Otávio Bueno

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed.

In this paper, I develop a new defense of logicism: one that combines logicism and nominalism. First, I defend the logicist approach from recent criticisms; in particular from the charge that a cruciai principie in the logicist reconstruction of arithmetic, Hume's Principle, is not analytic. In order to do that, I argue, it is crucial to understand the overall logicist approach as a nominalist view. I then indicate a way of extending the nominalist logicist approach beyond arithmetic. Finally, I argue that a nominalist can use the resulting approach to provide a nominalization strategy for mathematics. In this way, mathematical structures can be introduced without ontological costs. And so, if this proposal is correct, we can say that ultimately all the nominalist needs is logic (and, rather loosely, ali the logicist needs is nominalism)

Scientific change has two important dimensions: conceptual change and structural change. In this paper, I argue that the existence of conceptual change brings serious difficulties for scientific realism, and the existence of structural change makes structural realism look quite implausible. I then sketch an alternative account of scientific change, in terms of partial structures, that accommodates both conceptual and structural changes. The proposal, however, is not realist, and supports a structuralist version of van Fraassen’s constructive empiricism (structural empiricism).

The aim of this paper is to provide a unified account of scientific and mathematical change in a thoroughly empiricist setting. After providing a formal modelling in terms of embedding, and criticising it for being too restrictive, a second modelling is advanced. It generalises the first, providing a more open-ended pattern of theory development, and is articulated in terms of da Costa and French's partial structures approach. The crucial component of scientific and mathematical change is spelled out in terms of partial embeddings. Finally, an application of this second pattern is made, with the examination of the early formulation of set theory.

Ask a philosopher what a proof is, and you’re likely to get an answer hii empaszng one or another regimentationl of that notion in terms of a finite sequence of formalized statements, each of which is either an axiom or is derived from an axiom by certain inference rules. (Wecan call this the formal conception of proof) Ask a mathematician what a proof is, and you will rbbl poay get a different-looking answer. Instead of stressing a partic- l uar regimented notion of proof, the answer the mathematician will give ilikl..

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.

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.

In a recent debate, Eric Drexler and Richard Smalley have discussed the chemical and physical possibility of constructing molecular assemblers - devices that guide chemical reactions by placing, with atomic precision, reactive molecules. Drexler insisted on the mechanical feasibility of such assemblers, whereas Smalley resisted the idea that such devices could be chemically constructed, because we do not have the required control. Underlying the debate, there are differences regarding the appropriate goals, methods, and theories of nanotechnology, and the appropriate way of conceptualizing molecular assemblers. Not surprisingly, incommensurability emerges. In this paper, I assess the main features of the debate, the levels of the emerging incommensurability, and indicate one way in which the debate could be decided.

Styles of reasoning are important devices to understand scientific practice. As I use the concept, a style of reasoning is a pattern of inferential relations that are used to select, interpret, and support evidence for scientific results. In this paper, I defend the view that there is a plurality of styles of reasoning: different domains of science often invoke different styles. I argue that this plurality is an important source of disunity in scientific practice, and it provides additional arguments in support of the disunity claim. I also contrast Ian Hacking’s broad characterization of styles of reasoning with a narrow understanding that I favor. Drawing on examples from molecular biology, chemistry and mathematics, I argue that differences in style of reasoning lead to differences in the way the relevant results are obtained and interpreted. The result is a pluralist view about styles of reasoning that is sensitive to nuances of inferential relations in scientific activity.

In this paper, we provide a new formulation of a coherence theory of truth using the resources of the partial structures approach − in particular the notions of partial structure and quasi-truth. After developing this new formulation, we apply the resulting theory to the philosophy of mathematics, and argue that it can be used to develop a new account of nominalism in mathematics. This application illustrates the strength and usefulness of the proposed formulation of a coherence theory of truth.Neste artigo, propomos uma nova formulação de uma teoria coerentista da verdade utilizando os recursos da abordagem de estruturas parciais - em particular as noções de estrutura parcial e quase-verdade. Após desenvolver esta formulação, aplicamos a teoria resultante à filosofia da matemática, e argumentamos que aquela pode ser usada para desenvolver um novo tratamento do nominalismo na matemática. Esta aplicação ilustra a força e utilidade da formulação proposta de uma teoria coerentista da verdade.

Pyrrhonists provide a way of investigating the world in which conflicting views about a given topic are critically compared, assessed, and juxtaposed. Since Pyrrhonists are ultimately unable to decide between these views, they end up suspending judgment about the issues under examination. In this paper, I consider the question of whether Pyrrhonists can be realists or anti-realists about science, focusing, in particular, on contemporary philosophical discussions about it. Althoughprima faciethe answer seems to be negative, I argue that if realism and anti-realism are understood as philosophical stances rather than particular doctrines—that is, if they are conceptualized in terms of a mode of engagement, a style of reasoning, and some propositional attitudes—the apparent tension between Pyrrhonism, realism, and anti-realism vanishes. The result is a first step in the direction of bringing Pyrrhonism to bear on contemporary debates in the philosophy of science.

A first step is taken towards articulating a constructive empiricist philosophy of mathematics, thus extending van Fraassen's account to this domain. In order to do so, I adapt Field's nominalization program, making it compatible with an empiricist stance. Two changes are introduced: (a) Instead of taking conservativeness as the norm of mathematics, the empiricist countenances the weaker notion of quasi-truth (as formulated by da Costa and French), from which the formal properties of conservativeness are derived; (b) Instead of quantifying over spacetime regions, the empiricist only admits quantification over occupied regions, since this is enough for his or her needs.

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

Perceptual experiences provide an important source of information about the world. It is clear that having the capacity of undergoing such experiences yields an evolutionary advantage. But why should humans have developed not only the ability of simply seeing, but also of seeing that something is thus and so? In this paper, I explore the significance of distinguishing perception from conception for the development of the kind of minds that creatures such as humans typically have. As will become clear, it is crucial to pay careful attention to the different kinds of information that are involved in perceiving and conceiving (including the way such information is gathered and transmitted). By identifying such kinds of information and the role they play, we can then understand an important feature of why creatures like us have the kind of consciousness and mental processes we do.

One important role of belief systems is to allow us to represent information about a certain domain of inquiry. This paper presents a formal framework to accommodate such information representation. Three cognitive models to represent information are discussed: conceptual spaces, state-spaces, and the problem spaces familiar from artificial intelligence. After indicating their weakness to deal with partial information, it is argued that an alternative, formulated in terms of partial structures, can be provided which not only captures the positive features of these models, but also accommodates the partiality of information ubiquitous in science and mathematics.