Non-Transitive Logics: A New Approach to Paradoxes
The Research Problem
A paradox is a seemingly valid argument with seemingly true premises and seemingly false conclusion. Of course, not all these appearances can be true. Sometimes it is particularly difficult to reject the truth of the premises or the falsity of the conclusion, so that the only option left is revising the logic underlying the argument. This task can be carried out in different ways. In a first approach, we could reject some of the inferences present in the argument. This sort of strategy, however, comes usually with the unwanted loss of some concomitant inferences.
Now arguments in general require a certain number of inferences in order to reach the conclusion from the premises. A second strategy consists, not in the rejection of some particular inference, but in the rejection of the way inferences are related in the argument (that is, in the rejection of some "metainference"). The present project aims to study the foundations, possibilities of formulation and application of a strategy of this second kind. According to this strategy, logical consequence might fail to be transitive.