Contemporary mathematics serves as a model for his philosophy of science and provides some important techniques eg as used in his logic. His interest in universal quantification and his sense that mathematics aspires to barbara-type universal assertions is a very early cut at ideas which after an enormously long period of dormancy emerged in modern mathematical logic. Although Aristotle rejected the Platonic doctrine that mathematical beings are separate intermediate entities between perceptible things and forms he agreed with the Platonists that mathematics is about things that are beautiful and good since it offers insight into the nature of arrangement symmetry and definiteness Met1078a31b6.
In this sense it encompasses not only the modern field of physics but also biology chemistry geology psychology and.
Aristotelian logic dominated the field of logic for 2000 years and was widely used in mathematics and science until it was ultimately replaced by modern propositional and predicate logic in the early nineteenth century. Thus the study of mathematics reveals that beauty is not so much in the eye of the beholder as it is in the nature of things Hoinski and Polansky 2016. The postulates need not be self-evident but their truth must be sustained by the results derived from them. In Aristotles classification of the sciences discrete quantities were studied by arithmetic continuous quantities by geometry.