Citations of:
Άδύνατον and material exclusion 1
Australasian Journal of Philosophy 86 (2):165 – 190 (2008)
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I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...) 

Trivialism is the doctrine that everything is true. Almost nobody believes it, but, as Priest shows, finding a nonquestionbegging argument against it turns out to be a difficult task. In this paper, I propose a statistical argument against trivialism, developing a strategy different from those presented in Priest. 

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusionexpressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. (...) 

The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the subproblem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set theory, leads (...) 



In a recent paper, Jc Beall has employed what he calls ‘shriek rules’ in a putative solution to the longstanding ‘just false’ problem for glut theory. The purpose of this paper is twofold: firstly, I distinguish the ‘just false’ problem from another problem, with which it is often conflated, which I will call the ‘exclusion problem’. Secondly, I argue that shriek rules do not help glut theorists with either problem. 