Mathematical constructivism : Constructive mathematics

In the philosophy of mathematics, mathematical constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists. When you assume that an object doesn't exist, and derive a contradiction from that assumption, you still have not found it, and therefore not proved its existence, according to constructivists.

Constructivism is often confused with mathematical intuitionism, but in fact, intuitionism is only one kind of constructivism. Intuitionism maintains that the foundations of mathematics lie in the individual mathematician's intuition, thereby making mathematics into an intrinsically subjective activity. Constructivism doesn't, and is entirely consonant with an objective view of mathematics.

Mathematicians that have contributed to constructivism

• Leopold Kronecker[?]
• L.E.J. Brouwer
• Errett Bishop[?]

Branches of constructivist mathematics

• Constructivist logic[?]
• Constructivist type theory[?]
• Constructivist analysis

See also

• Mathematical intuitionism
• Finitism