This research area is focused on the traditional problems that the philosophy of mathematics has faced. As a result it will undertake a systematic study of the more recent recent developments in the main schools of the foundations and philosophy of mathematics (intuitionism, logicism, formalism, structuralism and predicativism). In this sense, it will continue with the work accomplished in the mathematical part of the FCT-Project "Poincaré. Philosopher of Science" (PTDC/FIL/64748/2006).
As a second aim, the research area will study a set of controversies in the philosophy of mathematics, such as the ones concerning Arabic astronomy in the FCT-Project "Argumentation and Scientific Change: a Case Study of How Ibn al –Haytham's al-Shukuk Changed the Course of Astronomy Forever" (PTDC/MHC-FIL/4904/2012).