Otávio Bueno

Newton da Costa and Steven French have argued that the concept of partial truth plays an important role in our understanding of significant aspects of scientific practice: from the status of scientific theories through the understanding of inconsistency in science to the nature of induction (see da Costa and French 2003). In this paper, I use the concept of partial truth and the associated framework of partial structures to offer a formulation of the concept of visual evidence, and I examine some of the roles that this notion plays in scientific activity. DOI:10.5007/1808-1711.2011v15n2p249

In this paper, 1 examine the role of the delta function in Dirac’s formulation of quantum mechanics (QM), and I discuss, more generally, the role of mathematics in theory construction. It has been argued that mathematical theories play an indispensable role in physics, particularly in QM [Colyvan, M. (2001). The inrlispensability of mathematics. Oxford University Press: Oxford]. As I argue here, at least in the case of the delta function, Dirac was very clear about its rlispensability. I first discuss the significance of the delta function in Dirac’s work, and explore the strategy that he devised to overcome its use. l then argue that even if mathematical theories turned out to be indispensable, this wouidn’t justify the commitment to the existence of mathematical entities. In fact, even in successful uses of mathematics, such as in Dirac’s discovery of antimatter, there’s no need to believe in the existence of the corresponding mathematical entities. An interesting picture about the application of mathematics emerges from a careful examination of Dirac’s work.

Scientific representation: A long journey from pragmatics to pragmatics Content Type Journal Article DOI 10.1007/s11016-010-9465-5 Authors James Ladyman, Department of Philosophy, University of Bristol, 9 Woodland Rd, Bristol, BS8 1TB UK Otávio Bueno, Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA Mauricio Suárez, Department of Logic and Philosophy of Science, Complutense University of Madrid, 28040 Madrid, Spain Bas C. van Fraassen, Philosophy Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

Thirteen up-and-coming researchers in the philosophy of mathematics have been invited to write on what they take to be the right philosophical account of mathematics, examining along the way where they think the philosophy of mathematics is and ought to be going. A rich and diverse picture emerges. Some broader tendencies can nevertheless be detected: there is increasing attention to the practice, language and psychology of mathematics, a move to reassess the orthodoxy, as well as inspiration from philosophical logic.

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.

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field (with infinitesimals). Our approach was inspired by the work of Whitehead (1919), though our philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time

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.

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.

This paper is a historical companion to a previous one, in which it was studied the so-called abstract Galois theory as formulated by the Portuguese mathematician José Sebastião e Silva ). Our purpose is to present some applications of abstract Galois theory to higher-order model theory, to discuss Silva’s notion of expressibility and to outline a classical Galois theory that can be obtained inside the two versions of the abstract theory, those of Mark Krasner and of Silva. Some comments are made on the universal theory of structures

Michael Dummett, Frege and other philosophers. Oxford:Clarendon Press, 1991. xii + 330pp. £35. ISBN W.Balzer and C.U.Moulines, Structuralist theory of science:focal issues, new results, Berlin; de Gruyter, 1996. xi + 295 pp.DM 210. ISBN 3-11-014075-6 Henry Prakken, Logical tools for modeling legal argument a study of defeasible reasoning in law.Dordrecht, The Netherlands:Kluwer Academic, 1997, xiii + 314pp.£75.00/$125.00 J.Srzednicki and Z.Stachniak Lesniewski’s Systems.Protothetic.Nijhoff International Philosophy Series, 54, Dordrecht, Boston and London:Kluwer, 1998. xiv + 310 pp, £99. ISBN 0-7923-4504-5

Throughout the last two decades, Newton da Costa and his collaborators have developed some frameworks to help the interpretation of science. Two of them are particularly noteworthy: partial structures and quasi-truth (that provide a way of accommodating the openness and partiality of scientific activity), and quasi-set theory (that allows one to take seriously the idea, put forward by several physicists, that we can't meaningfully apply the notion of identity to quantum particles). In this paper I explore the interconnection between these two frameworks. After reviewing the extant formulations of quasi-truth and quasi-set theory, I suggest a way of combining them, advancing a formulation of quasi-truth in quasi-set theory. In this way, a good sense can be made of the idea that quantum mechanics, if not true, is at least quasi-true. I then explore an application of this combined framework, arguing that it provides a conceptual setting appropriate to overcome two (philosophical) difficulties in van Fraassen's modal interpretation of quantum mechanics.

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

This comprehensive collection of original essays written by aninternational group of scholars addresses the central themes inLatin American philosophy. Represents the most comprehensive survey of historical andcontemporary Latin American philosophy available today Comprises a specially commissioned collection of essays, manyof them written by Latin American authors Examines the history of Latin American philosophy and itscurrent issues, traces the development of the discipline, andoffers biographical sketches of key Latin American thinkers Showcases the diversity of approaches, issues, and styles thatcharacterize the field

In this paper we argue that there are no categories of being⎯at least not in the robust metaphysical sense of something fundamental. Central arguments that metaphysicians provide in support of fundamental categories, such as indispensability and theoretical utility arguments, are not adequate to guarantee their existence. We illustrate this point by examining Jonathan Lowe’s [2006] four-category ontology, and indicating its shortcomings. In contrast, we offer an alternative, no-category ontology, which dispenses with any fundamental categories of being, and provides a deflationary understanding of any categorization in terms of concepts. Concepts, we insist, as opposed to fundamental ontological categories, can always be revised, refined, and recast. A distinctive deflationary, no-category ontology then emerges

In this paper, I offer an inferential conception of computer simulations, emphasizing the role that simulations play as inferential devices to represent empirical phenomena. Three steps are involved in a simulation: an immersion step, a derivation step, and an interpretation and correction step. After presenting the view, I mention some cases, such as simulations of the current flow between silicon atoms and buckyballs as well as of genetic regulatory systems. I argue that the inferential conception accommodates the integration of empirical and theoretical data; it makes sense of the role that is played by false traits in a simulation, andhighlights the similarities and differences between simulations and scientific instruments.

Can a constructive empiricist make sense of scientific representation? Usually, a scientific model is an abstract entity, and scientific representation is conceptualized as an intentional relation between scientific models and certain aspects of the world. On this conception, since both the models and the representation relation are abstract, a constructive empiricist, who is not committed to the existence of abstract entities, would be unable to invoke these notions to make sense of scientific representation. In this paper, instead of understanding representation as a relation between abstract entities, I focus on the activity of representing, and argue that it provides a way of making sense of representation within the boundaries of empiricism. The activity of representing doesn’t deal with abstract entities, but with concrete ones, such as inscriptions, templates, and blueprints. In the end, by examining the practice of representing, rather than an artificially reified product—the representation—the constructive empiricist has the resources to make sense of scientific representation in empiricist terms.

A number of people have recently argued for a structural approach to accounting for the applications of mathematics. Such an approach has been called "the mapping account". According to this view, the applicability of mathematics is fully accounted for by appreciating the relevant structural similarities between the empirical system under study and the mathematics used in the investigation ofthat system. This account of applications requires the truth of applied mathematical assertions, but it does not require the existence of mathematical objects. In this paper, we discuss the shortcomings of this account, and show how these shortcomings can be overcome by a broader view of the application of mathematics: the inferential conception.