In a recent paper, Jc Beall has employed what he calls ‘shriek rules’ in a putative solution to the long-standing ‘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.

In this article, we defend that incorporating a rejection operator into a paraconsistent language involves fully specifying its inferential characteristics within the logic. To do this, we examine a recent proposal by Berto for a paraconsistent rejection, which — according to him — avoids paradox, even when introduced into a language that contains self-reference and a transparent truth predicate. We will show that this proposal is inadequate because it is too incomplete. We argue that the reason it avoids trouble is (...) that the inferential characteristics of the new operator are left unspecified, exporting the task of specifying them to metaphysicians. Additionally, we show that when completing this proposal with some plausible rules for the rejection operator, paradoxes do arise. Finally, we draw some more general implications from the study of this example. (shrink)

Foreword : Consistency, Contradiction, and Consequence.

It is commonly held that the ascription of truth to a sentence is intersubstitutable with that very sentence. However, the simplest subclassical logics available to proponents of this view, namely K3 and LP, are hopelessly weak for many purposes. In this article, I argue that this is much more of a problem for proponents of LP than for proponents of K3. The strategies for recapturing classicality offered by proponents of LP are far less promising than those available to proponents of (...) K3. This undermines the ability of proponents LP to engage in public reasoning in classical domains. (shrink)

This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions ), including classical logic as a particular case. In \, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then (...) we propose our \ logic. Finally, we show how \ supports the dialetheic solution of the liar paradox. (shrink)

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 exclusion-expressing 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. (...) We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan. (shrink)

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 (...) results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

In this paper I advance and defend a very simple position according to which logic is subclassical but is weaker than the leading subclassical-logic views have it.

Francesco Berto has argued that a primitive concept of material exclusion could be employed to formulate a notion of absolute contradiction that not even dialetheists could accept. The machinery of material exclusion and absolute contradiction could then be employed as a common ground by both dialetheists as well as their opponents in debates about negation and truth. In this paper, we first put the idea on a clear basis, and then present some criticism to it. We shall argue that the (...) concepts of material exclusion and absolute contradiction hardly help with a clear basis for the debate on dialetheism; furthermore, the introduction of material exclusion threatens the coherence of dialetheism by allowing one to express the opposition between designated and undesignated values, with unwanted conclusions. (shrink)

Dialetheism is the view that some contradictions are true. One common motivation to the view concerns cases of contradictory concepts obtaining together. Allegedly, in these cases, such concepts lead to a true contradiction. In this paper, we argue that this path is closed as a motivation for dialetheism. There are two basic difficulties to articulate the view: i) once contradictory or incompatible concepts are granted to obtain together, there is no longer any reason to claim that they were incompatible to (...) begin with, and ii) it is not easy to go from such concepts to clear cases of negation-involving contradictions without already assuming the truth of dialetheism. Further difficulties discussed here concern the maintenance of the meaning of important concepts such as “contradiction” in a dialetheist setting. Those difficulties make the case for dialetheism hard to motivate via contradictory concepts. (shrink)

Dialetheism is the view that some true sentences have a true negation as well. Defending dialetheism, Graham Priest argues that the correct account of negation should allow for true contradictions and \) without entailing triviality. A negation doing precisely that is said to have ‘surplus content’. Now, to defend that the correct account of negation does have surplus content, Priest advances arguments to hold that classical Boolean negation does not even make sense without begging the question against the dialetheist. We (...) shall argue that Priest’s arguments may be turned upon themselves, and that he may also be accused of begging the question against the classical logician. We then advance an argument to the effect that Priest’s account of negation falls short of satisfying his own desiderata on a correct account of a negation: a theory of negation that attempts to represent contradictions cannot coherently allow surplus content, and vice-versa, a negation allowing for surplus content bans contradiction. (shrink)

A dialetheia is a sentence, A, such that both it and its negation, A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and (...) false. (shrink)

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.