithmetic from logic alone, and drew a distinction between the sense of an expression and what it refers to. He is often called the father of analytic philosophy, and his logical work is taken to mark the break between modern logic and the older tradition that went back to Aristotle.

He was born in 1848 in Wismar, on the northern coast of Germany, and spent his working life at the University of Jena. In 1879 he published his first book, the Begriffsschrift, which set out a new formal language for logic. A letter from Bertrand Russell later showed him that one of the principles in his great project led to a contradiction. He died in 1925.

The main ideas

  • A new logic. In the Begriffsschrift he built a formal system that was the first predicate calculus. It could analyse statements about 'all' and 'some', and it defined what counts as a proof in terms still accepted today.
  • Logicism. He held that the truths of arithmetic are truths of logic. In The Foundations of Arithmetic (1884) he criticised rival accounts of numbers, and in the two volumes of the Basic Laws of Arithmetic (1893 and 1903) he tried to derive arithmetic in his formal language.
  • Russell's paradox. Russell wrote to him that one of the axioms led to a contradiction. The axiom was one that Frege had added to make the derivation work, and the discovery meant the project did not succeed as he had planned. Many of his definitions survived.
  • Sense and reference. In 1892 he distinguished the sense of an expression, the way it presents something, from its reference, the thing it picks out. Two expressions can refer to the same thing and still differ in sense, which is why it can be informative to learn that they do.

What it looks like in practice

Picture a student who is told that the 'morning star' and the 'evening star' are the same planet. The two phrases refer to one thing, yet learning that they do is news. Frege's distinction explains why: the phrases present the planet in different ways. This is an illustration of the idea, not an example taken from the pages.

Books and moments

  • Begriffsschrift (1879) is the book that founded modern logic.
  • The Foundations of Arithmetic (1884) criticises rival accounts of number and sets out his own.
  • Basic Laws of Arithmetic (1893 and 1903) is his main attempt to carry out the plan.
  • Russell's letter brought the contradiction to light.

Questions and criticism

  • Was logicism ever possible? After the contradiction, later thinkers asked whether any version of the idea that arithmetic is logic could work.
  • Why this logic? His system settled how to analyse statements about 'all' and 'some'. It is fair to ask what in ordinary reasoning it leaves out.
  • Is meaning only sense and reference? His distinction is clear and useful, but readers still ask whether it captures everything that makes a sentence meaningful.

Close neighbours

Frege influenced Russell, Carnap and Wittgenstein, and the page on Wittgenstein shows one of the ways his ideas were taken further.

Written by epchē in our own words, and checked against independent sources on 9 October 2026. The sources are listed below.

Who they connect to

Influenced

  • Bertrand Russell · Russell built his logic on Frege's, and his famous paradox was first sent to Frege.
  • Edmund Husserl · Frege's review of an early book of Husserl's is said to have pushed him away from psychologism. (scholars disagree about this link)
  • Ludwig Wittgenstein · Wittgenstein's Tractatus took its questions about sense and reference from Frege.
  • Michael Dummett · He wrote the first major books on Frege and built his own philosophy of language from them.
  • Rudolf Carnap · He attended Frege's lectures in Jena and took up his new logic.
  • W. V. O. Quine · Quine's logic and his talk of what a theory commits us to grew from Frege. (scholars disagree about this link)

Influenced by

  • Gottfried Leibniz · Frege's aim of a precise formal language followed Leibniz's dream of a calculus of reasoning.
  • Immanuel Kant · Frege accepted Kant's view of geometry as known independently of experience while rejecting it for arithmetic.

Reacted against

  • John Stuart Mill · Frege's Foundations of Arithmetic attacked Mill's view that numbers come from experience.

Other Analytic thinkers

Sources we used

  • Gottlob Frege · Stanford Encyclopedia of Philosophy, read on 9 October 2026
  • Frege, Gottlob · Internet Encyclopedia of Philosophy, read on 9 October 2026
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