Matthias Schirn

In 2014, he delivered a series of lectures on Frege’s philosophy of mathematics at the University of Oxford and carried out related research at Wolfson College.

Besides German, he speaks English, Spanish, Portuguese and French fluently and reads modern philosophical texts in Italian with relative ease.

Concerning Frege’s philosophy of mathematics, Schirn has more recently focused and published on the introduction of logical objects by means of second-order abstraction principles, their logical, semantic and epistemological nature, the problem of referential indeterminacy of abstract singular terms to which those principles give rise in a Fregean context, cross-sortal identity claims, the foundations of cardinal arithmetic, of real analysis and of geometry, platonism and mathematical creation, identity and the cognitive value of logical equations and last but not least on some aspects of neo-logicism.

One important result of their published work is that Peano Arithmetic proves its own consistency indirectly in one step and that recursively enumerable extensions of QF-IA (QF = quantifier free — IA = induction axiom) likewise prove their own consistency indirectly in one step.

Schirn and Niebergall are also known for their analysis of Hilbert’s extensions of the finitist point of view in the light of Gödel’s incompleteness theorems and their attempted refutation of W. W. Tait’s widely accepted thesis[2] that all finitist reasoning is primitive recursive (W.W. Tait, ‘Finitism’, Journal of Philosophy 78, 524-46).