Otávio Bueno

Central to the philosophical understanding of music is the status of musical works. According to the Platonist, musical works are abstract objects; that is, they are not located in space or time, and we have no causal access to them. Moreover, only a particular physical occurrence of these musical works is instantiated when a performance ofthe latter takes place. But even if no performance ever took place, the Platonist insists, the musical work would still exist, since its existence is not tied to spatiotemporal constraints (Kivy [1993], and Dodd [2007]). In this paper, I offer a critical assessment of the Platonist view. I argue that, despite some benefits, Platonism faces significant difficulties in the interpretation of music. In spite ofthe Platonist’s attempt to overcome the problem, the view ultimately doesn’t mesh well with the way we actively respond to performances and fail to respond, in any way similar, to abstract patterns. Platonism also makes knowledge of music something extremely mysterious, given that we have no access to the abstract objects that, according to the Platonist, characterize the musical works. The ability to understand how we respond to musical works is, of course, central to any interpretation of music. This ability is also crucial in explaining the role music plays in various aspects of our culture, Rom bounding with others to music therapy. Given the problems faced by Platonism, it makes more sense to adopt an altemative, non-Platonist view. I conclude the paper by sketching such a non-Platonist proposal.

According to Luciano Floridi (2008), informational structural realism provides a framework to reconcile the two main versions of realism about structure: the epistemic formulation (according to which all we can know is structure) and the ontic version (according to which structure is all there is). The reconciliation is achieved by introducing suitable levels of abstraction and by articulating a conception of structural objects in information-theoretic terms. In this essay, I argue that the proposed reconciliation works at the expense of realism. I then propose an alternative framework, in terms of partial structures, that offers a way of combining information and structure in a realist setting while still preserving the distinctive features of the two formulations of structural realism. Suitably interpreted, the proposed framework also makes room for an empiricist form of informational structuralism (structural empiricism). Pluralism then emerges.

Ontic Structural Realism is a version of realism about science according to which by positing the existence of structures, understood as basic components of reality, one can resolve central difficulties faced by standard versions of scientific realism. Structures are invoked to respond to two important challenges: one posed by the pessimist meta-induction and the other by the underdetermination of metaphysics by physics, which arises in non-relativistic quantum mechanics. We argue that difficulties in the proper understanding of what a structure is undermines the realist component of the view. Given the difficulties, either realism should be dropped or additional metaphysical components not fully endorsed by science should be incorporated.

Quine has famously put forward the indispensability argument to force belief in the existence of mathematical objects (such as classes) due to their indispensability to our best theories of the world (Quine 1960). Quine has also advocated the indeterminacy of reference argument, according to which reference is dramatically indeterminate: given a language, there’s no unique reference relation for that language (see Quine 1969a). In this paper, I argue that these two arguments are in conflict with each other. Whereas the indispensability argument supports realism about mathematics, the indeterminacy of reference argument, when applied to mathematics, provides a powerful strategy in support of mathematical anti-realism. I conclude the paper by indicating why the indeterminacy of reference phenomenon should be preferred over the considerations regarding indispensability. In the end, even the Quinean shouldn’t be a realist (platonist) about mathematics.

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.

We examine, from the partial structures perspective, two forms of applicability of mathematics: at the “bottom” level, the applicability of theoretical structures to the “appearances”, and at the “top” level, the applicability of mathematical to physical theories. We argue that, to accommodate these two forms of applicability, the partial structures approach needs to be extended to include a notion of “partial homomorphism”. As a case study, we present London's analysis of the superfluid behavior of liquid helium in terms of Bose‐Einstein statistics. This involved both the introduction of group theory at the top level, and some modeling at the “phenomenological” level, and thus provides a nice example of the relationships we are interested in. We conclude with a discussion of the “autonomy” of London's model.

In this paper a constructive empiricist account of scientific change is put forward. Based on da Costa's and French's partial structures approach, two notions of empirical adequacy are initially advanced (with particular emphasis on the introduction of degrees of empirical adequacy). Using these notions, it is shown how both the informativeness and the empirical adequacy requirements of an empiricist theory of scientific change can then be met. Finally, some philosophical consequences with regard to the role of structures in this context are drawn.Now, we daily see what science is doing for us. This could not be unless it taught us something about reality; the aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relations between things; outside those relations there is no reality knowable.

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..

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.

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.

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.