This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book (...) describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science. (shrink)

In this paper, we introduce a quasi-set theory without atoms. The quasi-sets (qsets) can have as elements completely indiscernible things which do not turn out to be the very same thing as it would be implied if its underlying logic was classical logic. A quasi-set can have a cardinal, called its quasi-cardinal, but this is made so that, at least for the finite case, the quasi-cardinal is not an ordinal, and hence the indistinguishable elements of a quasi-set cannot be ordered. (...) In the last sections, we show how the theory can be used to ground a quantum metaphysics of properties, which sees the quantum entities as bundles of properties, and we also introduce a new approach for the use of quantifiers in quantum physics. (shrink)

We critically examine the claim that identity is a fundamental concept. According to those putting forward this thesis, there are four related reasons that can be called upon to ground the fundamental character of identity: identity is presupposed in every conceptual system; identity is required to characterize individuality; identity cannot be defined; the intelligibility of quantification requires identity. We address each of these points and argue that none of them advances compelling reasons to hold that identity is fundamental; in fact, (...) most of the tasks that seem to require identity may be performed without identity. So, in the end, identity may not be a fundamental concept after all. (shrink)

Is it possible to find resistance in the thought of Michel Foucault? Amid the diversity of his ideas, would he have left us clues to think the resisting act? By directing his intellectual production to power dispositfs, by invoking the figure of the "specific intellectual", and, also, in the later years of his life, then turning towards the constitution of subjectivities, Foucault provides us with unique ways to conceive and operate resistances. In this article we explore two directions of the (...) resistances in the thought of the philosopher. One of them, the resistances coextend the field of power, keeping a special relationship with the specific role of the intellectual and with Philosophy. In second place, we indicate that the resistances are “starting points” or “key supports” for the issues that Foucault confronts in his work, becoming an essential part of your own research method. (shrink)

This work mainly concerns the—here introduced—category of \(\mathscr {Q}\) -sets and functional morphisms, where \(\mathscr {Q}\) is a commutative semicartesian quantale. We prove it enjoys all limits and colimits, that it has a classifier for regular subobjects (a sort of truth-values object), which we characterize and give explicitly. Moreover: we prove it to be \(\kappa \) -locally presentable, (where \(\kappa =max\{|\mathscr {Q}|^+, \aleph _0\}\) ); we also describe a hierarchy of monoidal structures in this category.

O presente artigo constitui, antes de mais, uma exposição da tentativa feita por Maurice Merleau-Ponty de sistematização de um método psicológico convergente com algumas das principais metas estabelecidas pela Fenomenologia de inspiração husserliana. Constatando de que modo o autor da Fenomenologia da Percepção considera os diversos âmbitos da cultura, a começar pela arte e pela psicanálise, como indicadores da decadência do cartesianismo, o artigo analisa o estatuto da ciência justamente como uma das esferas culturais das quais é possível extrair categorias (...) que exprimam de forma mais precisa e rigorosa o real, mostrando-se de que modo as investigações científicas são indispensáveis para uma identificação dos temas a serem filosoficamente tratados, pois os dados obtidos por tais pesquisas são imprescindíveis para o trabalho filosófico enquanto tal Neste sentido, o autor propõe uma relação entre Filosofia e Ciência que não é mais uma relação de hierarquização, tal como defendia Husserl, mas sim uma de complementaridade, tal como defendia Bergson. Com efeito, postulando-se a não necessidade de fragmentar o real para que se legitime um tal acordo, ou seja, dado que a cisão entre o espiritual e o material não pode mais ser mantida, o artigo sublinha a absoluta necessidade de que Filosofia e Ciência se encontrem. Por outras palavras, a integração entre ambas não depende de que uma e outra se refiram à mesma, e justa, metade da realidade, mas tão-somente que cada uma delas remeta para a mesma camada fenomenal, seja para descrever cientificamente os organismos em seu contacto com o meio seja para expor filosoficamente a nova ontologia ali contida. Em suma, o artigo mostra até que ponto, apesar de realizar a intenção bergsoniana de integrar explicação quantitativa e descrição qualitativa e assimilar a crítica de Husserl ao objectivismo, o método fenomenoló-gico não esgota a tarefa ontológica da filosofia. /// The present article analyzes de attempt made by Maurice Merleau-Ponty in order to systematize a psychological method convergent with some of the main goals established by the phenomenological movement issued from HusserL Taking into account the way in which the author of the Phenomenology of Perception considers the different realms of the cultural sphere, beginning with art and psychoanalysis, as special indicators of cartesianisms decadence, the article analyses the statute of science inasmuch as it is one of the cultural spheres from which it is possible to extract the categories that express in a more precise and rigorous way the real, whereby it is shown in what way scientific research is indispensable for an identification of the themes to be treated philosophically. In this sense, the author proposes a relation between Philosophy and Science that is no more one of hierarchysation, as defended by Husserl, but one of complementarity, such as defended by Bergson. By postulating that there is no longer a necessity for a fragmentation of the real so that such an accord between Philosophy and Science could be reached, and this precisely since there is no longer a way of maintaining a division between the spiritual and the material, the article underlines the necessity that Philosophy and Science must come together. In other words, the integration between the Wo no longer depends of the fact that one and the other refer to the same portion of the real, but only of the capacity that each one of them has of referring to the same set of phenomena, being that in order to achieve a scientific description of organisms in contact with the environment or being that in order to advance a philosophical exploration of the new ontology in it contained. Above all, the article shows the measure in which, regardless of the fact that the methodological approach of phenomenology realizes the bergsonian intention of an integration of quantitative explanation and qualitative description, it. cannot properly be said that such method exhausts the ontological task of Philosophy. (shrink)

Na atualidade, parece não haver nenhuma outra categoria que goze de unanimidade tão generalizada e transversal, quanto o de pessoa. Nenhum discurso que pretenda estar em público de forma teórico, jurídico e politicamente correta coloca em questão sua nobreza, principalmente em seu nexo com o direito. Os direitos da pessoa são justamente sobre o quê não se deve tergiversar. No entanto, há um paradoxo incontornável do nosso tempo: nunca como agora, a nobreza da categoria de pessoa foi tão incensada, mas (...) também nunca como agora, tantas vidas humanas foram tão humilhadas pela fome, miséria, epidemias, exílios, etc. O objetivo desse texto é seguir uma trilha já aberta por alguns pensadores de matriz franco-italiana de crítica a essa unanimidade. (shrink)

Discutimos algumas quest~oes relacionadas a uma possvel teoriade quase-objetos, isto e, objetos para os quais as condic~oes usuais de identidaden~ao se aplicariam. Desde que a principal motivac~ao para uma tal teoriae a mec^anica qu^antica, a discuss~ao e realizada tendo-se essa intepretac~ao pretendidaem mente.We discuss some questions related to a possible theory of quasiobjects,that is, objects for which the standard identity conditions should nothold. Since the main motivation for such a theory is quantum mechanics,the discussion is posed with this intended interpretation (...) in mind. (shrink)

In this paper we consider the notions of structure and models within the semantic approach to theories. To highlight the role of the mathematics used to build the structures which will be taken as the models of theories, we review the notion of mathematical structure and of the models of scientific theories. Then, we analyse a case-study and argue that if a certain metaphysical view of quantum objects is adopted, one seeing them as non-individuals, then there would be strong reasons (...) to ask for a different mathematical framework for describing the structures that would be the models of the corresponding theory. In departing from the standard frameworks (those worked on within standard mathematics), we hope to bring to the scene, within the scope of the semantic approach, the importance of paying attention to some fundamental concepts usually only superficially touched by philosophers of science (if touched). (shrink)

Steven French and Decio Krause examine the metaphysical foundations of quantum physics. They draw together historical, logical, and philosophical perspectives on the fundamental nature of quantum particles and offer new insights on a range of important issues. Focusing on the concepts of identity and individuality, the authors explore two alternative metaphysical views; according to one, quantum particles are no different from books, tables, and people in this respect; according to the other, they most certainly are. Each view comes with (...) certain costs attached and after describing their origins in the history of quantum theory, the authors carefully consider whether these costs are worth bearing. Recent contributions to these discussions are analyzed in detail and the authors present their own original perspective on the issues. The final chapter suggests how this perspective can be taken forward in the context of quantum field theory. (shrink)

The concept of indiscernibility in a structure is analysed with the aim of emphasizing that in asserting that two objects are indiscernible, it is useful to consider these objects as members of (the domain of) a structure. A case for this usefulness is presented by examining the consequences of this view to the philosophical discussion on identity and indiscernibility in quantum theory.

This volume, The Brazilian Studies in the Philosophy and History of Science, is the first attempt to present to a general audience, works from Brazil on this subject. The included papers are original, covering a remarkable number of relevant topics of philosophy of science, logic and on the history of science. The Brazilian community has increased in the last years in quantity and in quality of the works, most of them being published in respectable international journals on the subject. The (...) chapters of this volume are forwarded by a general introduction, which aims to sketch not only the contents of the chapters, but it is conceived as a historical and conceptual guide to the development of the field in Brazil. The introduction intends to be useful to the reader, and not only to the specialist, helping them to evaluate the increase in production of this country within the international context. (shrink)

It is not an exaggeration to say that quantum mechanics is at odds with most of our received metaphysical notions. In particular, an alleged revision is brought about by the theory on the metaphysical notion of ‘individuality’. Certainly, this should figure as being of great interest for metaphysicians and philosophers of science alike. What makes issues even more interesting is that some of the founding fathers of the theory, with their typical philosophical inclinations, suggested that the entities dealt with by (...) the theory had something different regarding individuality: according to them, quantum entities somehow fail individuality. (shrink)

Physics is not just mathematics. This seems trivial, but poses difficult and interesting questions. In this paper we analyse a particular discrepancy between non-relativistic quantum mechanics and ‘classical’ space and time. We also suggest, but not discuss, the case of the relativistic QM. In this work, we are more concerned with the notion of space and its mathematical representation. The mathematics entails that any two spatially separated objects are necessarily different, which implies that they are discernible —we say that the (...) space is T2, or “Hausdorff”, or yet “separable”. But when enters QM, sometimes the systems need to be taken as completely indistinguishable, so that there is no way to tell which system is which, and this holds even in the case of fermions. But in the NST setting, it seems that we can always give an identity to them by means of their individuation, which seems to be contra the quantum physical situation, where individuation does not entail identity. Here we discuss this topic by considering a case study and conclude that, taking into account the quantum case, that is, when physics enter the discussion, even NST cannot be used to say that the systems do have identity. This case study seems to be relevant for a more detailed discussion on the interplay between physical theories and their underlying mathematics, in a simple way apparently never realized before. (shrink)

One of the main criticisms of the theory of collections of indiscernible objects is that once we quantify over one of them, we are quantifying over all of them since they cannot be discerned from one another. In this way, we would call the collapse of quantifiers: ‘There exists one x such as P’ would entail ‘All x are P’. In this paper we argue that there are situations (quantum theory is the sample case) where we do refer to a (...) certain quantum entity, saying that it has a certain property, even without committing all other indistinguishable entities with the considered property. Mathematically, within the realm of the theory of quasi-sets $$\mathfrak {Q}$$, we can give sense to this claim. We show that the above-mentioned ‘collapse of quantifiers’ depends on the interpretation of the quantifiers and on the mathematical background where they are ranging. In this way, we hope to strengthen the idea that quantification over indiscernibles, in particular in the quantum domain, does not conform with quantification in the standard sense of classical logic. (shrink)

In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the contrary, it leads us to unavoidable conclusions which may have consequences in how we articulate certain concepts related to quantum theory. Behind the discussion, there is a general argument which suggests the possibility of a metaphysics of non-individuals, based on (...) a reasonable interpretation of quantum basic entities. I close the paper with a suggestion that consists in emphasizing that quanta should be referred to by the cardinalities of the collections to which they belong, for which an adequate mathematical framework seems to be possible. (shrink)

A orientação filosófica de João Mendes Júnior, por E. de Figueiredo Ferraz.--Pressupostos filosófico-jurídicos da revisão constitucional, por T. Cavalcanti Filho.--A justiça como história, por R. Cirell Czerna.--As regras de trato social em confronto com o direito, por D. de Santis Garcia.--Estado e direito, por C. Ashcar.--Doutrinas interpretativas do fenômeno jurídico, por J. Cretella Júnior.

Nonreflexive quantum mechanics is a formulation of quantum theory based on a non- classical logic termed nonreflexive logic. In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are non-individuals in some sense, and also to take into account the fact that they may (...) be absolutely indistinguishable. The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible. Here, we present the ideas of the development of nonreflexive quantum mechanics and discuss some philosophical motivations and consequences of it. (shrink)

Review of the KRAUSE, Décio "Introdução aos Fundamentos Axiomáticos da Ciência" São Paulo EPU, 2002.

Background Doctors often deal with end-of-life issues other than assisted death, such as incompetent patients and treatment withdrawal, including food and fluids. Methods A link to a questionnaire was sent by email three times, at one-week intervals, to the doctors registered in the Northern Section of the Portuguese Medical Association. Results The questionnaire was returned by 1148 (9%) physicians. This study shows that only a minority of Portuguese doctors were willing to administer drugs in lethal doses to cognitively incompetent patients (...) at the request of a family member or other close person, and even less would do it on their initiative. Most doctors favored the withdrawal of life support measures in advanced and progressive diseases at the patient’s request. Still, much fewer doctors agreed with the suspension of supportive life measures at the request of a family member, another close person, or by their own unilateral decision. However, fewer agreed with that action concerning the rest of the food and fluids. Portuguese doctors favor the administration of drugs for suffering control, even foreseeing they could shorten life. Conclusion Most doctors in this study respect patients’ autonomy but disagree with measures decided by others that have an impact on patients’ survival. They also agree with the administration of drugs for suffering control, even considering the possibility of shortening life. (shrink)

In this paper we present an overview of Professor Newton C. A. da Costa’s work in logic, emphasizing the main results obtained by him in the several areas of his research activity. The text furnish a detailed bibliographic reference of his works, which are listed in the last section.

Partindo da investigação dos conceitos de “molar” e “molecular” no pensamento de Gilles Deleuze e Félix Guattari, o artigo busca desenvolver a ideia de megamáquina política. Trata se de um conjunto complexo de forças que entretém relações com o poder, as resistências e a soberania que só pode ser desvendado por meio da distinção entre macro e micropolíticas.

Trata-se, neste artigo, de analisar o princípio fundamental ─ like effects prove like causes ─ sobre o qual Cleanthes, nos Diálogos sobre a Religião Natural de Hume, apoia sua defesa do argumento do desígnio, bem como examinar a estratégia argumentativa de Philo para enfraquecer paulatinamente a força do argumento defendido por Cleanthes.

resumo Neste artigo, pre t e ndemos mostrar como a concepção de Merleau- Po nty acerca das relações ent re sujeito perceptivo e mu ndo muda no decorrer de sua obra. Em seu livro Fenomenologia da Percepção, public a do em 1945, Merleau- Ponty atribui a tal sujeito a capacida de de assimilar ade q ua da mente o ser do mu ndo. No ent a nto, no início dos ano s cinqüenta, seu estudo da obra do psicólogo Kurt Koffka (...) explicita alguns resultados incompatíveis com a atribuição de tal capacida de ao sujeito. Por fim, em O Visível e o Invisível , Merleau-Ponty reconhece que as capacidades de assimilação perceptiva do ser do mundo possuem limitações. palavras-chave percepção; mundo percebido; mundo geográfico; fé perceptiva; ser. (shrink)

We show that using quasi-set theory, or the theory of collections of indistinguishable objects, we can define an algebra that has most of the standard properties of an orthocomplete orthomodular lattice, which is the lattice of all closed subspaces of a Hilbert space. We call the mathematical structure so obtained $\mathfrak{I}$-lattice. After discussing (in a preliminary form) some aspects of such a structure, we indicate the next problem of axiomatizing the corresponding logic, that is, a logic which has $\mathfrak{I}$-lattices as (...) its Lindembaum algebra, which we postpone to a future work. Thus we conclude that the initial intuitions by Birkhoff and von Neumann that the ``logic of quantum mechanics" would be not classical logic (a Boolean algebra), is consonant with the idea of considering indistinguishability right from the start, that is, as a primitive concept. In the first sections, we present the main motivations and a ``classical'' situation which mirrors that one we focus on the last part of the paper. This paper is our first analysis of the algebraic structure of indiscernibility. (shrink)

Non-relativistic quantum mechanics is grounded on ‘classical’ space and time. The mathematical description of these con- cepts entails that any two spatially separated objects are necessarily dif- ferent, which implies that they are discernible — we say that the space is T2, or "Hausdorff". But quantum systems, in the most interesting cases, some- times need to be taken as indiscernible, so that there is no way to tell which system is which, and this holds even in the case of fermions. (...) But in the NST setting, it seems that we can always give an identity to them, which seems to be contra the physical situation. In this paper we discuss this topic for a case study and con- clude that, taking into account the quantum case, that is, when physics enter the discussion, even NST cannot be used to say that the systems do have identity. (shrink)

Some of the forerunners of quantum theory regarded the basic entities of such theories as 'non-individuals'. One of the problems is to treat collections of such 'things', for they do not obey the axioms of standard set theories like Zermelo- Fraenkel. In this paper, collections of objects to which the standard concept of identity does not apply are termed 'quasi-sets'. The motivation for such a theory, linked to what we call 'the Manin problem', is presented, so as its specific axioms. (...) At the end, it is shown how quantum statistics can be obtained within quasi-set thbeory. (shrink)

In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate (...) in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal , for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science. (shrink)

This work seeks to highlight the central role of the concept of death for a theory of non-sense and a psychoanalysis of meaning in Gilles Deleuze. It is important to note that Deleuze summons Blanchotian reflections and gives them centrality, prior to the creation of schizoanalysis with Felix Guattari, in the formation of an idea of psychoanalysis of meaning based on Difference and Repetition and Logic of Meaning. We seek to show how, in this proposal that articulates philosophy and psychoanalysis, (...) there is a transition from genital thinking to thinking about the outside, to which the concept of death also contributes to the elucidation. (shrink)

H. Post's conception of quantal particles as non-individuals is set in a formal logico-mathematical framework. By means of this approach certain metaphysical implications of quantum mechanics can be further explored.

This paper is a continuation of the authors' attempts to deal with the notion of indistinguishability (or indiscernibility) from a logical point of view. Now we introduce a two-sorted first-order modal logic to enable us to deal with objects of two different species. The intended interpretation is that objects of one of the species obey the rules of standard S5, while the objects of the other species obey only the rules of a weaker notion of indiscernibility. Quantum mechanics motivates the (...) development. The basic idea is that in the ‘actual’ world things may be indiscernible but in another accessible world they may be distinguished in some way. That is, indistinguishability needs not be seen as a necessary relation. Contrariwise, things might be distinguished in the ‘actual’ world, but they may be indiscernible in another world. So, while two quantum systems may be entangled in the actual world, in some accessible world, due to a measurement, they can be discerned, and on the other hand, two initially separated quantum systems may enter in a state of superposition, losing their individualities. Two semantics are sketched for our system. The first is constructed within a standard set theory (the ZFC system is assumed at the metamathematics). The second one is constructed within the theory of quasi-sets, which we believe suits better the purposes of our logic and the mathematical treatment of certain situations in quantum mechanics. Some further philosophically related topics are considered. (shrink)

Com base na crítica que Hume faz ao argumento do desígnio, especialmente nas partes 10 e 11 dos Diálogos sobre a Religião Natural, meu objetivo neste artigo é, a partir de uma análise da relação entre a existência do mal no mundo e a suposta existência de uma divindade possuidora dos atributos tradicionais do teísmo, defender a tese segundo a qual o tratamento que Hume dá ao problema do mal corresponde, digamos assim, à cartada final – o último e decisivo (...) recurso que Philo personagem que articula essa crítica) aciona para mostrar que o argumento do desígnio não fornece bases suficientemente sólidas e consistentes para dar suporte à crença na existência de um Deus maximamente poderoso, justo e benevolente; e que, portanto, a existência do mal no mundo tem uma força argumentativa tal que a improbabilidade da existência de Deus é maior do que com base nos argumentos apresentados nas partes 2 a 8 dos Diálogos. Isso significa que eu tomo aqui o problema do mal como o maior problema para o teísta experimental – cuja argumentação pretende provar a existência de Deus a partir da observação dos fenômenos do mundo. (shrink)