Putnam’s indispensability argument revisited, reassessed, revived

Crucial to Hilary Putnam’s realism in the philosophy of mathematics is to maintain the objectivity of mathematics without the commitment to the existence of mathematical objects. Putnam’s indispensability argument was devised as part of this conception. In this paper, I reconstruct and reassess Putnam’s argument for the indispensability of mathematics, and distinguish it from the more familiar, Quinean version of the argument. Although I argue that Putnam’s approach ultimately fails, I develop an alternative way of implementing his form of realism about mathematics that, by using different resources than those Putnam invokes, avoids the difficulties faced by his view

Constructive Empiricism, Partial Structures and the Modal Interpretation of Quantum Mechanics

Van Fraassen's modal interpretation of non-relativistic quantum mechanics is articulated to support an anti-realist account of quantum theory. However, given the particular form of van Fraassen's anti-realism (constructive empiricism), two problems arise when we try to make it compatible with the modal interpretation: one difficulty concerns the tension between the need for modal operators in the modal interpretation and van Fraassen's skepticism regarding real modality in nature; another addresses the need for the truth predicate in the modal interpretation and van Fraassen's rejection of truth as the aim of science. After examining these two problems, I suggest a formal framework in which they can be accommodated – using da Costa and French's partial structures approach – and indicate a variant of van Fraassen's modal interpretation that does not face these difficulties.Quanta 2014; 3: 1–15

A evidência visual na ciência

In this article, I characterize the concept of visual evidence as a particular kind of evidence in which counterfactual conditions analogous to those met by perception are present. I argue that visual evidence can also be produced by scientific instruments, such as various kinds of microscopes for which we know that the relevant conditions are, in fact, satisfied. Thus, both perception and the information generated by instruments that yield visual evidence share the same epistemic properties. Drawing on this fact, I finally offer a way of extending the observable beyond instances of unaided perception, but which still preserves, within an empiricist view, cases in which certain objects cannot be observed.Neste artigo, proponho uma formulação do conceito de evidência visual como um tipo particular de evidência no qual condições contrafáticas análogas àquelas encontradas na percepção estão presentes. Argumento que a evidência visual pode ser produzida também por instrumentos científicos, tais como diversos tipos de microscópios para os quais sabemos que as condições em apreço são, de fato, satisfeitas. Como resultado, tanto a percepção como as informações geradas por instrumentos que produzem evidência visual satisfazem as mesmas propriedades epistêmicas. Com base nesse fato, proponho, finalmente, uma forma de estender o observável para além da percepção a olho nu, mas que ainda preserva, no interior de uma concepção empirista, casos em que determinados objetos não podem ser observados

Follow the Flow: sets, relations, and categories as special cases of functions with no domain

We introduce, develop, and apply a new approach for dealing with the intuitive notion of function, called Flow Theory. Within our framework functions have no domain at all. Sets and even relations are special cases of functions. In this sense, functions in Flow are not equivalent to functions in ZFC. Nevertheless, we prove both ZFC and Category Theory are naturally immersed within Flow. Besides, our framework provides major advantages as a language for axiomatization of standard mathematical and physical theories. Russell's paradox is avoided without any equivalent to the Separation Scheme. Hierarchies of sets are obtained without any equivalent to the Power Set Axiom. And a clear principle of duality emerges from Flow, in a way which was not anticipated neither by Category Theory nor by standard set theories

Modalidade, abordagem semântica e mecânica quântica

De acordo com o argumento da indispensabilidade, devemos nos comprometer ontologicamente com entidades matemáticas, por serem elas indispensáveis às nossas melhores teorias científicas. Hartry Field (1980) notoriamente opõe-se ao argumento, desenvolvendo um programa de reformulação de teorias científicas sem quantificação sobre objetos matemáticos. Em particular, Field elaborou detalhadamente a nominalização da teoria gravitacional de Newton, indicando como ela poderia ser formulada sem quantificação sobre números reais. Field forneceu também um argumento de por que o uso de operadores modais não garante uma estratégia adequada para nomear teorias científicas. Neste artigo, discuto o argumento de Field contrário à afirmação de que a modalidade possa ser um substituto geral para a ontologia. Após opor-me a esse argumento, indico um quadro alternativo que esclarece as razões pelas quais a modalidade pode desempenhar esse papel.According to the indispensability argument, we ought to be ontologically committed to mathematical entities, given that they are indispensable to our best scientific theories. Hartry Field (1980) has famously resisted the argument, developing a program to reformulate scientific theories without quantification over mathematical objects. In particular, Field worked out in detail the nominalization of Newtonian gravitacional theory, indicating how the theory could be formulated without quantification over real numbers. Field also provided an argument why the use of modal operators doesn't providean adequate strategy to nominalize scientific theories. In this paper, I discuss Field's argument against the claim that modality can be a general surrogate for ontology. After resisting this argument, I indicate an alternative picture that makes it clear why modality can play such a role

Follow the Flow: sets, relations, and categories as special cases of functions with no domain

We introduce, develop, and apply a new approach for dealing with the intuitive notion of function, called Flow Theory. Within our framework all functions are monadic and none of them has any domain. Sets, proper classes, categories, functors, and even relations are special cases of functions. In this sense, functions in Flow are not equivalent to functions in ZFC. Nevertheless, we prove both ZFC and Category Theory are naturally immersed within Flow. Besides, our framework provides major advantages as a language for axiomatization of standard mathematical and physical theories. Russell's paradox is avoided without any equivalent to the Separation Scheme. Hierarchies of sets are obtained without any equivalent to the Power Set Axiom. And a clear principle of duality emerges from Flow, in a way which was not anticipated neither by Category Theory nor by standard set theories. Besides, there seems to be within Flow an identification not only with the common practice of doing mathematics (which is usually quite different from the ways proposed by logicians), but even with the common practice of teaching this formal science

Relación docente-discente en Enfermería y problemas en la formación para el Sistema Único de Salud

OBJETIVO: Investigar o processo ensino-aprendizado em uma Instituição de Ensino Superior da Região Norte do Brasil, com relação ao modelo pedagógico e a formação do enfermeiro para o Sistema Único de Saúde/ Programa de Saúde da Família (SUS/PSF). METODOS: Grupo focal e entrevistas individuais semi-estruturadas, com seis discentes do último período do curso investigado, analisadas através do marco teórico freireano e literatura do SUS/PSF, por hermenêutica dialética. RESULTADOS: Verticalidade na relação entre docentes e discentes, com falta de autonomia e silenciamento dos alunos, além de falta de articulação entre ensino e a prática do SUS/PSF. CONCLUSÃO: Há necessidade de reorientação do ensino em Enfermagem no curso investigado.OBJECTIVE: To describe the teaching and learning process of a pedagogical model to educate nurses for the Brazilian universal health care system / family health program (UHS/FHP) in use at a higher education institution in the north of Brazil. METHODS: Focus groups and individualized semi-structured interviews with 6 senior nursing students were used to collect the data. The education theory of Paulo Freire and the UHS/FHP literature guided this hermeneutic study. RESULTS: There was a vertical relationship between nursing faculty and students, a lack of autonomy among nursing students, a lack of power for articulation among nursing students, and a lack of articulation of nursing faculty regarding the relationship between the teaching and learning process and the nursing practice in the UHS/FHP. CONCLUSION: There is a need for re-orientation of the teaching and learning process of nursing at the institution studied.OBJETIVO: Investigar el proceso enseñanza-aprendizaje en una Institución de Enseñanza Superior de la Región Norte del Brasil, con relación al modelo pedagógico y la formación del enfermero para el Sistema Único de Salud/ Programa de Salud de la Familia (SUS/PSF). MÉTODOS: Se utilizaron Grupo focal y entrevistas individuales semi-estructuradas, con seis discentes del último período de la Institución investigada, cuyos datos fueron analizados a través del marco teórico freireano y literatura del SUS/PSF, por hermenéutica dialéctica RESULTADOS: Verticalidad en la relación entre docentes y discentes, con falta de autonomía y silenciamiento de los alumnos, además de falta de articulación entre enseñanza y práctica del SUS/PSF. CONCLUSIÓN: Hay necesidad de reorientación de la enseñanza en Enfermería en la Institución investigada

Making Sense of Non-Individuals in Quantum Mechanics

In this work, we focus on a very specific case study: assuming that quantum theories deal with “particles” of some kind (point particles in orthodox non-relativistic quantum mechanics, field excitations in quantum field theories), what kind of entity can such particles be? One possible answer, the one we shall examine here, is that they are not the usual kind of object found in daily life: individuals. Rather, we follow a suggestion by Erwin Schrödinger, according to which quantum mechanics poses a revolutionary kind of entity: non-individuals. While physics, as a scientific field, is not concerned with whether entities posited by a specific physical theory are individuals or not, answering this question is part of the quest for a better understanding of physical reality. Here lies, in large measure, the relevance of ontology

The Non-Individuals Interpretation of Quantum Mechanics

The non-individuals interpretation of quantum mechanics is presented with the aim of clarifying it and highflying some of its salient features. Alternative formulations of it are proposed and examined