Biography

I began studying philosophy in Italy, where I took my BA and MA, with a dissertation on the history of the vector calculus, focussing on the work of Hermann Grassmann and Giuseppe Peano. I then moved to the UK, where I obtained a PhD from the University of Sheffield: my thesis makes use of neglected but important results in the foundations of measurement to develop a novel account of the applicability of mathematics. I became a fixed-term Lecturer at UEA in September 2009. From September 2010 I was a permanent member of staff in the School of Philosophy. Since 2015 I am a permanent member of the School of PPL (Politics, Philosophy, Languages and Communication Studies).   

Academic Background

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

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

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

Additional Contacts

Academia.euu.Personal Page

All Publications

Rizza, D.

(2017)

A Study of Mathematical Determination through Bertrand’s Paradox,

in Philosophia Mathematica

Full Text UEA Repository

(Article)

(E-pub ahead of print)


Breitenbach (Cambridge), A., Rizza, D.

(2017)

Introduction to Special Issue: Aesthetics in Mathematic,

in Philosophia Mathematica

Full Text

(Editorial)

(E-pub ahead of print)


Rizza, D.

(2016)

Divergent mathematical treatments in utility theory,

in Erkenntnis

81

(6)

pp. 1287–1303

Full Text UEA Repository

(Article)

(Published)


Rizza, D.

(2016)

Supertasks and Numeral Systems,

in AIP Conference Proceedings.

AIP Publishing

Full Text UEA Repository

(Conference contribution)

(Published)


Rizza, D.

(2015)

Nonstandard utilities for lexicographically decomposable orderings,

in Journal of Mathematical Economics

60

pp. 105–109

Full Text UEA Repository

(Article)

(Published)


Rizza, D.

(2014)

Arrow's theorem and theory choice,

in Synthese

191

(8)

pp. 1847-1856

UEA Repository

(Article)

(Published)


Rizza, D.

(2013)

Deconstructing a topological sorites,

in Philosophia Mathematica

21

(3)

pp. 361-364

Full Text UEA Repository

(Article)

(Published)


Rizza, D.

(2013)

The applicability of mathematics: Beyond mapping-based accounts,

in Philosophy of Science

80

(3)

pp. 398-412

Full Text UEA Repository

(Article)

(Published)


Rizza, D.

(2012)

Resolving paradoxes in judgment aggregation,

in The Philosophical Quarterly

62

(247)

pp. 337-354

Full Text UEA Repository

(Article)

(Published)


Rizza, D.

(2011)

Mathematics and Reality – Mary Leng,

in The Philosophical Quarterly

61

(244)

pp. 655-657

Full Text UEA Repository

(Article)

(Published)


Rizza, D.

(2011)

Magicicada, Mathematical Realism and Mathematical Explanation,

in Erkenntnis

74

(1)

pp. 101-114

Full Text UEA Repository

(Article)

(Published)


Rizza, D.

(2010)

Discernibility by symmetries,

in Studia Logica

96

(2)

pp. 175-192

Full Text UEA Repository

(Article)

(Published)


Rizza, D.

(2009)

Abstraction and Intuition in Peano's Axiomatizations of Geometry,

in History and Philosophy of Logic

30

(4)

pp. 349-368

Full Text UEA Repository

(Article)

(Published)


Rizza, D.

(2009)

Mathematical Nominalism and Measurement,

in Philosophia Mathematica

18

(1)

pp. 53-73

Full Text UEA Repository

(Article)

(Published)


Rizza, D.

(2008)

The Nature of Applied Mathematics: Remarks on Field’s View,

in Praxis

1

pp. 69-87

UEA Repository

(Article)

(Published)


Rizza, D.

(2006)

Measurement-theoretic Observations on Field's Instrumentalism and the Applicability of Mathematics,

in Abstracta

2

pp. 148-171

UEA Repository

(Article)

(Published)


Key Research Interests

My current research revolves around understanding how mathematical concepts are used as instruments of intervention on theoretical models and on adopting alternative mathematical resources in order to obtain more satisfactory treatments of certain models or problems.  

Recent Work

Divergent mathematical treatments in utility theory (on Erkenntnis 81): In this paper I show how one can remove negative results in simple economic models by changing the numerical set on which a utility function takes values. In particular, I show how impossibility theorems concerning intergenerational equity essentially depend on the structure of the real numbers.

Supertasks and numeral systems (on American Institute of Physics Proceedings 1776). I study some mechanical supertask paradoxes as effects of a single phenomenon: the lack of expressive resources sufficient to obtain a sequential representation of an infinitely long, completed process. The expressive limitation lies at the level of the coice of a numeral system. Once  traditional numeral systems, in a fixed base, are replaced by the stronger numeral system introduced by Yaroslav Sergeyev, which allows computations with infinitely large and small quantities, paradoxes can be replaced by arithmetically computable resolutions.

Work in progress
I am currently working on the application of Yaroslav Sergeyev's new computational methodology to problems and paradoxes in probability theory and decision theory. I have recently developed a combinatorial treatment of Bertrand's paradox under which it is possible to evaluate unambiguously the probability of selecting at random, among the chords of a circle, one shorter than the side of the inscribed equilateral triangle. Under this approach, the distinct methods of selection devised by Bertrand all yield the same probability value, up to an infinitesimal error. My forthcoming work is devoted to addressing, within the same mathematical framework, certain problems in decision theory that arise from the lack of suitable mathematical instruments for the study of infinite decision models. 

Teaching Interests

First Year

  • Reasoning and Logic
  • Great Books (early Marx, Proudhon, Landauer, Weil)
  • Philosophical Problems


Honours Level

  • Logic
  • Philosophy of Science 
  • Philosophy of Social Science 
  • Philosophy of Religion