Replacing truth

Kevin Scharp proposes an original account of the nature and logic of truth, on which truth is an inconsistent concept that should be replaced for certain theoretical purposes. He argues that truth is best understood as an inconsistent concept; develops an axiomatic theory of truth; and offers a new kind of possible-worlds semantics for this theory

Logics of formal inconsistency

Orientadores: Walter Alexandre Carnielli, Carlos M. C. L. CaleiroTexto em ingles e portuguesTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias HumanasTese (doutorado) - Universidade Tecnica de Lisboa, Instituto Superior TecnicoResumo: Segundo a pressuposição de consistência clássica, as contradições têm um cará[c]ter explosivo; uma vez que estejam presentes em uma teoria, tudo vale, e nenhum raciocínio sensato pode então ter lugar. Uma lógica é paraconsistente se ela rejeita uma tal pressuposição, e aceita ao invés que algumas teorias inconsistentes conquanto não-triviais façam perfeito sentido. A? Lógicas da Inconsistência Formal, LIFs, formam uma classe de lógicas paraconsistentes particularmente expressivas nas quais a noção meta-teónca de consistência pode ser internalizada ao nível da linguagem obje[c]to. Como consequência, as LIFs são capazes de recapturar o raciocínio consistente pelo acréscimo de assunções de consistência apropriadas. Assim, por exemplo, enquanto regras clássicas tais como o silogismo disjuntivo (de A e {não-,4)-ou-13, infira B) estão fadadas a falhar numa lógica paraconsistente (pois A e (nao-A) poderiam ambas ser verdadeiras para algum A, independentemente de B), elas podem ser recuperadas por uma LIF se o conjunto das premissas for ampliado pela presunção de que estamos raciocinando em um ambiente consistente (neste caso, pelo acréscimo de (consistente-.A) como uma hipótese adicional da regra). A presente monografia introduz as LIFs e apresenta diversas ilustrações destas lógicas e de suas propriedades, mostrando que tais lógicas constituem com efeito a maior parte dos sistemas paraconsistentes da literatura. Diversas formas de se efe[c]tuar a recaptura do raciocínio consistente dentro de tais sistemas inconsistentes são também ilustradas Em cada caso, interpretações em termos de semânticas polivalentes, de traduções possíveis ou modais são fornecidas, e os problemas relacionados à provisão de contrapartidas algébricas para tais lógicas são examinados. Uma abordagem formal abstra[cjta é proposta para todas as definições relacionadas e uma extensa investigação é feita sobre os princípios lógicos e as propriedades positivas e negativas da negação.Abstract: According to the classical consistency presupposition, contradictions have an explosive character: Whenever they are present in a theory, anything goes, and no sensible reasoning can thus take place. A logic is paraconsistent if it disallows such presupposition, and allows instead for some inconsistent yet non-trivial theories to make perfect sense. The Logics of Formal Inconsistency, LFIs, form a particularly expressive class of paraconsistent logics in which the metatheoretical notion of consistency can be internalized at the object-language level. As a consequence, the LFIs are able to recapture consistent reasoning by the addition of appropriate consistency assumptions. So, for instance, while classical rules such as disjunctive syllogism (from A and (not-A)-or-B, infer B) are bound to fail in a paraconsistent logic (because A and (not-.4) could both be true for some A, independently of B), they can be recovered by an LFI if the set of premises is enlarged by the presumption that we are reasoning in a consistent environment (in this case, by the addition of (consistent-/!) as an extra hypothesis of the rule). The present monograph introduces the LFIs and provides several illustrations of them and of their properties, showing that such logics constitute in fact the majority of interesting paraconsistent systems from the literature. Several ways of performing the recapture of consistent reasoning inside such inconsistent systems are also illustrated. In each case, interpretations in terms of many-valued, possible-translations, or modal semantics are provided, and the problems related to providing algebraic counterparts to such logics are surveyed. A formal abstract approach is proposed to all related definitions and an extended investigation is carried out into the logical principles and the positive and negative properties of negation.DoutoradoFilosofiaDoutor em Filosofia e Matemátic

Thinking the Impossible: Counterfactual Conditionals, Impossible Cases, and Thought Experiments

In this thesis I present an account of the formal semantics of counterfactuals that systematically deals with impossible antecedents. This, in turn, allows us to gain a richer understanding of what makes certain thought experiments informative in spite of the impossibility of the situations they consider. In Chapter II, I argue that there are major shortcomings in the leading theories of counterfactuals. The leading theories of counterfactuals (based on classical two-valued logic) are unable to account for counterfactuals with impossible antecedents. In such accounts, everything and anything follows from an impossible antecedent. In Chapter III, I examine some crucial notions such as conceivability, imaginability, and possibility. Herein I argue that there is a distinction to be made between the notions of conceiving and imagining. Conceivability, it turns out, is a sufficient condition for being a case. Recent literature on the semantics for relevance logic have made some use of the notion of a “state”, which differs from a world in that contradictions are true in some states; what is not done in that literature is to clarify how the notion of a state differs from an arbitrary collection of claims. I use the notion of a case as a (modal) tool to analyze counterfactuals with impossible antecedents, one for which, unlike the notion of states, it is clear why arbitrary collections of claims do not count. In Chapter IV, I propose a new account of counterfactuals. This involves modifying existing possible worlds accounts of counterfactuals by replacing possible worlds by the “cases” identified in Chapter III. This theory discerns counterfactuals such as: “If Dave squared the circle, he would be more famous than Gödel” which seems true, from others like: “If Dave squared the circle, the sun would explode”, which seems false. In Chapter V I discuss one of the main pay offs of having an account of counterfactuals that deals systematically with counterfactuals with impossible antecedents. To apply the new account of counterfactual to thought experiments, first we have to transform the thought experiment in question into a series of counterfactuals. I show how this is to be done, in Chapter V. There are two advantages of such an account when we apply it to thought experiments: First, for thought experiments with impossible scenarios, our new account can explain how such thought experiments can still be informative. Secondly, for thought experiments like the Chinese Room, where it is not clear whether there is a subtle impossibility in the scenario or not, this new account with its continuous treatment of possible and impossible cases makes clear why the debate about such thought experiments looks the way it does. The crucial question is not whether there is such an impossibility, but what is the "nearest" situation in which there is a Chinese Room (whether it is impossible or not) and what we would say there (about the intentionality of the room). On traditional accounts, it becomes paramount to deal with the possibility question, because if it is an impossible scenario the lessons we learn are very different from the ones we learn if it is possible. There are no available theories of thought experiments that account for thought experiments with impossible/incomplete scenarios. With the new account of counterfactual and by applying it to thought experiments we over come this difficulty