'Why Infinitary Logic is Genuinely Logical' Guest Lecture Professor Alexander Paseau (Oxford)

Just as one can distinguish pure geometry (roughly the study of what follows from some geometric axioms) from applied geometry (the geometry of our physical world or worlds like it), one can distinguish pure logic (the mathematical study of any logic) from applied logic (the study of what really follows from what). My talk will be an exercise in applied logic. A tenet of contemporary thought is that applied logic is finitary: any logically valid argument must be capturable in a finitary logic, e.g. first-order logic. Infinitary logics are a relatively minor area of mathematical study but are not generally regarded as correct, i.e. as genuinely logical in the applied logician’s sense. Against this, I shall give some reasons for thinking that infinitary logic is genuinely logical. The talk will overlap with Part II of my book One True Logic, co-authored with Owen Griffiths (Oxford UP 2022).