TOWARDS A PHILOSOPHICAL UNDERSTANDING OF THE LOGICS OF FORMAL INCONSISTENCY

Abstract In this paper we present a philosophical motivation for the logics of formal inconsistency , a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC , a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence.

One reason, several logics

Humans have used arguments for defending or refuting statements long before the creation of logic as a specialized discipline. This can be interpreted as the fact that an intuitive notion of "logical consequence" or a psychic disposition to articulate reasoning according to this pattern is present in common sense, and logic simply aims at describing and codifying the features of this spontaneous capacity of human reason. It is well known, however, that several arguments easily accepted by common sense are actually "logical fallacies", and this indicates that logic is not just a descriptive, but also a prescriptive or normative enterprise, in which the notion of logical consequence is defined in a precise way and then certain rules are established in order to maintain the discourse in keeping with this notion. Yet in the justification of the correctness and adequacy of these rules commonsense reasoning must necessarily be used, and in such a way its foundational role is recognized. Moreover, it remains also true that several branches and forms of logic have been elaborated precisely in order to reflect the structural features of correct argument used in different fields of human reasoning and yet insufficiently mirrored by the most familiar logical formalisms.

Remarks on an algebraic semantics for paraconsistent Nelson's logic

In the paper Busaniche and Cignoli (2009) we presented a quasivariety of commutative residuated lattices, called NPc-lattices, that serves as an algebraic semantics for paraconsistent Nelson's logic. In the present paper we show that NPc-lattices form a subvariety of the variety of commutative residuated lattices, we study congruences of NPc-lattices and some subvarieties of NPc-lattices.

Matrix- based logic for avoiding paradoxes and its paraconsistent alternative

The present article shows that there are consistent and decidable many- valued systems of propositional logic which satisfy two or all the three criteria for non- trivial inconsistent theories by da Costa (1974). The weaker one of these paraconsistent system is also able to avoid a series of paradoxes which come up when classical logic is applied to empirical sciences. These paraconsistent systems are based on a 6- valued system of propositional logic for avoiding difficulties in several domains of empirical science (Weingartner (2009)).

Constituição de professores universitários de disciplinas sobre ensino de Química

This paper focuses on the teaching development practice in the field of chemistry covering such disciplines as chemistry teaching practice, chemistry teaching instrumentation and chemistry teaching methodology and/or didactics, thereby describing and analysing the logics of the development practice and the role of teachers as well as the epistemological identity configurations (knowledges which are proper to said identity) within this discipline field.

Newton da Costa and the school of Curitiba

This paper intends to report on the beginning of the publications of Newton da Costa outside Brazil. Two mathematicians played an important role in this beginning: Marcel Guillaume from the University of Clermont-Ferrand and Paul Dedecker from the Universities of Lille and Liège. At the same time we recall the role played by Newton da Costa and Jayme Machado Cardoso in the development of what we call here the School of Curitiba [Escola de Curitiba]. Paraconsistent logic was initiated in this school under the influence of Newton da Costa. As another contribution of this school we mention the development of the theory of quasigroups; Jayme Machado Cardoso's name has been given, by Sade, to some particular objects which are now called Cardoso quasigroups.

The dawn of paraconsistency: Russia's logical thought in the turn of XX century

The paper deals with the factors which enabled N. A. Vasiliev to put forward in 1910 - 12 the idea of logics free of the laws of contradiction and excluded middle, the idea of metalogic and to construct his imaginary logic as novel non-classical system. It is shown that background of Vasiliev's ideas lies deeply in Russia's culture and particular approach to logical discourse. Several Russian scholars expressed ideas similar to Vasiliev's though not in such explicit form. This period might be called the prehistory of paraconsistency. Real history of paraconsistency starts with N.C.A. da Costa's works.

Da Costa on ontology: a naturalistic interpretation

Da Costa's conception of being modifies that of Quine to incorporate relativization to non-classical logics. A naturalistic view of this conception is discussed. This view tries to extend to logic some ideas of Maddy's naturalism concerning mathematics.

The role of consistency in empirical science

Any inconsistent theory whose underlying logic is classical encompasses all the sentences of its own language. As it denies everything it asserts, it is useless for explaining or predicting anything. Nevertheless, paraconsistent logic has shown that it is possible to live with contradictions and still avoid the collapse of the theory. The main point of this paper is to show that even if it is formally possible to isolate the contradictions and to live with them, this cohabitation is neither desired by working scientists not desirable for the progress of science. Several cases from the recent history of physics and cosmology are analyzed.

Form(s)-of-life: agamben's reading of Wittgenstein and the potential uses of a notion

Giorgio Agamben and Ludwig Wittgenstein seem to have very little in common: the former is concerned with traditional ontological issues while the latter was interested in logics and ordinary language, avoiding metaphysical issues as something we cannot speak about. However, both share a crucial notion for their philosophical projects: form of life. In this paper, I try to show that, despite their different approaches and goals, form of life is for both a crucial notion for thinking ethics and life in-common. Addressing human existence in its constitutive relation to language, this notion deconstructs traditional dichotomies like bios and zoé, the cultural and the biological, enabling both authors to think of a life which cannot be separated from its forms, recognizing the commonality of logos as the specific trait of human existence. Through an analogical reading between both theoretical frameworks, I suggest that the notion of form-of-life, elaborated by Wittgenstein to address human production of meaning, becomes the key notion in Agamben's affirmative thinking since it enables us to consider the common ontologically in its relation to Human potentialities and to foresee a new, common use of the world and ourselves.