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Philosophy of Mathematics and Philosophy of Logic


 

PIs: Marco Panza, Andrea Sereni (Philosophy of Mathematics), Massimiliano Carrara, Vittorio Morato (Philosophy of Logic)
AIs: Francesca Boccuni, Giovanna Corsi, Guido Gherardi, Pierdaniele Giaretta, Enrico Martino, Sebastiano Moruzzi, Eva Picardi, Giuseppe Spolaore, Delia Belleri, Eugenio Orlandelli, Michele Palmira, Matteo Plebani
PhD and Master students: Luca Zanetti, Maria Paola Sfogliani
External researchers: Tatiana Arrigoni, Francesco Berto, Valeria Giardino, Federico Perelda, Alfredo Tomasetta.

 

 

Scientific aim of the project
The project will focus on fundamental issues in the Philosophy of Mathematics and the Philosophy of Logic. On the one hand, seminars and workshops will be dedicated to the epistemological problems concerning mathematical truth and mathematical objects, to the debate between mathematical platonism and various forms of nominalism, to foundational issues, and to most recent debates in the subject, such as mathematical explanation, naturalism in mathematics, and mathematical practice. On the other hand, attention will be devoted to the main themes in the philosophy of logic (with particular attention to the notions of "logical consequence", "logical form" and "logical constant") and the main branches of philosophical logic (with particular attention to modal and temporal logics, and paraconsistent logics).

The interaction between the two disciplines, both as concerns epistemological, formal and foundational problems is among the main aims of the project.

Methodology 
The project started with a pilot seminar (in the academic year 2009-2010, see http://cogito.lagado.org/node/450) dedicated to the epistemological problems for mathematical platonism first posed by Benacerraf’s works, and to recent responses to them (logicism, structuralism, fictionalism).

In the academic year 2010-2011, seminars and workshops will be held on the history and foundation of set-theory and on the notion of logical consequence.

Expected results 
Research
The project will lead to individual and joint publications in international peer-reviewed journals.

Educational
the project will give Master and PhD students a chance to study some of the main themes in the relevant areas and to familiarise themselves with discussion in these areas of philosophy, and will give PhD students the opportunity of concentrating on the researched topics in their final theses.

The project bears strong connections with other projects of the Research Centre, especially with those in Epistemology and in History of Analytic Philosophy, thus allowing students to deepen their understanding of the relations among different areas of philosophy.

Internationalization 
We aim to create collaborations with similarly oriented research groups mostly based in Europe, and to invite scholars at international levels to contribute to events such as workshops and seminars series.

 

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