Maths & Logic Workshop: Peter Sullivan

Peter tentatively argued for a positive answer to the question, 'Is logic transcendental?'. An 'easy' positive answer can be gleaned from some remarks of Nagel's: any attempt to doubt logic will presuppose logical principles. Thus, scepticism about logic is self-undermining. But this is unsatisfying, as it looks not to vindicate logic but to excuse it from vindication, and brings in worries concerning the possibility of logical relativism. In search of a better alternative, Peter offered a detailed reconstruction of a line of thought found in Mark Sacks', Objectivity and Insight. Broadly speaking, the strategy is to argue that certain "structuring principles of thought" are the sources of answerability. As such, it is misguided to think of these principles themselves as answerable to anything. Whilst Mark thinks of these structuring principles as concerning 'the very structure of experience', Peter's emphasis is on 'the laws of truth' (in Frege's sense). These provide us with a structure that, "can be grounded neither in the world, nor in the mind, since it is prior to both: it is the structure that at once opens up the world to us, and defines mind as standing in coordination with that world." It makes no sense to ask whether in respect of its being structured by these principles, the mind is answerable to anything.

The paper was very rich, and I have only sketched one of the central lines of thought. One issue that came up in discussion was whether there is room for the thought of alternative 'structuring principles' that are the source not of answerability, but of schmanswerability, thus raising the relativist worry again. Another concerned to what extent we should take seriously Nagel's original thought, since logical principles can be coherently doubted if one takes them one at a time.