On a finite and discrete algebraic model for educing space and movement from prime matter - Costa, Rodolfo Petrônio da (Revista Archai, 2018)
In this paper we aim at presenting a finite and discrete algebraic model for the Aristotelian concept of substratum or prime matter (proté hylé), based upon further developments on this concept as carried out by Thomas Aquinas. Rather than considering it to be an outdated and obscure concept, it is shown how much profitable and current this Aristotelian insight is, both on the reality (yet not an individual) of a substratum that would pervade the whole of physical nature and on being the basic matrix for bodily genesis and corruption. This basic insight, despite of being a much controverted object over time, has been accepted by renowned authors, although in no way examined through any mathematical modeling. Additionally, it is essential that this substratum be endowed with qualities which allow the extraction of both space and bodily movement from itself. In this work, we present an algebraic model ex hypothesis isomorphic to the substratum, from which some relevant results like space extension and the dynamic character of matter are derived, and also a basic relation between operators which are obtained from dual vector spaces on the algebra and that provides the discrete case for Heisenberg’s uncertainty relations.