Research

My main interests are philosophy of mathematics and its history, and computational methods for philosophy.

My current research, as a member of Arianna Betti’s Concepts in Motion group, is a combination of my both main interests: on the one hand, I do philosophical research into concepts which are foundational in mathematics and the methodology of the sciences in general (such as consequence, explanation, set, and infinite), on the other hand, as a team and in collaboration with computational experts, we explore and further develop computational methods which are to fascilitate such philosophical research.

The rationale behind the computational research we carry out in our team is that computer methods can provide huge amounts of data which are impossible to obtain by traditional philosophical research, that is, by close-reading of texts. Computer methods would for example make it possible to study the development of concepts over a long period of time. However, in order to make the data obtained from philosophical texts by means of computational tools valuable, we need a solid methodology which guarantees that the information obtained is accurate and relevant to our philosophical research questions. The main aim of the research carried out in our team is to develop such a solid methodology for the application of computational methods in philosophical research.

Thusfar, several use cases (using our tools SalVe, BolVis) showed that information retrieval tools are of valuable help in the interpretation of relatively large amounts of philosophical text. But we think that even more useful results can be obtained when such `bottom-up’ approaches are combined with `top-down’ approaches which capture expert knowledge to guide the exploration of these texts. To this aim, we investigate the use of ontologies to capture philosophical knowledge and how these ontologies can be combined with information retrieval. Furthermore, I am looking into the potential of using Formal Concept Analysis, both as a way to model expert knowledge of philosophical texts and to use it in combination with information retrieval.

My favorite philosopher to study is without doubt the Czech polymath Bernard Bolzano (1781 – 1848). Bolzano was a highly innovative thinker with ground-breaking ideas on mathematics, logic, and the methodology of the sciences (see my profile of Bolzano (in Italian)). His thoroughness and the clarity of his writing make his works furthermore an ideal test-case for the application of computational methods. Topics in Bolzano on which I am currently working (both as aims in themselves and as test-cases for the application of computational methods) are:

  • Bolzano’s conception of necessary truth;
  • Bolzano’s conception of the analytic-synthetic distinction;
  • Bolzano’s conception of explanatory proof or grounding;
  • Bolzano’s conception of size for infinite sets.

During my PhD, I did less historical and more systematic research on the cross-roads of philosophy of mathematics and philosophy of physics. In my dissertation, I investigated two philosophical paradoxes in physics (the “paradox of phase transitions” and “Norton’s dome”) and argued that these paradoxes are due to the classical mathematical framework which is employed in the physics, in particular to its conception of the infinite as the set-theoretical notion of actual infinity.

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