Another remark on connexivity and set theory

We show that Wiredu’s result in [26] is not the doom for connexive set theories, not even for those based in logics similar to CC1, one of the original target logics. For this purpose, we present the necessary assumptions for Wiredu’s proof, making some precisions on the connexive requirements. Then we present a non-reflexive variant of CC1 in which Wiredu’s proof can be blocked. Finally, we discuss the prospects of a connexive set theory based on both the non-reflexive and non-transitive variants of CC1, which, even assuming non-triviality, are not very rosy.