Boolean negation and all that

Abstract

We have seen that proofs of soundness of (Boolean) DS, EFQ and of ABS - and hence the legitimation of these inferences - can be achieved only be appealing to the very form of reasoning in question. But this by no means implies that we have to fall back on classical reasoning willy-nilly. Many logical theories can provide the relevant boot-strapping. Decision between them has, therefore, to be made on other grounds. The grounds include the many criteria familiar from the philosophy of science: theoretical integrity (e.g., paucity of ad hoc hypotheses), adequacy to the data (explaining the data of inference -all inferences, not just those chosen from consistent domains!) and so on. This paper ..