Latin American Philosophy of Science, Logic, and Mathematics

Latin America plays an increasingly important role in the development of modern Christianity yet it has been underrepresented in current scholarship on religion and science. In this first edited volume on the subject, contributors explore the different ways that religion and science relate to each other, how developments in natural science shaped religious views from the pre-Hispanic period until the nineteenth century and the current debates over evolution and creationism. It will appeal to those researching theology, divinity, philosophy, history of (...) science and Latin American studies. (shrink)

Las preguntas importantes, o que parecen importantes, no tienen por qué tener respuestas importantes, incluso no tienen por qué tener respuestas. Me propongo explorar qué respuestas, importantes o no importantes, puede recibir, si es que puede recibir alguna respuesta, la importante pregunta “¿qué es un buen argumento?”.Important questions, or questions that seem important, need not have important answers, moreover, they need not have answers at all. I propose to explore what answers, whether important or not, we could obtain, if some (...) answer can be obtained at all, to the important question “what is a good argument?”. (shrink)

Professor Bunge makes the distinction between the logical concept of existence and the ontological one. I agree with him and in this paper I am formalizing his existence predicate into the powerful language of type theory.I am also proving the logical equivalence of this for mulation with a briefer one, which says that to exist conceptually is the same as to be a conceptual object. Accordingly, from this point on I investigate what conceptual objects are. I reach the conclusion that (...) it is better to study a restricted area each time, where existence could even be assigned in different degrees. For instance, in set theory -like in Animal Farm of Orwell every set exists but so me “exist more” than others. Of course, in relating degrees of existence to degrees of definability I am not following Bunge. (shrink)

(No abstract is available for this citation).

Current versions of nominalism in the philosophy of mathematics have the benefit of avoiding commitment to the existence of mathematical objects. But this comes with the cost of not taking mathematical theories literally. Jody Azzouni's _Deflating Existential Consequence_ has recently challenged this conclusion by formulating a nominalist view that lacks this cost. In this paper, we argue that, as it stands, Azzouni's proposal does not yet succeed. It faces a dilemma to the effect that either the view is not nominalist (...) or it fails to take mathematics literally. After presenting the dilemma, we suggest a possible solution for the nominalist. (shrink)

Based on da Costa's and French's notions of partial structures and pragmatic truth, this paper examines two possible characterizations of the concept of empirical adequacy, one depending on the notion of partial isomorphism, the other on the hierarchy of partial models of phenomena, and both compatible with an empiricist view. These formulations can then be employed to illuminate certain aspects of scientific practice.An empirical theory must single out a specific part of the world, establish reference to that part, and say—by (...) way of contingent, substantial claim about the world—that its models fit that. Now, how exactly can this be done? Bas C. van Fraassen. (shrink)

1. EI dilema de Jørgensen. 2. La salución propuesta. 3. Breve historia de un prejudicio filosófico. 4. Normas sin lógica. 4.1. Imperativos sin lógica. 4.2. Normas y proposicienesnormativas. 4.3. Proposiciones normativas y normas verdaderas. 4.4. Mundos posibles. 4.5. Validez e invalidez. 4.6. La racionalidad del legislador. 5. La noción abstracta, sintáctica y semántica de consecuencia. 5.1. La noción abstracta de consecuencia. 5.2. La noción sintáctica de consecuencia. 5.3. La noción semántica de consecuencia. 5.4. EI sentido dado por las reglas de (...) uso en un contexto. 5.5. Qué operadores para la lógica. 5.6. Solo en un contexto la parte cobra sentido. 6. La lógica deóntica. 7. De donde la solución del dilema interesa a toda la lógica. 8. Consecuendas para la informática. (shrink)

Summary Opinion is divided as to whether chemistry is reducible to physics. The problem can be given a satisfactory solution provided three conditions are met: that a science not be identified with its theories; that several notions of theory dependence be distinguished; and that quantum chemistry, rather than classical chemistry, be compared with physics. This paper proposes to perform all three tasks. It does so by analyzing the methodological concepts concerned as well as by examining the way a chemical rate (...) constant is derivable with the help of the quantum atomic theory. The conclusion is that chemistry, and in particular quantum chemistry, is not a part of physics although it is certainly based on the latter. (shrink)

The central thesis of this paper is that physicists have as much to learn from scientifically oriented philosophy as philosophers have to learn from physics. To begin with, any discussion of basic physical ideas and procedures is bound to be conducted in the light of some philosophy or other. Now, the standard philosophy of physics of our century is operationism. And philosophers, with the help of recent developments in semantics, epistemology and the theory of scientific inference, have shown that operationism (...) is untenable. Thus most physicists are dragging a dead philosophy that may not be of any help in conceiving of new ideas and procedures. This, then, is a first contribution philosophy can make to physics, namely to overhaul its philosophy. A second contribution is to the organization of physics, in particular to the axiomatic reconstruction of physical theories and the analysis and validation of empirical procedures. The various theses and antitheses discussed in the article are illustrated with examples taken from contemporary physics. (shrink)

According to the semantic view, a theory is characterized by a class of models. In this paper, we examine critically some of the assumptions that underlie this approach. First, we recall that models are models of something. Thus we cannot leave completely aside the axiomatization of the theories under consideration, nor can we ignore the metamathematics used to elaborate these models, for changes in the metamathematics often impose restrictions on the resulting models. Second, based on a parallel between van Fraassen’s (...) modal interpretation of quantum mechanics and Skolem’s relativism regarding set-theoretic concepts, we introduce a distinction between relative and absolute concepts in the context of the models of a scientific theory. And we discuss the significance of that distinction. Finally, by focusing on contemporary particle physics, we raise the question: since there is no general accepted unification of the parts of the standard model (namely, QED and QCD), we have no theory, in the usual sense of the term. This poses a difficulty: if there is no theory, how can we speak of its models? What are the latter models of? We conclude by noting that it is unclear that the semantic view can be applied to contemporary physical theories. (shrink)