Search

International audience; In this article, 1) we will start by explaining the connection between dialetheism and other important related concepts, such as the ones of trivialism and paraconsistency. Next, we will describe 2) the history of dialetheism and 3) the motivations for the modern dialetheic renaissance, among which the logical (semantic and set-theoretic) paradoxes figure prominently, though not exclusively. We will then 4) indicate and discuss some of the objections to dialetheism, and 5) its connections with the notion of rationality. Finally, 6) we will point at some possible themes for further inquiry and future philosophical research in the field.

International audience; In this article, 1) we will start by explaining the connection between dialetheism and other important related concepts, such as the ones of trivialism and paraconsistency. Next, we will describe 2) the history of dialetheism and 3) the motivations for the modern dialetheic renaissance, among which the logical (semantic and set-theoretic) paradoxes figure prominently, though not exclusively. We will then 4) indicate and discuss some of the objections to dialetheism, and 5) its connections with the notion of rationality. Finally, 6) we will point at some possible themes for further inquiry and future philosophical research in the field.

International audience; In this article, 1) we will start by explaining the connection between dialetheism and other important related concepts, such as the ones of trivialism and paraconsistency. Next, we will describe 2) the history of dialetheism and 3) the motivations for the modern dialetheic renaissance, among which the logical (semantic and set-theoretic) paradoxes figure prominently, though not exclusively. We will then 4) indicate and discuss some of the objections to dialetheism, and 5) its connections with the notion of rationality. Finally, 6) we will point at some possible themes for further inquiry and future philosophical research in the field.

Orientadores: Giorgio Venturi, Rodolfo Ertola Biraben Cristian Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas Resumo: O problema essencial das teorias de conjuntos não clássicas é a falta de modelos naturais. Em particular, não temos modelos que sejam matematicamente expressivos. Nesta tese, pretendemos abordar este problema para várias classes de teorias de conjuntos não clássicas. Nós fornecemos modelos de teorias de conjuntos paraconsistentes e paracompletos na forma de modelos com valores algébricos. Mais especificamente, construímos uma classe de modelos paraconsistentes do fragmento livre de negação de ZF e construímos uma classe de modelos não clássicos de ZF que não são paraconsistentes nem paracompletos. Em seguida, exploramos duas extensões diferentes deste trabalho: (1) expandindo a linguagem da álgebra subjacente com diferentes operadores e (2) modificando a interpretação da pertinência e igualdade do conjunto em nossos modelos de valores algébricos. Isso dá origem a várias classes de modelos paraconsistentes da teoria dos conjuntos e a uma classe de modelos paracompletos da teoria dos conjuntos. Além disso, mostramos que esses modelos não satisfazem as mesmas sentenças da linguagem da teoria dos conjuntos e que podemos construir um modelo paraconsistente de ZFC baseado na Lógica do Paradoxo de Priest. Acreditamos que isso sugere que as teorias de conjuntos não clássicas e, em particular, as teorias de conjuntos paraconsistentes podem capturar uma quantidade razoável de matemática clássica Abstract: The essential weakness of non-classical set theories is their lack of natural models. In particular, we lack models that are mathematically expressive. In this thesis, we aim to tackle this problem for several classes of non-classical set theories. We provide models of paraconsistent and paracomplete set theories in the form of algebra-valued models. More especifically, we construct a class of paraconsistent models of the negation-free fragment of ZF and we build a class of non-classical models of ZF which are neither paraconsistent nor paracomplete. Then, we explore two different extensions of this work: (1) expanding the language of the underlying algebra with different operators and (2) modifying the interpretation of set membership and equality in our algebra-valued models. This gives rise to a several classes of paraconsistent models of set theory and to a class paracomplete models of set theory. Moreover, we show that these models are different from each other and that we can construct paraconsistent model of ZFC based on Priest's Logic of Paradox. We believe that this suggests that non-classical set theories and, in particular, paraconsistent set theories can capture a reasonable amount of standard mathematics Doutorado Filosofia Doutor em Filosofia FAPESP 2017/23853-0

El objetivo de mi tesis doctoral es defender la plausibilidad de una aproximación dialeteísta a uno de los dogmas del cristianismo, la doctrina de la encarnación. Defiendo la idea de que la doctrina de la encarnación —la teoría que dice que Jesucristo, la segunda persona de la Trinidad, es verdadera y completamente divino y verdadera y completamente humano— es efectivamente una teoría contradictoria o dialeteísta en la medida en que incluye contradicciones que son verdaderas y que, sin embargo, no hay ningún problema en aceptar este hecho, pese a las posibles críticas que puedan suscitar los intentos por abandonar el principio de no contradicción. The objective of my doctoral thesis is to defend the plausibility of a dialetheist approach to one of the dogmas of Christianity, the doctrine of the incarnation. I defend the idea that the doctrine of the incarnation - the theory that Jesus Christ, the second person of the Trinity, is entirely and truly divine and entirely and truly human - is indeed a contradictory or dialetheist theory and that, however, there is no problem in accepting such a contradiction, despite possible criticism of attempts to abandon the principle of non-contradiction. Doctor en Filosofía Doctorado

This paper starts from the Equal Validity Paradox, a paradoxical argument connected to the so-called phenomenon of faultless disagreement. It is argued that there are at least six strategies for solving the paradox. After presenting the first five strategies and their main problems, the paper focuses on the sixth strategy which rejects the assumption that every proposition cannot be both true and false. Dialetheism is the natural candidate for developing strategy six. After presenting strategy six in detail, we formulate a normative problem for the dialetheist and offer a tentative solution to it. We then elaborate further considerations connecting strategy six to pluralism about truth and logic. Even if strategy six is a hard path to take, its scrutiny highlights some important points on truth, logic and the norms for acceptance and rejection.

In this chapter, a generic definition of fundamentality as an ontological minimality thesis is sought and its applicability examined. Many discussions of fundamentality are focused on a mereological understanding of the hierarchical structure of reality, which may be combined with an atomistic, object-oriented metaphysics. But recent work in structuralism, for instance, calls for an alternative understanding and it is not immediately clear that the conception of fundamentality at work in structuralism is commensurable with the mereological conception. However, it is proposed that once we understand fundamentality as an ontological minimality thesis, these two as well as further conceptions of fundamentality can all be treated on a par, including metaphysical infinitism of the ‘boring’ type, where the same structure repeats infinitely.

Grounding is a powerful metaphysical concept; yet there is widespread scepticism about the intelligibility of the notion. In this paper, I propose an account of an entity’s nature or essence, which I then use to provide grounding conditions for that entity. I claim that an understanding of an entity’s nature, together with an account of how logically complex entities are grounded, provides all we need to understand how that entity is grounded. This approach not only allows us to say what grounds what, it also sheds light on the formal features of the grounding relation. It provides a principled argument for the orthodox view that grounding is irreflexive, asymmetrical, and transitive; but it allows that it may not be well-founded. The resulting approach gives us a powerful framework for understanding nature, grounding, and the relationship between them.

Lewisian Genuine Realism (GR) about possible worlds is often deemed unable to accommodate impossible worlds and reap the benefits that these bestow to rival theories. This thesis explores two alternative extensions of GR into the terrain of impossible worlds. It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for impossible worlds, and the central problem that such worlds present for GR: How can GR even understand the notion of an impossible world, given Lewis’ reductive theoretical framework? Since the desideratum is to incorporate impossible worlds into GR without compromising Lewis’ reductive analysis of modality, Chapter II defends that analysis against (old and new) objections. The rest of the thesis is devoted to incorporating impossible worlds into GR. Chapter III explores GR-friendly impossible worlds in the form of set-theoretic constructions out of genuine possibilia. Then, Chapters IV-VI venture into concrete impossible worlds. Chapter IV addresses Lewis’ objection against such worlds, to the effect that contradictions true at impossible worlds amount to true contradictions tout court. I argue that even if so, the relevant contradictions are only ever about the non-actual, and that Lewis’ argument relies on a premise that cannot be nonquestion- beggingly upheld in the face of genuine impossible worlds in any case. Chapter V proposes that Lewis’ reductive analysis can be preserved, even in the face of genuine impossibilia, if we differentiate the impossible from the possible by means of accessibility relations, understood non-modally in terms of similarity. Finally, Chapter VI counters objections to the effect that there are certain impossibilities, formulated in Lewis’ theoretical language, which genuine impossibilia should, but cannot, represent. I conclude that Genuine Realism is still very much in the running when the discussion turns to impossible worlds.

Wittgenstein speaks of the ‘superstitious dread and veneration by mathematicians in face of a contradiction’ and recommends that, instead of adopting this attitude, people might have wanted to produce a contradiction and ‘would be glad to lead their lives in the neighbourhood of a contradiction’ Gödel thought such remarks ‘nonsense’ and few authors have dissented from that verdict. Perhaps the most striking claim Wittgenstein makes (and defends both early and late) is that contradictions are not false. This paper seeks to defend Wittgenstein’s outrageous view, and to show its relevance to solving a variety of logico-semantical paradoxes.