Editing Ultrafinitism (section)

== People associated with ultrafinitism ==
Serious work on ultrafinitism was led, from 1959 until his death in 2016, by [[Alexander Esenin-Volpin]], who in 1961 sketched a program for proving the consistency of [[Zermelo–Fraenkel set theory]] in ultrafinite mathematics.  Other mathematicians who have worked in the topic include [[Doron Zeilberger]], [[Edward Nelson]], [[Rohit Jivanlal Parikh]], and [[Jean Paul Van Bendegem]]. The philosophy is also sometimes associated with the beliefs of [[Ludwig Wittgenstein]], [[Robin Gandy]], [[Petr Vopěnka]], and [[Johannes Hjelmslev]].

[[Shaughan Lavine]] has developed a form of set-theoretical ultrafinitism that is consistent with classical mathematics.<ref name="stanford1">{{cite web|url=http://plato.stanford.edu/entries/philosophy-mathematics/ |title=Philosophy of Mathematics (Stanford Encyclopedia of Philosophy) |publisher=Plato.stanford.edu |access-date=2015-10-07}}</ref>
Lavine has shown that the basic principles of arithmetic such as "there is no largest natural number" can be upheld, as Lavine allows for the inclusion of "indefinitely large" numbers.<ref name="stanford1"/>