Otávio Bueno

Typical accounts of reference demand that referring terms denote existent objects. This assumption is shared by theories across a variety of areas of philosophy, in particular, direct reference views in philosophy of language; neo-Fregean conceptions in the philosophy of mathematics, and easy-ontology approaches in metaphysics. In this paper, this assumption is resisted and the significance and the possibility of referring to the nonexistent is highlighted. After identifying difficulties in all these three theories and resisting a free-logic approach, ontologically neutral quantifiers, which do not require the existence of what is quantified over, are suggested as providing a better conception. It is concluded that the difficulties raised to the previous theories do not affect the ontologically neutral approach, while the approach, properly conceived, allows for nonexistent objects to have properties.

This comprehensive collection of original essays written by an international group of scholars addresses the central themes in Latin American philosophy. Represents the most comprehensive survey of historical and contemporary Latin American philosophy available today Comprises a specially commissioned collection of essays, many of them written by Latin American authors Examines the history of Latin American philosophy and its current issues, traces the development of the discipline, and offers biographical sketches of key Latin American thinkers Showcases the diversity of approaches, issues, and styles that characterize the field.

Proofs are central to mathematical practice in large part due to the heuristic role that some of them play. Not only do they help establish a result, but often provide new avenues of mathematical research. Jody Azzouni has argued that underlying the practice of creating mathematical proofs there is a very specific norm: to each proof there should be a corresponding algorithmic derivation, a derivation in an algorithmic system. Here a framework is provided to classify and assess mathematical proofs. It is argued that there is a plurality of kinds of proofs in mathematics and a plurality of roles these proofs play. In the end, mathematical practice is far less unified in this respect than it may seem to be.

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.

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.

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.

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..

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.