Research on the Philosophy of Mathematics Research on the Philosophy of Mathematics

Davide Rizza works on philosophical issues connected with mathematical modelling in social science. His current research focusses on exploring the advantages of appeals to infinitesimal methods in model building. A central idea is that of mathematical determination: Very often, qualitative features of empirical settings cannot be rendered mathematically operative by standard means. They are mathematically indeterminate. Their elusive features remain inferentially inert or their recalcitrance to mathematical treatment generates negative results and paradoxical scenarios. These difficulties can be eliminated by introducing mathematical resources that are capable of supplying the missing mathematical determinations. In several interesting cases, this can be achieved by means of infinitesimal methods (e.g. nonstandard analysis, ultrasmall and ultralarge numbers, the grossone methodology). From a philosophical point of view, the idea of mathematical determination can be further elaborated to yield an account of mathematisation as a methodological approach to the study of empirical problems. This is a major theme of Dr Rizza’s ongoing work.

D. Rizza (2017): A study of mathematical determination through Bertrand’s paradox. Philosophia Mathematica.

D. Rizza (2016): Divergent mathematical treatments in utility theory. Erkenntnis, 81(6), 1287-1303.

D. Rizza (2015): Nonstandard utilities for lexicographically decomposable orderings. Journal of Mathematical Economics, 60 (1), 103-109.

Dr Rizza has edited (with Angela Breitenbach, Cambridge) the special issue of Philosophia Mathematica on Aesthetics in Mathematics (2018) and organised the 2014 British Society of Aesthetics Connections conference on the topic at UEA.

Dr Rizza collaborates with distinguished mathematician Yaroslav Sergeyev, to develop applications of a new computational methodology, which employ a new numeral system with an infinite base and greatly simplify calculations with limits. Applications in mathematics education are currently trialled by an impact project. This also includes experimental studies on students’ intuitions surrounding the concept of infinity, in British and Italian schools.