Ultrafinitism

Ultrafinitismus (also called Ultraintuitionismus ) is a particularly strict interpretation of finitism in the philosophy of mathematics.

Ultrafinitisten deal with the construction of mathematical objects taking into account the physical limitations of man. They reject not only, like other followers of finitism, the existence of mathematical structures from to their construction an infinite number of steps would be required ( as in the set of natural numbers ), but also doubt about the meaning of numbers such as ( the largest natural number, which is smaller than Skewes ' number). This they explained by the fact that no one has calculated this number so far and that it may be physically impossible to calculate them. The number of elementary particles in the observable universe is estimated as Skewes ' number is.

Although Ultrafinitismus is a form of mathematical constructivism, he is considered by the vast majority of constructivists as impractical. The constructive logician AS Troelstra formulated this in Constructivism in Mathematics (1988 ): There is currently no satisfactory preparation (no satisfactory development exists at present).

Alexander Esenin - Volpin is since 1959 a leading proponent of Ultrafinitismus.