A neglected response to the Grim result
Is there a set of all truths? According to a familiar argument by Patrick Grim the answer is ‘no’. Grim’s argument is a reductio which runs as follows.1 Suppose, for reductio, that there is a set of all truths; call it ‘T’. Let 3(T) be the powerset of T. To each element si of 3(T) there exists a truth. For example, to each si corresponds the following truth si ∈ 3(T) Alternatively, let t1 be a truth. Then for every element si of 3(T), one of the following is a truth