Otávio Bueno

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.

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, 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.

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.

Logical pluralism is the view according to which there is more than one relation of logical consequence, even within a given language. A recent articulation of this view has been developed in terms of quantification over different cases: classical logic emerges from consistent and complete cases; constructive logic from consistent and incomplete cases, and paraconsistent logic from inconsistent and complete cases. We argue that this formulation causes pluralism to collapse into either logical nihilism or logical universalism. In its place, we propose a modalist account of logical pluralism that is independently well motivated and that avoids these collapses.

One major motivation for nominalism, at least according to Hartry Field, is the desirability of intrinsic explanations: explanations that don’t invoke objects that are causally irrelevant to the phenomena being explained. There is something right about the search for such explanations. But that search must be carefully implemented. Nothing is gained if, to avoid a certain class of objects, one only introduces other objects and relations that are just as nominalistically questionable. We will argue that this is the case for two alleged nominalist views: Field’s fictionalism, and Frank Arntzenius and Cian Dorr’s geometricalism. Central to our competing approach to nominalism is a distinction between terms that refer to objects and ones that instead code empirical phenomena while being referentially empty. We next contrast our approach to nominalism, which uses this term-grained distinction between coding and referring, with approaches that instead attempt to make a sentence-grained distinction between mathematical and non-mathematical content. We show the latter approach fails to be responsive to objections raised by van Fraassen. In the end, only one last approach to nominalism is left standing. 1 Introduction2 Troubles for Mathematical Fictionalism2.1 A distinction2.2 Field’s programme2.3 Parts of nominalistically acceptable entities are nominalistically acceptable2.4 Structural assumptions: How far can these be pushed?2.5 Cases of indispensable theories where the mathematical posits are known not to be real2.6 How does science distinguish between the indispensable structural presuppositions taken to be real and those that aren’t?2.7 Do physicists distinguish between mathematical posits and non-mathematical posits?2.8 Mathematical coding versus genuine metaphysics. Case study: Fields2.9 The upshot3 Troubles for Topologism4 Contrasts: Kitcher, Maddy, Sober, and van Fraassen4.1 Sober’s approach4.2 Maddy’s approach4.3 Kitcher’s approach4.4 Where do we go from here?4.5 Van Fraassen’s objection to Maddy’s approach to ontological commitment5 Conclusion.

This paper provides a rationale for advocating pancritical rationalism. First, it argues that the advocate of critical rationalism may accept (but not be internally justified in accepting) that there is ‘justification’ in an externalist sense, specifically that certain procedures can track truth, and suggest that this recognition should inform practice; that one should try to determine which sources and methods are appropriate for various aspects of inquiry, and to what extent they are. Second, it argues that if there is external justification, then a critical rationalist is better off than a dogmatist from an evolutionary perspective.

The aim of this paper is two-fold: (1) To contribute to a better knowledge of the method of the Argentinean mathematicians Lia Oubifia and Jorge Bosch to formulate category theory independently of set theory. This method suggests a new ontology of mathematical objects, and has a profound philosophical significance (the underlying logic of the resulting category theory is classical iirst—order predicate calculus with equality). (2) To show in outline how the Oubina-Bosch theory can be modified to give rise to a strong paraconsistent category theory; strong enough to be taken as the basis for a paraconsistent mathematics which encompasses all classical mathematical results

In this paper, I shall discuss the heuristic role of symmetry in the mathematical formulation of quantum mechanics. I shall first set out the scene in terms of Bas van Fraassen’s elegant presentation of how symmetry principles can be used as problem-solving devices (see van Fraassen [1989] and [1991]). I will then examine in what ways Hermann Weyl and John von Neumann have used symmetry principles in their work as a crucial problem-solving tool. Finally, I shall explore one consequence of this situation to recent debates about structural realism (SR) and empiricism in physics (Worrall [1989], Ladyman [1998], and French [1999]).