Thinker · TH-0265
L. E. J. Brouwer
L. E. J. Brouwer was a Dutch mathematician and philosopher at the University of Amsterdam, known both for fundamental results in topology and for…
On the Coordinates: 4.4 Non-Classical Logics · 6.9 Philosophy of Mathematics
Also known as Luitzen Egbertus Jan Brouwer, Bertus Brouwer
1881 – 1966 · Overschie (Rotterdam); Amsterdam; Blaricum
Traditions: Analytic
L. E. J. Brouwer was a Dutch mathematician and philosopher at the University of Amsterdam, known both for fundamental results in topology and for founding intuitionism. He held that mathematics is a mental construction rooted in the intuition of time, so a mathematical statement is true only when a construction proving it has been carried out. On this basis he rejected the unrestricted law of excluded middle for infinite domains, a stance that helped give rise to intuitionistic logic.
Key ideas
- Mathematics is the mind's construction, grounded in the intuition of the passage of time.
- A mathematical statement is true only when we possess a construction that proves it.
- The law of excluded middle cannot be assumed for statements about infinite totalities.
- Logic is derived from mathematical practice, not the foundation on which mathematics rests.
Major works
- Leven, Kunst en Mystiek (Life, Art and Mysticism, 1905)
- Over de grondslagen der wiskunde (On the Foundations of Mathematics, 1907)
- "De onbetrouwbaarheid der logische principes" (The Unreliability of the Logical Principles, 1908)
- "Intuitionism and Formalism" (1912 inaugural address; English 1913)
In the conversation
- Debate Intuitionists are right to refuse the law of excluded middle for infinite collections
- Debate Giving up excluded middle would cost school mathematics far too much
- Debate Gödel’s “perception” of sets explains nothing about how we actually know mathematics
- Reading group Reading group: Dummett’s ‘The Philosophical Basis of Intuitionistic Logic’
- Debate Predicate logic was discovered, not invented
In the Coordinates
The questions of philosophy where L. E. J. Brouwer takes a place, from The Coordinates of Thought.
- 4.4 Non-Classical Logics Which parts of classical logic, if any, should be revised — and for which problems?
- 6.9 Philosophy of Mathematics Are numbers discovered or invented?