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.

In this paper, I argue that symmetry principles in physics (in particular, in quantum mechanics) have a methodological character, rather than an ontological or an epistemological one. First, I provide a framework to address three related issues regarding the notion of symmetry: (i) how the notion can be characterized; (ii) one way of discussing the nature of symmetry principles, and (iii) a tentative account of some types of symmetry in physics. To illustrate how the framework functions, I then consider the case of the early formulation of quantum mechanics, examining the different roles played by symmetry in this context. Finally, I raise difficulties for ontological and purely episte.

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.

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.

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.

Mathematical concepts play at least three roles in the application of mathematics: an inferential role, a representational role, and an expressive role. In this paper, I argue that, despite what has often been alleged, platonists do not fully accommodate these features of the application of mathematics. At best, platonism provides partial ways of handling the issues. I then sketch an alternative, anti-realist account of the application of mathematics, and argue that this account manages to accommodate these features of the application process. In this way, a better account of mathematical applications is, in principle, available.

In this paper, I provide an account of scientific representation that makes sense of the notion both at the nanoscale and at the quantum level: the partial mappings account. The account offers an extension of a proposal developed by R. I. G. Hughes in terms of denotation, demonstration, and interpretation (DDI). I first argue that the DDI account needs some amendments to accommodate representation of nano and quantum phenomena. I then introduce a generalized framework with the notions of unsharp denotation, unsharp interpretation, and partial mappings. I conclude by arguing that the resulting view not only accommodates nano and quantum representations but also makes sense of representation by imaging in (scanning tunneling) microscopy.

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

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. 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.

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.

As part of the development of an epistemology for mathematics, some Platonists have defended the view that we have (i) intuition that certain mathematical principles hold, and (ii) intuition of the properties of some mathematical objects. In this paper, I discuss some difficulties that this view faces to accommodate some salient features of mathematical practice. I then offer an alternative, agnostic nominalist proposal in which, despite the role played by mathematical intuition, these difficulties do not emerge.

Descartes seems to hold two inconsistent accounts of the ontological status of mathematical essences. Meditation Five apparently develops a platonist view about such essences, while the Principles seems to advocate some form of “conceptualism”. We argue that Descartes was neither a platonist nor a conceptualist. Crucial to our interpretation is Descartes’ dispositional nativism. We contend that his doctrine of innate ideas allows him to endorse a hybrid view which avoids the drawbacks of Gassendi’s conceptualism without facing the difficulties of platonism. We call this hybrid view “quasi-platonism.” Our interpretation explains Descartes’ account of the nature of mathematical essences, dissolves the tension between the two texts, and highlights the benefits of Descartes’ view.