The standard Hilbert-style of axiomatic system yields the assertion of axioms and, via the use of rules, the assertion of theorems. However, there has been little work done on the corresponding axiomatic rejection of non-theorems. Such Hilbert-style rejection would be achieved by the inclusion of certain rejection-axioms (r-axioms) and, by use of rejection-rules (r-rules), the establishment of rejection-theorems (r-theorems). We will call such a proof a rejection-proof (r-proof). The ideal to aim for would be for the theorems and r-theorems to (...) bemutually exclusive and exhaustive. That is, if a formula A is a theorem then it is not an r-theorem, and if A is a non-theorem then it is an r-theorem. In this paper, I present a rejecion system for the first-degree formulae of a large number of relevant logics. (shrink)

Deleuze never explicitly formulates his philosophy of logical truth‐values. It thus remains an open question as to the number and types he held there to be. Despite his explicit comments on these matters, additional textual evidence suggests that in his thinking on the event, he favored a third truth‐value, holding either the analetheic view that some truth‐bearers can be truth‐valueless or the dialetheic view that some truth‐bearers can be both true and false. I first argue that taking a logical approach (...) to Deleuze's thinking is feasible, despite his and others' claims that might suggest otherwise. Next, I examine his explicit statements to show that they cannot be taken at face value and that, rather, we need to transpose his claims into contemporary terminology in order to accurately assess them. I lastly turn to his Leibniz‐inspired philosophy of time to argue that the affirmations involved in this conception strongly suggest a dialetheic tendency in his thinking. (shrink)