Davide Rizza
University of East Anglia
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Featured researches published by Davide Rizza.
Synthese | 2014
Davide Rizza
In a recent paper (Okasha, Mind 120:83–115, 2011), Samir Okasha uses Arrow’s theorem to raise a challenge for the rationality of theory choice. He argues that, as soon as one accepts the plausibility of the assumptions leading to Arrow’s theorem, one is compelled to conclude that there are no adequate theory choice algorithms. Okasha offers a partial way out of this predicament by diagnosing the source of Arrow’s theorem and using his diagnosis to deploy an approach that circumvents it. In this paper I explain why, although Okasha is right to emphasise that Arrow’s result is the effect of an informational problem, he is not right to locate this problem at the level of the informational input of a theory choice rule. Once the informational problem is correctly located, Arrow’s theorem may be dismissed as a problem.
Studia Logica | 2010
Davide Rizza
In this paper I introduce a novel strategy to deal with the indiscernibility problem for ante rem structuralism. The ante rem structuralist takes the ontology of mathematics to consist of abstract systems of pure relata. Many of such systems are totally symmetrical, in the sense that all of their elements are relationally indiscernible, so the ante rem structuralist seems committed to positing indiscernible yet distinct relata. If she decides to identify them, she falls into mathematical inconsistency while, accepting their distinctness, she finds herself unable to account for it. I show that the ante rem structuralist has in fact the resources to account for the distinctness of indiscernibles and that these resources come from the very symmetry properties of the mathematical objects that seem to pose problems for her.
History and Philosophy of Logic | 2009
Davide Rizza
Peanos axiomatizations of geometry are abstract and non-intuitive in character, whereas Peano stresses his appeal to concrete spatial intuition in the choice of the axioms. This poses the problem of understanding the interrelationship between abstraction and intuition in his geometrical works. In this article I argue that axiomatization is, for Peano, a methodology to restructure geometry and isolate its organizing principles. The restructuring produces a more abstract presentation of geometry, which does not contradict its intuitive content but only puts it into a particular form.
Erkenntnis | 2011
Davide Rizza
Philosophia Mathematica | 2018
Davide Rizza
Philosophia Mathematica | 2018
Angela Breitenbach; Davide Rizza
Erkenntnis | 2016
Davide Rizza
Journal of Mathematical Economics | 2015
Davide Rizza
Philosophia Mathematica | 2013
Davide Rizza
The Philosophical Quarterly | 2012
Davide Rizza