Latin American Philosophy of Science, Logic, and Mathematics

Entre las figuras que hicieron de parteaguas para la filosofía en México después del exilio español de fines de los años treinta, una cuya importancia está todavía por conocerse y difundirse es la de Eduardo Nicol, que murió apenas en 1990. Su amplia obra intelectual se articula durante alrededor de cincuenta años. En las siguientes líneas se recogen pasajes de dos capítulos que forman parte de Ideas de vario linaje, y que revelan ciertos trazos del pensamiento del pensador catalán, pertinentes (...) para la situación actual de la cultura. (shrink)

Le réalisme scientifique occupe une place centrale dans le système philosophique de Mario Bunge. Au cœur de cette thèse, on trouve l’affirmation selon laquelle nous pouvons connaître le monde partiellement. Il s’ensuit que les théories scientifiques ne sont pas totalement vraies ou totalement fausses, mais plutôt partiellement vraies et partiellement fausses. Ces énoncés sur la connaissance scientifique, à première vue plausible pour quiconque est familier avec la pratique scientifique, demandent néanmoins à être clarifiés, précisés et, ultimement, à être inclus dans (...) un cadre théorique plus large et rigoureux. Depuis ses toutes premières publications sur ces questions et jusqu’à récemment, Mario Bunge n’a cessé d’interpeller les philosophes afin qu’ils développent une théorie, au sens propre du terme, de la vérité partielle afin de clarifier les enjeux épistémologiques liés au réalisme scientifique. Bunge a lui-même proposé plusieurs parties de cette théorie au fil des années, mais aucune de ces propositions ne l’a satisfait pleinement et la construction de cette théorie demeure un problème entier. Dans ce texte, nous passerons rapidement en revue certaines des approches proposées par Bunge dans ses publications et nous esquisserons certaines pistes qui devraient servir à tout le moins de desiderata pour la construction d’une théorie de la vérité partielle. (shrink)

The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent object-theoretic versions of the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory in the definition of worlds. Next the authors show that an (...) object-theoretic analysis of the Kaplan paradox reveals that there is no genuine paradox at all, as the central premise of the paradox is simply a logical falsehood and hence can be rejected on the strongest possible grounds—not only in object theory but for the very framework of propositional modal logic in which Kaplan frames his argument. The authors close by fending off a possible objection that object theory avoids the Russell paradox only by refusing to incorporate set theory and, hence, that the object-theoretic solution is only a consequence of the theory’s weakness. (shrink)

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)

Nominalism and the application of mathematics Content Type Journal Article Category Book Review Pages 1-4 DOI 10.1007/s11016-012-9653-6 Authors Otávio Bueno, Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

We argue that standard definitions of ‘vagueness’ prejudice the question of how best to deal with the phenomenon of vagueness. In particular, the usual understanding of ‘vagueness’ in terms of borderline cases, where the latter are thought of as truth-value gaps, begs the question against the subvaluational approach. According to this latter approach, borderline cases are inconsistent (i.e., glutty not gappy). We suggest that a definition of ‘vagueness’ should be general enough to accommodate any genuine contender in the debate over (...) how to best deal with the sorites paradox. Moreover, a definition of ‘vagueness’ must be able to accommodate the variety of forms sorites arguments can take. These include numerical, total-ordered sorites arguments, discrete versions, continuous versions, as well as others without any obvious metric structure at all. After considering the shortcomings of various definitions of ‘vagueness’, we propose a very general non-question-begging definition. (shrink)

Batterman raises a number of concerns for the inferential conception of the applicability of mathematics advocated by Bueno and Colyvan. Here, we distinguish the various concerns, and indicate how they can be assuaged by paying attention to the nature of the mappings involved and emphasizing the significance of interpretation in this context. We also indicate how this conception can accommodate the examples that Batterman draws upon in his critique. Our conclusion is that ‘asymptotic reasoning’ can be straightforwardly accommodated within the (...) inferential conception. 1 Introduction2 Immersion, Inference and Partial Structures3 Idealization and Surplus Structure4 Renormalization and the Stability of Mathematical Representations5 Explanation and Eliminability6 Requirements for Explanation7 Interpretation and Idealization8 Explanation, Empirical Regularities and the Inferential Conception9 Conclusion. (shrink)

After presenting a brief history of philosophy in Hispanic-America since the XVI century, we discuss whether the idea of province and empire is applicable to contemporary Hispanic-American philosophy, investigate the form these ideas adopt in this region, and inquire into the ways in which provincialism i s present in philosophical work. We conclude that there are three main groups that understand their peripheral position in different ways, with different views on the way in which they should insert into the mainstream (...) of Western philosophy. (shrink)

El presente trabajo de Alex Ibarra Peña recoge los resultados de una investigación cuyo tema es la constitución de un campo de estudios ligado a la filosofía analítica en Chile. El autor se propone una tarea informativa y crítica en la que cifra la novedad de su propuesta. En otros términos, la suya es una labor de rescate, de algunos filósofos y corrientes de pensamiento relegados en las narraciones hegemónicas de la institucionalización de la filosofía en Chile y una tarea (...) que busca corregir el papel asignado a Chile en las visiones panorámicas de mayor circulación sobre la emergencia de la filosofía analítica en nuestro continente. En el cruce de estos dos vectores radica la novedad de la empresa de Ibarra Peña: proponer una visión más ajustada de la recepción de los filósofos analíticos en Chile. En nuestra reseña comentamos los núcleos centrales del trabajo y proponemos algunas hiótesis sobre los conflictos internos al campo cultural que subyacen a las opciones realizadas por el autor. Para finalizar indicamos lo que nos parece ser una falencia del trabajo: un estudio de la constitución de la filosofía analística como campo de estudios no debería dejar de tener en cuenta que el énfasis en la delimitación de la cientificidad por la filosofía analítica tenía en los años 60 y 70 adversarios concretos en el marxismo y el psicoanálisis. (shrink)

Continúa mi primer escrito: "Darwinlandia". España no es darwinista. Un planeta para las variaciones. El darwinismo crítico de Bunge. El darwinismo de derechas de Pinker. Los enfermos contra el darwinismo.

As an illustration of the complexities involved in connecting physics and molecular biology at the nanoscale, in this paper I discuss two case studies from nanoscience. The first examines the use of a biological structure to build nanostructures in a controlled way. The second discusses the attempt to build a single molecular wire, and then decide whether such a wire is indeed conducting. After presenting the central features of each case study, I examine the role played in them by microscopic (...) imaging, the different styles of reasoning involved, and the various theoretical, methodological, and axiological differences. I conclude by arguing that, except for the probe microscopes that are used, there is very little in common between the two cases. At the nanoscale, physics and molecular biology seem to meet in a non-unified way. (shrink)

(No abstract is available for this citation).

This article argues that ethics and spirituality are therefore interdependent. One cannot be practiced without paying attention to the other. One needs to be shaped and informed by the other. This article intends to support this claim by briefly using the book and story of the Old Testament prophet Amos. Here, a brief but fair description and definition of postmodernity is provided in order to prepare the ground for an examination, discussion, and reflection of the interdependency of ethics and spirituality (...) rooted in the book of Amos. This is followed by a description and discussion of the several principles or issues that are pertinent to address and attend to the interdependency between ethics and spirituality as it relates the story of the Old Testament Amos. Principles and issues are grounded the author’s perspective and experiences of the reality of the Hispanic Latin-American/Hispanic Pentecostal Church. The author is speaking and writing as a Puerto Rican – from which fairly or unfairly many assertions, statements, and conclusions that may or may not apply to the entire Hispanic/Latino(a) context are gathered. Critical and reflective thoughts conclude this article. (shrink)

__Forging People __explores the way in which Hispanic American thinkers in Latin America and Latino/a philosophers in the United States have posed and thought about questions of race, ethnicity, and nationality, and how they have interpreted the most significant racial and ethnic labels used in Hispanic America in connection with issues of rights, nationalism, power, and identity. Following the first introductory chapter, each of the essays addresses one or more influential thinkers, ranging from Bartolomé de Las Casas on race and (...) the rights of Amerindians; to Simon Bolívar's struggle with questions of how to forge a nation from disparate populations; to modern and contemporary thinkers on issues of race, unity, assimilation, and diversity. Each essay carefully and clearly presents the views of key authors in their historical and philosophical context and provides brief biographical sketches and reading lists, as aids to students and other readers. “Latin American philosophy has a long history of engagement with issues of race, ethnicity, and nationality. To date, however, there has been no volume that focused on the contributions of the major figures in the Latin American tradition, to illustrate their connections, and to illuminate the context in which much of their work occurred. This volume fills that gap and takes an important step in remedying this shortcoming in the existing philosophical literature, and also in the literature of related fields such as Latin American studies, ethnic studies, and the cross-disciplinary work of race, ethnicity, and nationality.” —_Manuel Vargas, University of San Francisco _. (shrink)

En esta nota crítica (i) se hace una breve descripción de cada uno de los artículos que componen Orayen: de la forma lógica al significado, (ii) se señalan algunas cuestiones que no están claras en ellos o en las réplicas de Orayen y, (iii) en la medida de lo posible, se indica si los autores desarrollan ulteriormente los problemas abordados en sus artículos. The aim of this critical note is threefold: (i) it briefly describes and comments on each of the (...) articles of Orayen: de la forma lógica al significado; (ii) identifies some issues that may not be clear enough or not fully developed whether in the articles or even in Orayen's replies; (iii) as far as possible, it refers to further studies made by the authors themselves on the same, or quite related, subjects addressed by them in their papers. (shrink)

In this paper we show that any reasoning process in which conclusions can be both fallible and corrigible can be formalized in terms of two approaches: (i) syntactically, with the use of defeasible reasoning, according to which reasoning consists in the construction and assessment of arguments for and against a given claim, and (ii) semantically, with the use of partial structures, which allow for the representation of less than conclusive information. We are particularly interested in the formalization of scientific reasoning, (...) along the lines traced by Lakatos’ methodology of scientific research programs. We show how current debates in cosmology could be put into this framework, shedding light on a very controversial topic. (shrink)

Second-order logic has a number of attractive features, in particular the strong expressive resources it offers, and the possibility of articulating categorical mathematical theories (such as arithmetic and analysis). But it also has its costs. Five major charges have been launched against second-order logic: (1) It is not axiomatizable; as opposed to first-order logic, it is inherently incomplete. (2) It also has several semantics, and there is no criterion to choose between them (Putnam, J Symbol Logic 45:464–482, 1980 ). Therefore, (...) it is not clear how this logic should be interpreted. (3) Second-order logic also has strong ontological commitments: (a) it is ontologically committed to classes (Resnik, J Phil 85:75–87, 1988 ), and (b) according to Quine (Philosophy of logic, Prentice-Hall: Englewood Cliffs, 1970 ), it is nothing more than “set theory in sheep’s clothing”. (4) It is also not better than its first-order counterpart, in the following sense: if first-order logic does not characterize adequately mathematical systems, given the existence of non - isomorphic first-order interpretations, second-order logic does not characterize them either, given the existence of different interpretations of second-order theories (Melia, Analysis 55:127–134, 1995 ). (5) Finally, as opposed to what is claimed by defenders of second-order logic [such as Shapiro (J Symbol Logic 50:714–742, 1985 )], this logic does not solve the problem of referential access to mathematical objects (Azzouni, Metaphysical myths, mathematical practice: the logic and epistemology of the exact sciences, Cambridge University Press, Cambridge, 1994 ). In this paper, I argue that the second-order theorist can solve each of these difficulties. As a result, second-order logic provides the benefits of a rich framework without the associated costs. (shrink)

Abstract: According to Luciano Floridi (2008) , informational structural realism provides a framework to reconcile the two main versions of realism about structure: the epistemic formulation (according to which all we can know is structure) and the ontic version (according to which structure is all there is). The reconciliation is achieved by introducing suitable levels of abstraction and by articulating a conception of structural objects in information-theoretic terms. In this essay, I argue that the proposed reconciliation works at the expense (...) of realism. I then propose an alternative framework, in terms of partial structures, that offers a way of combining information and structure in a realist setting while still preserving the distinctive features of the two formulations of structural realism. Suitably interpreted, the proposed framework also makes room for an empiricist form of informational structuralism (structural empiricism). Pluralism then emerges. (shrink)

The design, maintenance and use of all measuring instruments involve indicators of the thing, property, or event they are expected to detect or measure. And every quantitative indicator is a functional relation between imperceptible and perceptible facts—for example, the “flow” of time and the rotation of a watch’s hands. The empirical test of any quantitative hypothesis involves the translation of the unobservable variables occurring in it into the observable variable(s) in the indicator hypothesis. Yet, indicators have escaped the notice of (...) nearly all philosophers of science—a fact that may indicate unfamiliarity with laboratory work. (shrink)

Nos daremos a la tarea de presentar una discusión que se encuentra en la obra del filósofo colombiano Julio Enrique Blanco, y en particular en dos de sus primeros escritos: “De la causalidad biológica I” (1917) y “Caminos de perfección” (1918). Para hacerlo debimos primero recurrir a uno de los textos centrales del inglés John Stuart Mill: Un sistema de lógica (1843). Lo que ha resultado de estas tres lecturas es la reconstrucción de una propuesta metodológica realizada por el colombiano, (...) propuesta que presentamos con complementos que son el resultado de las lecturas de éstas y otras obras suyas. Finalmente, intentaremos demostrar que ante la evaluación de los fundamentos cognoscitivos de nociones heredadas, una de las posibilidades que se presenta es inmovilizar aquellas que sean de carácter hipotético antes que hipertético. (shrink)

In spite of the ‘experimental turn’ now fashionable in the philosophy of science, the question of the structure and identity criteria of scientific theories continues to be a central issue for the philosophical analysis of empirical science. We need a precise metatheory of empirical theories to deal with this issue. Metatheoretical structuralism appears to offer the most adequate approach in this sense so far. First, some basic intuitions about what empirical theories are, and how they are structured, are laid out. (...) Then, the main notions used by metatheoretical structuralism to analyze theories are explained, and they are illustrated by applying them to an example of a simple physical theory. Finally, it is argued that the picture of the structure and identity of empirical theories coming out of structuralistic analysis adequately corresponds to the basic intuitions stated at the beginning. (shrink)

This volume contains the most extensive exposition of Latin American philosophy to date. I know of no other comparable anthology on the subject in any language. The width of its scope is quite impressive. At least for this reason, and whatever its shortcomings might be (to some of them I’ll come to speak below), it is a welcome collective work.

There is very little study of Latin American Philosophy in the English-speaking philosophical world. This can sometimes lead to the impression that there is nothing of philosophical worth in Latin American philosophy or its history. The present article offers some reasons for thinking that this impression is mistaken, and indeed, that we ought to have more study of Latin American philosophy than currently exists in the English-speaking philosophical world. In particular, the article argues for three things: (1) an account of (...) cultural resources that is useful for illuminating the fact of cultural differences and variations in cultural complexity, (2) a framework for understanding the value of philosophy, and (3) the conclusion that there is demonstrable value to Latin American philosophy and its study. (shrink)

Abstract: Ernest Sosa has recently articulated an insightful response to skepticism and, in particular, to the dream argument. The response relies on two independent moves. First, Sosa offers the imagination model of dreaming according to which no assertions are ever made in dreams and no beliefs are involved there. As a result, it is possible to distinguish dreaming from being awake, and the dream argument is blocked. Second, Sosa develops a virtue epistemology according to which in appropriately normal conditions our (...) perceptual beliefs will be apt. Hence, in these conditions, we will have at least animal knowledge, and the conclusion of the dream argument is undermined. In this article, I examine various moves that the skeptic can make to resist Sosa's challenge, and I contrast the proposal to a neo-Pyrrhonian stance. In the end, there is surprisingly little disagreement about the status of ordinary perceptual beliefs in the two stances. (shrink)

The aim of this paper is to describe the situation of mutual ignorance between American and Hispanic philosophical traditions, paying special attention to the figure and thought of the founder of pragmatism, Charles S. Peirce (1839-1914). In order to do this, first of all I will justify the usage of the expression "Hispanic Philosophy", highlighting its heuristic and practical value. Secondly, I will discuss some of Peirce's comments in relation with the Hispanic world. And finally, by way of conclusion, I (...) will mention some of the connections that lie nearly hidden under the cloak of ignorance which divides the two traditions. (shrink)

Current versions of nominalism in the philosophy of mathematics face a significant problem to understand mathematical knowledge. They are unable to characterize mathematical knowledge as knowledge of the objects mathematical theories are taken to be about. Oswaldo Chateaubriand’s insightful reformulation of Platonism (Chateaubriand 2005) avoids this problem by advancing a broader conception of knowledge as justified truth beyond a reasonable doubt, and by introducing a suitable characterization of logical form in which the relevant mathematical facts play an important role in (...) the truth of the corresponding mathematical propositions. In this paper, I contrast Chateaubriand’s proposal with an agnostic form of nominalism that is able to accommodate mathematical knowledge without the commitment to mathematical facts. (shrink)