Da Costa and French explore the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. Their framework sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.

Quasi-set theory is a theory for dealing with collections of indistinguishable objects. In this paper we discuss some logical and philosophical questions involved with such a theory. The analysis of these questions enable us to provide the first grounds of a possible new view of physical reality, founded on an ontology of non-individuals, to which quasi-set theory may constitute the logical basis.

An introduction to the model-theoretic approach in the philosophy of science is given and it is argued that this program is further enhanced by the introduction of partial structures. It is then shown that this leads to a natural and intuitive account of both "iconic" and mathematical models and of the role of the former in science itself.

Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, (...) as a key element of the formal structure of the theory, “right from the start”. In order to show the feasibility of our interpretational project we present an outline of a paraconsistent approach to quantum superpositions which attempts to account for the contradictory properties present in general within quantum superpositions. This approach must not be understood as a closed formal and conceptual scheme but rather as a first step towards a different type of understanding regarding quantum superpositions. (shrink)

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can (...) be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed. (shrink)

We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P.\ -D.\ F\'evrier's 'logic of complementarity' as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is based on a paraconsistent logic termed 'paraclassical logic'.

Our purpose in this paper is to delineate an ontology for quantum mechanics that results adequate to the formalism of the theory. We will restrict our aim to the search of an ontology that expresses the conceptual content of the recently proposed modal-Hamiltonian interpretation, according to which the domain referred to by non-relativistic quantum mechanics is an ontology of properties. The usual strategy in the literature has been to focus on only one of the interpretive problems of the theory and (...) to design an interpretation to solve it, leaving aside the remaining difficulties. On the contrary, our aim in the present work is to formulate a “global” solution, according to which different problems can be adequately tackled in terms of a single ontology populated of properties, in which systems are bundles of properties. In particular, we will conceive indistinguishability between bundles as a relation derived from indistinguishability between properties, and we will show that states, when operating on combinations of indistinguishable bundles, act as if they were symmetric with no need of a symmetrization postulate. (shrink)

In this expository paper, we examine some philosophical and technical issues brought by paraconsistency (such as, motivations for developing a paraconsistent logic, the nature of this logic, and its application to set theory). We also suggest a way of accommodating these issues by considering some problems in the philosophy of logic from a new perspective.

We investigate the higher-order modal logic , which is a variant of the system presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schrödinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent discussions on the logical foundations of quantum mechanics; for example, that some terms like 'electron' have (...) no precise reference and that 'identical' particles cannot be named unambiguously. In the last section, we sketch a classical semantics for quasi set theory. (shrink)

The apparently paradoxical nature of self-deception has attracted a great deal of controversy in recent years. Focussing on those aspects of the phenomenon which involve the holding of "contradictory" beliefs, it is our intention to argue that this presents no "paradox" if a non-classical, "paraconsistent", doxastic logic is adopted. (On such logics, see, for example, N. C. A. da Costa, 'On the theory of inconsistent formal systems', Notre Dame J Formal Logic 11(1974), 497-510, and A. I. Arruda, 'A survey (...) of paraconsistent logic', in A. I. Arruda, N. C. A da Costa and R Chuaqui, _Mathematical Logic in Latin America, North-Holland, 1984, pp. 1-41.). (shrink)

The issue of what consequences to draw from the existence of non-classical logical systems has been the subject of an interesting debate across a diversity of fields. In this paper the matter of alternative logics is considered with reference to a specific belief system and its propositions :the Azande are said to maintain beliefs about witchcraft which, when expressed propositionally, appear to be inconsistent. When the Azande have been presented with such inconsistencies, they either fail to see them as such (...) or else accept them as non-problematical. Is our knowledge of logical truths a relative and culturally determined phenomenon, or is there some (transcendent) criterion that allows us to adjudicate between alternative logical systems? The authors propose an approach for resolving disputes about the status of Azande reasoning which assumes a paraconsistent framework, thus providing a new perspective on this debate. (shrink)

We study some metamathematical properties of various classicaland paraconsistent logical systems. In particular, we discuss the concept ofa k-transform of a formula and consider some of its applications.

In this paper we discuss and outline a version of non-relativistic quantum mechanics based on a new non-reflexive logic, where the basic entities (elementary particles) lack identity conditions. Some relationships with quantum field theories are also sketched.

We apply the recently elaborated notions of 'pragmatic truth' and 'pragmatic probability' to the problem of the construction of a logic of inductive inference. It is argued that the system outlined here is able to overcome many of the objections usually levelled against such attempts. We claim, furthermore, that our view captures the essentially cumulative nature of science and allows us to explain why it is indeed reasonable to accept and believe in the conclusions reached by inductive inference.

The purpose of the present paper is to consider the traditional interpretive problems of quantum mechanics from the viewpoint of a modal ontology of properties. In particular, we will try to delineate a quantum ontology that (i) is modal, because describes the structure of the realm of possibility, and (ii) lacks the ontological category of individual. The final goal is to supply an adequate account of quantum non-individuality on the basis of this ontology.

An improvement on Horwich's so-called "pseudo-proof" of Russell's principle of induction is offered, which, we believe, avoids certain objections to the former. Although strictly independent of our other work in this area, a connection can be made and in the final section we comment on this and certain questions regarding rationality, etc.

“Tell me," Wittgenstein once asked a friend, "why do people always say, it was natural for man to assume that the sun went round the earth rather than that the earth was rotating?" His friend replied, "Well, obviously because it just looks as though the Sun is going round the Earth." Wittgenstein replied, "Well, what would it have looked like if it had looked as though the Earth was rotating?” What would it have looked like if we looked at all (...) sciences from the viewpoint of Wittgenstein’s philosophy? Wittgenstein is undoubtedly one of the most influential philosophers of the twentieth century. His complex body of work has been analysed by numerous scholars, from mathematicians and physicists, to philosophers, linguists, and beyond. This volume brings together some of his central perspectives as applied to the modern sciences and studies the influence they may have on the thought processes underlying science and on the world view it engenders. The contributions stem from leading scholars in philosophy, mathematics, physics, economics, psychology and human sciences; all of them have written in an accessible style that demands little specialist knowledge, whilst clearly portraying and discussing the deep issues at hand. (shrink)

This chapter contains sections titled: Introduction Paraconsistent Logic and Latin America Thinking about Logic The Nature of Paraconsistent Logic A History of Paraconsistent Logic Philosophical Aspects of Paraconsistent Logic References Further Reading.

Abstract A general framework is proposed for accommodating the recent results of studies into ?natural? decision making. A crucial element of this framework is the notion of a ?partial structure?, recently introduced into the semantic approach to scientific theories. It is through the introduction of this element that connections can be made with certain problems regarding inconsistency and rationality in general.

In this paper, we provide a new formulation of a coherence theory of truth using the resources of the partial structures approach − in particular the notions of partial structure and quasi-truth. After developing this new formulation, we apply the resulting theory to the philosophy of mathematics, and argue that it can be used to develop a new account of nominalism in mathematics. This application illustrates the strength and usefulness of the proposed formulation of a coherence theory of truth.Neste artigo, (...) propomos uma nova formulação de uma teoria coerentista da verdade utilizando os recursos da abordagem de estruturas parciais - em particular as noções de estrutura parcial e quase-verdade. Após desenvolver esta formulação, aplicamos a teoria resultante à filosofia da matemática, e argumentamos que aquela pode ser usada para desenvolver um novo tratamento do nominalismo na matemática. Esta aplicação ilustra a força e utilidade da formulação proposta de uma teoria coerentista da verdade. (shrink)

The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free logic and supervaluations), and apply the (...) resulting approach to accommodate semantic paradoxes. (shrink)

Problems of logical theory choice are current being widely dis- cussed in the context of anti-exceptionalist views on logic. According to those views, logic is not a special science among others, so, in particular, the methodology for theory choice should be the same in logic as for other scientific disciplines. Richard Routley advanced one such methodology which meshes well with anti-exceptionalism, and argued that it leads one to choosing one single logic, which is a kind of ultralogic. We argue that (...) the choice for only one correct system of logic may be rejected on the basis of the methodology proposed by Routley and, furthermore, that taking anti-exceptionalism about logic seriously recommends that a pluralist view of logic should be accepted. We call this view “full-blooded anti-exceptionalism”, and the resulting view on logic, lacking a proper name, “local pluralism”. (shrink)