Editing Finitism (section)

== Other related philosophies of mathematics ==
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[[Ultrafinitism]] (also known as ultraintuitionism) has an even more conservative attitude towards mathematical objects than finitism, and has objections to the existence of finite mathematical objects when they are too large.

Towards the end of the 20th century [[John Penn Mayberry]] developed a system of finitary mathematics which he called "Euclidean Arithmetic". The most striking tenet of his system is a complete and rigorous rejection of the special foundational status normally accorded to iterative processes, including in particular the construction of the natural numbers by the iteration "+1". Consequently Mayberry is in sharp dissent from those who would seek to equate finitary mathematics with [[Peano arithmetic]] or any of its fragments such as [[primitive recursive arithmetic]].