Denial and Disagreement (Topoi)

Topoi, 2014

We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express disagreement with the assertion of A by denying A. We show that, if denial is to serve as a means to express disagreement, it must be exclusive, in the sense of being correct only if what is denied is false only. Hence, it can't be expressed in the glut theorist's language, essentially for the same reasons why Boolean negation can't be expressed in such a language either. We then turn to an alternative proposal, recently defended by Beall (in Analysis 73(3):438-445, 2013; Rev Symb Log, 2014), for expressing truth and falsity only, and hence disagreement. According to this, the exclusive semantic status of A, that A is either true or false only, can be conveyed by adding to one's theory a shrieking rule of the form A^:A ' ?, where ? entails triviality. We argue, however, that the proposal doesn't work either. The upshot is that glut theorists face a dilemma: they can either express denial, or disagreement, but not both. Along the way, we offer a bilateral logic of exclusive denial for glut theorists-an extension of the logic commonly called LP. Keywords Disagreement Á Dialetheism Á Denial Á Shrieking Á Revenge Suppose Marc asserts: (1) Dover is North of London, and Lisa disagrees. 1 Classically, Lisa may express disagreement by asserting the negation of what Marc said: (2) Dover is not North of London. Glut theorists, however, may not follow suit: if A is a glut, i.e. if it is both true and false, they won't in general take assertions of both A and :A to express disagreement. 2 So how, if at all, can they express disagreement? In a number of publications, Graham Priest has suggested that they may do so by denying what was said (Priest 1999, 2006a, b). In order for this to work, asserting :A must not commit one to denying A, i.e. denial must not be reducible to the assertion of :A (Parsons 1984). Thus, glut theorists must reject, and reject, the right-to-left direction of the classical theory of denial, that to deny A is equivalent to asserting :A: Classical denial. A is correctly denied iff :A is correctly asserted. 3 The paraconsistent denial of A is stronger than the assertion of :A. Unlike paraconsistent negation, which allows for overlap between truth and falsity (Asenjo 1966;

We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express disagreement with the assertion of A by denying A. We show that, if denial is to serve as a means to express disagreement, it must be exclusive, in the sense of being correct only if what is denied is false only. Hence, it can't be expressed in the glut theorist's language, essentially for the same reasons why Boolean negation can't be expressed in such a language either. We then turn to an alternative proposal, recently defended by Jc Beall (2013, 2014), for expressing truth and falsity only, and hence disagreement. According to this, the exclusive semantic status of A, that A is either true or false only, can be conveyed by adding to one's theory a shrieking rule of the form A & ~A |- ♯, where ♯ entails triviality. We argue, however, that the proposal doesn't work either. The upshot is that glut theorists face a dilemma: they can either express denial, or disagreement, but not both. Along the way, we offer a bilateral logic of exclusive denial for glut theorists---an extension of the logic commonly called LP.

forthcoming

2015

T-biconditionals have often been regarded as insufficient as axioms for truth. This verdict is based on Tarski’s observation that the typed T-sentences suffer from deductive weakness. As indicated by McGee, the situation might change radically if we consider type-free disquotational theories of truth. However, finding a well-motivated set of untyped T-biconditionals that is consistent and recursively enumerable has proven to be very difficult. Moreover, some authors (e.g. Glanzberg) have argued that any solution to the semantic paradoxes necessarily involves ‘inflationary’ means, thus spelling doom to deflationist and minimalist theories of truth in particular. The situation is indeed worrisome as formal theories of minimalist truth are (almost) missing so far. This makes it very hard to properly evaluate the tenets of minimalism. In this article, we will show how to find legitimate instances of the T-schema just by relying on syntactic features of the sentences of our language—in particular, we will explore Quine’s idea of stratification. Based on that, we will introduce some disquotational truth theories that are deductively very strong.

There are a variety of reasons why we would want a paraconsistent account of logic, that is, an account of logic where an inconsistent theory does not have every sentence as a consequence. The one which will occupy our attention is metaphysical or semantic. One might, for various reasons, endorse that there are ‘true contradictions’, or as they are sometimes called, truth-value gluts – true sentences of the form p ^ not-p, claims which are both true and false. In this paper, we explore how various metaphysical commitments can motivate the adoption of different paraconsistent logics.

Lecture Notes in Computer Science, 1995

Journal of Applied Logic, 2017

2016

FLAP, 2021

In our introduction we make some remarks on the main topics of this issue: assertion and proof. We briefly describe how each of the papers in the present publication has contributed from either different or complementary perspectives to the logical reflection on assertion and proof, while also specifying the relation between them. It may sound like a philosophical cliché, but one could not stress enough the importance of the notions of assertion and proof for logic, philosophy of logic and philosophy of language. Although these two notions have been undergoing development since the second half of the 19th century in a relatively independent way within research programs in logic and linguistics alike, the conceptual relationships between them are undeniable. In this short contribution to the Special Issue (Assertion and Proof ) we will illustrate some of the (possible) links between proof and assertion. With "assertion" we denote prima facie at least two rather different entities; the first is a kind of act, i.e. an illocutionary act, namely the act of asserting something;

Liars and Heaps: New Essays on Paradox