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Epistemology of Mathematics and Logic

Short description

The Epistemology of Mathematics and Logic project substantiates a long-term development strategy for philosophical research at IUSS and NEtS Center. Its aim is to support advanced research, activities, and networking in the specialized, and still rather vast and multi-disciplinary, area of the epistemology and philosophy of mathematics and logic. Research is promoted on several themes concerning major contemporary debates in the philosophy of mathematics and logic, especially when merging technical and formal skills with broader theoretical issues in epistemology, ontology, logic, philosophy of language and philosophy of science.

 

Description

Within its broader field of interests, the project fosters research in the following privileged  — although non-exclusive — areas of inquiry: 

  • the nature of mathematical and logical knowledge;
  • epistemic problems of the major philosophical accounts of mathematics (logicism, neo-logicism, structuralism, nominalism, fictionalism, etc.);
  • origins and heritage of classical foundational projects, with particular attentions to the logicist, formalist, intuitionist and structuralist traditions;
  • issues concerning mathematical definitions, especially as abstractionist programmes are concerned;
  • semantic issues for logical and mathematical language;
  • the applicability of mathematics and philosophical issues concerning mathematical practice; the nature of mathematical explanation and its interactions with scientific and logical explanation;
  • the application of theories of grounding to the metaphysics and epistemology of mathematics and logic;
  • the justification and revisability of classical and non-classical logical laws;
  • abductive methodology in the choice of logical and mathematical theories;
  • applications of experimental epistemology to mathematics and logic;
  • problems of philosophical methodology and the justification of logical and mathematical theories;
  • pluralist and relativist views in logic and mathematics.

Within the project, several activities are organized (workshop, seminars, reading groups, masterclasses, etc.), incoming and outgoing visiting exchanges are promoted for both younger and established scholars, and dissemination of knowledge via teaching and participation to conferences is encouraged.

See all dedicated subsections for a summary of our activities and research, and for opportunities to work with us!

 

Involved persons

Project Coordinator

Andrea Sereni (andrea.sereni@iusspavia.it)

Andrea’s research covers several topics in the philosophy of mathematics and logic (beyond other interests in epistemology and the philosophy of language), including Frege’s philosophy of mathematics, mathematical platonism, Benaceraff’s challenges to the epistemology of mathematics, indispensability arguments, mathematical explanation, Frege’s Constraint and the applicability of mathematics, neo-logicism and abstractionst reconstructions of arithmetic, mathematical structuralism, logical pluralism and anti-exceptionalism.

Post-docs

Maria Paola Sforza Fogliani (mariapaola.sforzafogliani@iusspavia.it)

Maria Paola’s research focuses mainly on the philosophy and epistemology of logic, and in particular on the justifiability and revisability of logical laws, on counterexamples to basic rules of inference, on logical pluralism and anti-exceptionalism, and on the relationships between the philosophy of logic and the philosophy of mathematics.

Luca Zanetti (luca.zanetti@iusspavia.it

Luca's research focuses on abstractionism in the philosophy of mathematics; his current projects concern the development of a form of mathematical pluralism in response to the so-called Bad Company and Good Company problems for mathematical abstractionism, minimalist and trivialist abstractionist projects, and the development of novel forms of conceptual grounding.

PhD Students

Silvia Bianchi (silvia.bianchi@iusspavia.it)

Silvia’s research focuses on connections between scientific and mathematical structuralism and their articulation in terms of ontological dependence and metaphysical grounding. Her dissertation develops a novel structuralist approach, called Weak Structuralism, which is meant to avoid the problems of eliminativist positions. This view also entails a reconceptualization of the notions of fundamentality, priority and metaphysical explanation.

Matteo Baggio (matteo.baggio@iusspavia.it)

Matteo’s current research focuses on various issues that lie at the crossroads of epistemology and the philosophy of logic. These include the foundation of logical knowledge and the metaphysics of logic, as well as issues of philosophical methodology and the nature of intuitions. These inquiries are supported by background framework in the theories of the a priori, reliabilist epistemology, and sui generis accounts of intuition.

Mohammad Maarefi (mohammad.maarefi@iusspavia.it)

Mohammad’s research focuses on mathematical logic in general and on model theory in particular, including model-theoretic explanation in mathematics. Inquiries in these areas will be pursued by exploring concrete case-studies from logico-mathematical practice (e.g. the elimination of imaginaries in the pairs of ACVFs), within a philosophical account of how formal and syntactic methods bring about mathematical contribution in such concrete examples.

 

 

Partners

The project promotes networking activities and partnerships with national and international institutes, both on a regular and on an occasional basis.

IUSS is part of a Federation including Scuola Normale Superiore and Scuola Sant’Anna in Pisa. Joint study and research activities, also on project-related themes, are part of the aim of the Federation.

Other project-related stable collaborations are:

Vita-Salute San Raffaele University, Milan: a joint PhD Program in Cognitive Neuroscience and Philosophy of Mind [see dedicated website section] is activated between IUSS and San Raffaele, where philosophy of mathematics and philosophy of logic research projects are often selected.

IHPST, Paris 1 Panthéon-Sorbonne: a Reciprocal Agreement on Academic Collaboration has been signed with between IUSS and IHSPT, leading to several fruitful collaborations (see below funded projects, as well as visiting and conference sections).

University of Vienna: an Erasmus+ training and study exchange agreement, offered to both undergraduate, post-graduate, and faculty members has been signed with the University of Vienna, leading to several exchanges and joint activities (see visiting and masterclasses section)

We plan to expand our network of permanent partnerships in the short future, keep checking this page!

Joint Funded Projects

Vinci Grant 2018, Université franco-italienne. Philosophy of Mathematics and Conceptual Change. IUSS/IHPST Joint Project. Researcher: Marina Imocrante.

 

Check the link above for info about:

  • members profiles
  • studying and visiting opportunities
  • project activities
  • publications
  • talks