Workshop in Intensionality in Mathematics, May 11-12, 2013, Lund
Organised by Paula Quinon, Marianna Antonutti and Carlo Proietti
The theme of the workshop is the mathematical and philosophical investigation of the choice of background models, with particular attention to models for computation and the choice of axiom systems for arithmetic which have great importance for the epistemology of mathematics. The specific light in which these topics will be investigated is the role of intensionality. The general aim of the workshop is to foster the dialogue among researches working on issues related to intensionality in logic, philosophy of language, philosophy of mathematics, computer science, computability theory, number theory and also study the reasons for intensionality from the cognitive science perspective.
Some examples of the issues that the workshop aims at addressing include the Frege-Hilbert controversy on the axiomatic method and the distinction between syntax and semantics; structuralist versus (neo)-Fregean approaches to the choice of axioms (the existence of a mathematical structure is granted by the possibility of describing it with a coherent and hopefully categorical set of axioms, versus the idea that the first principles of a mathematical theory should capture the properties of the mathematical entities in question); to what extent does the choice of axioms determine what is further knowable about the mathematical structure which is being described; what intensional logics can better tackle intensional and epistemic paradoxes; what are logical connectives, whether there are intensional constraints on the choice of natural numbers as the domain for the formal treatment of the informal notion of effective computability, and what would be the philosophical consequences of understanding Church’s Thesis on arbitrary domains. Moreover, we will discuss topics related to the formation of mathematical concept as studied in psychology or cognitive sciences, and also the usefulness of cognitive science methods in epistemology of mathematics.