A MATHEMATICAL MODEL OF DELEUZE'S ONTOLOGY OF BECOMING

While analyzing Plato's theory of ideas Deleuze claims that it 1) is based on the process of comparing and selection of pretenders and 2) can be "reversed" through presenting this process as an infinite process of becoming never coming to any identity or stability. To build a mathematical model of this philosophy we can take Deleuze's words literally and consider objects together with their comparison to each other on the basis of better or worse conformity to the ideal prototype. This gives us a partial order relation and in this way, we arrive to Heyting algebras or partially ordered sets with special properties. In mathematics these algebras in particular serve as locales in the so-called pointless topology. In this topology, the point is a derivable notion and is defined as ultrafilter. In the context of Deleuze's ontology, the latter plays the role of the transcendent idea - the end of becoming. Thus pointless topology equips us with a theory in which the system of locale's differences "simulates" identities of points. This suggests this topology as a mathematical model of Deleuze's ontology of becoming. This is even more so if we take into account that there are locales without points, which provide us with a model of Deleuzian becoming without end.