B.A. Philosophy, University of Milan (2001)

M.A. Philosophy, University of Milan (2003)

Ph.D. Philosophy, University of Sheffield (2009)

My current research focuses on the fields of philosophy of mathematics and philosophy of economics.

In philosophy of mathematics, I am primarily interested in the providing a comprehensive and realistic account of the applicability of mathematics in those situations in which it exhibits a closer interaction with experimental practice and design. The more theoretical applications of mathematics, notably to physical theory, have been widely studied and are currently understood as applications of mathematical structures to empirical structures, accomplished by means of mappings that preserve certain formal features of the empirical systems that they embed into mathematical models. My aim is to describe types of applications that are of a less theoretical kind and that, because of this, cannot be correctly qualified as applications of mathematical structures, either because no known empirical structure is given to be embedded into a mathematical model (this happens when e.g. the problem is to find out whether a certain object, like a chromosome or a portion of a chromosome, exhibits certain structural features, like a linear arrangement of its parts) or because the role standardly played by a mathematical model is played by mathematical concepts which can be used to present the empirical problem directly in a form amenable to mathematical solution (this happens when e.g. one is studying the design of an electrical network by means of graph-theoretical language).
I plan to build upon this critique of standard accounts of applications to provide a detailed study of types of application that have been neglected by the philosophical literature, with a focus on the social sciences.

I am also interested in the foundations of measurement, especially the role played by symmetry in the characterization of measurement scales and the use of results from measurement theory in defence of mathematical nominalism (both along the lines of Hartry Field's book 'Science without numbers' and in alternative ways).


In philosophy of economics, my interests revolve around two main themes:

a) The interpretation of impossibility theorems in social choice theory. Since at least the 1950’s, economists working on collective deliberation methods (like e.g. voting rules) have obtained a wealth of negative results to the effect that it is impossible to design deliberation procedures that satisfy certain seemingly plausible properties. A famous example is Arrow’s theorem, which shows how relatively weak assumptions on a voting rule suffice to provide a characterization of dictatorships, i.e. rules in which, roughly, the decision of a fixed individual always coincide with the outcome of the deliberation. The groundbreaking work of Donald Saari in voting theory has shown that negative results of this kind need not be interpreted as illustrating inherent limits of collective decision-making but rather as expected results that depend on certain shortcomings of the deliberation procedures involved which may not be easily detected at first. In my research I have shown how Saari’s remarks also apply to the impossibilities obtained in the recently emerged area of judgment aggregation. I am currently interested in assessing the significance of negative results in the theory of preference aggregation.

b) The notion of tractability, which is often invoked by economists when introducing standard mathematical assumptions in their models or when they choose specific analytical formulation of certain problems. Whilst the term ‘tractability’ seems to refer to accessory assumptions that simplify the treatment of a problem, these assumptions often play vastly different roles: in certain models, they are essential to the provability of key results (e.g. topological assumptions on the space of commodity bundles for the existence of utility maxima); in other models, they are entirely dispensable (e.g. continuity assumptions in the aggregation of infinite utility streams). My task is to disentangle the disparate roles of mathematical assumptions that are conflated under the umbrella term of tractability and to understand what motivates them in model-construction.

Recent Publications

Rizza, D. (forthcoming), 'Resolving Paradoxes in Judgment Aggregation', The Philosophical Quarterly.
Rizza, D. 2011. 'Magicicada, Mathematical Realism and Mathematical Explanation’, Erkenntnis 74, pp.101-114.
Rizza, D., 2010. ‘Mathematical Nominalism and Measurement’, Philosophia Mathematica 18, pp.53-73.

 

• I convene and teach Reasoning and Logic, Logic, Philosophy of Social Science, History and Philosophy of Science. I co-teach Philosophical Problems (contributing introductory lectures on Philosophy of Mind), Public Choice, Political Philosophy and Great Books.