The foundations of mathematics as a study of life: an effective but non-recursive function

Mark van Atten (1)

1 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

The Dutch mathematician and philosopher L. E. J. Brouwer (1881-1966) developed a foundation for mathematics called 'intuitionism'. Intuitionism considers mathematics to consist in acts of mental construction based on internal time awareness. According to Brouwer, that awareness provides the fundamental structure to all exact thinking. In this note, it will be shown how this strand of thought leads to an intuitionistic function that is effectively computable yet non-recursive.

Mots clés: philosophy of mathematics

Domaines: Histoire, Philosophie et Sociologie des sciences

Mark van Atten. The foundations of mathematics as a study of life: an effective but non-recursive function. Progress in Theoretical Physics, 2008, 173, pp.38-47. ⟨halshs-00791006⟩