A Curry paradox about truth is generated by the following sentence, written on the board in room 101:If the sentence on the board in room 101 is true then 1 ≠ 1.A Curry paradox about validity is generated by the following argument, written on the board in room 102:The argument on the board in room 102 is valid. Therefore, 1 ≠ 1.Though the sentence and the argument generate Curry paradoxes, they also generate more basic paradoxes, in a sense to be (...) made clear. I argue that if we solve these more basic paradoxes, we have solutions to both kinds of Curry paradox. The positive proposal is in part inspired by a brief remark of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concepts of truth and validity, for example, are everywhere applicable except for certain singular points or singularities. A second central claim is that 'true' and 'valid' are context-sensitive predicates. This contextual-singularity approach to the Curry paradoxes applies also to other paradoxes of truth, validity, denotation, and predicate-extension. So a more general aim of the paper is to provide a unified response to semantic paradox. (shrink)

In some logics, anything whatsoever follows from a contradiction; call these logics explosive. Paraconsistent logics are logics that are not explosive. Paraconsistent logics have a long and fruitful history, and no doubt a long and fruitful future. To give some sense of the situation, I’ll spend Section 1 exploring exactly what it takes for a logic to be paraconsistent. It will emerge that there is considerable open texture to the idea. In Section 2, I’ll give some examples of techniques for (...) developing paraconsistent logics. In Section 3, I’ll discuss what seem to me to be some promising applications of certain paraconsistent logics. In fact, however, I don’t think there’s all that much to the concept ‘paraconsistent’ itself; the collection of paraconsistent logics is far too heterogenous to be very productively dealt with under a single label. Perhaps that will emerge as we go. (shrink)

En este artículo discutimos la tesis de Jc Beall según la cual no hay negación lógica. Evaluamos la solidez del argumento con el que defiende su tesis y presentamos dos razones para rechazar una de sus premisas: que la negación tiene que ser excluyente o exhaustiva. La primera razón involucra una presentación alternativa de las reglas de la negación en sistemas de secuentes diferentes al que Beall presupone. La segunda razón establece que la negación no tiene que ser excluyente o (...) exhaustiva. (shrink)

Históricamente, en los principales análisis filosóficos sobre el concepto de ‘verdad’ estuvo implícita lo que hoy se conoce como la teoría correspondentista de la verdad, la cual puede ser trazada desde Aristóteles hasta Immanuel Kant. A principios del siglo XIX, los detractores de la teoría correspondentista de la verdad comenzaron a argumentar, entre otras cosas, que esta postura es oscura, demasiado estrecha y autocomplaciente o argumentativamente circular. No obstante, en el ámbito científico algunos defensores de ciertas posturas realistas de la (...) ciencia han considerado que la verdad es la meta cognoscitva más importante de la actividad científica. Este estudio se realizó para establecer la plausibilidad de este argumento realista. Mediante el análisis de la validez de algunos argumentos de tipo ontológico, semántico y epistémico propuestos por algunos defensores de distintas versiones del llamado ‘Realismo Científico’, con los que se intenta relacionar el éxito empírico y predictivo de las mejores teorías científicas con la verdad, se muestra que, desde un punto de vista lógico, parece difícil confirmar que tales teorías nos proporcionen conocimiento confiable del mundo natural. Se sugiere que los científicos no son agentes confirmadores; sino agentes probabilísticos, esto es, agentes que buscan calcular la probabilidad con la que un hacedor de verdad convierte en verdadero a un portador de verdad con el que la ciencia comunica sus resultados. (shrink)

Rampant non-factualism is the view that all non-fundamental matters are non-factual, in a sense inspired by Kit Fine (2001). The first half of this paper argues that if we take non-factualism seriously for any matters, such as morality, then we should take rampant non-factualism seriously. The second half of the paper argues that rampant non-factualism makes possible an attractive theory of vagueness. We can give non-factualist accounts of non-fundamental matters that nicely characterize the vagueness they manifest (if any). I suggest (...) that such non-factualist theories dissolve philosophical puzzlement about vagueness. In particular, the approach implies that philosophers should not try to say which of the sorites-paradox-forming claims are true; we should not try to solve the sorites paradox in that sense. (shrink)

This paper reflects on metametaphysics and as such develops a metametameta-physical view: that quietist metametaphysics requires dialetheism, and in turn a paraconsistent logic. I demonstrate this using Carnap’s metametaphysical position in his 'Empiricism, Semantics and Ontology' as an example, with regard to how it exhibits self-reference and results in inconsistency. I show how applying Carnap’s position to itself produces a dilemma, both horns of which lead to a contradiction. Such inconsistency commonly arises from meta-theories with global scope, as the 'meta' (...) approach aims to transcend the scope of that which it is theorizing about, whilst the global nature will place itself back within the scope of that which it is theorizing about, which together result in the theory referring to itself whilst refuting itself. I argue that any global metametaphysical theory that draws a limit to thought will face self-reference problems leading to contradictory realms. My conclusion is conditional: If we want to meta-philosophize in such a way and treat quietist meta-theories as being true, then we need to be dialetheist and utilize a paraconsistent logic in order to accommodate the contradictions that result from such theorizing. (shrink)

Noniterative approaches to the sorites paradox accept single steps of soritical reasoning, but deny that these can be combined into valid chains of soritical reasoning. The distributed sorites is a puzzle designed to undermine noniterative approaches to the sorites paradox, by deriving an inconsistent conclusion using only single steps, but not chains, of soritical reasoning. This paper shows how a dialetheist version of the noniterative approach, the strict-tolerant approach, also solves the distributed sorites paradox, at no further cost, by accepting (...) the inconsistent conclusion. (shrink)

This paper briefly defends theses in Beall 2014 against objections advanced in Weber et al. 2014. The second part of the paper both defends and fortifies an objection to the ‘inclosure’ argument for glut theory, spelling an end to the inclosure strategy (or at least its application to the sorites).

I argue that there is nothing about the structure of inference to the best explanation (IBE) that prevents it from establishing a contradiction in general, though there are some potential limitations on when it can be used for this purpose. Studying the relationship between IBE and contradictions is worthwhile for three reasons. First, it enhances our understanding of IBE. We see that, in many cases, IBE does not require explanations to be consistent, though there are some cases where consistency may (...) be required. Second, the argument has implications for the debate over scientific realism. Many scientific theories appear to be inconsistent. The best argument for scientific realism, however, appeals to IBE. My argument thus shows that a certain kind of realist faces a threat from inconsistent theories. Third, the argument is important for dialetheism. Dialetheists maintain that some contradictions are true. Many of the arguments in favour of dialetheism appeal to explanatory considerations. What I say here provides support for defending dialethism using an IBE-based methodology. (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.