Skepticism and naturalism bear important connections with one another. Do they conflict or are they different sides of the same coin? In this paper, by considering the ways in which Sextus and Hume have examined these issues, I offer a Pyrrhonian response to Penelope Maddy's attempt to reject skepticism within the form of naturalism that she calls “second philosophy” (Maddy, 2007, 2017) and to Timothy Williamson's attempt to avoid skepticism from emerging within his knowledge‐first approach (Williamson, 2000). Some lessons about (...) Pyrrhonism result. (shrink)

This chapter contains sections titled: Introduction Platonism in Mathematics Nominalism in Mathematics Conclusion References.

This chapter contains sections titled: Information and Structural Realism Partial Information and Partial Structures Partial Structures, Structural Objects, and Informational Structuralism Conclusion Acknowledgments References.

This chapter contains sections titled: Introduction Logical Consequence Logical Pluralism Applications of Logic Conclusion References.

How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? What has been called 'the unreasonable effectiveness of mathematics' sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character, whereas others have pointed to the range of structures that mathematics offers. Otavio Bueno and Steven French offer a middle way, which focuses on the moves that have to be made (...) in both the mathematics and the relevant physics in order to bring the two into appropriate relation. This relation can be captured via the inferential conception of the applicability of mathematics, which is formulated in terms of immersion, inference, and interpretation. In particular, the roles of idealisations and of surplus structure in science and mathematics respectively are brought to the fore and captured via an approach to models and theories that emphasize the partiality of the available information: the partial structures approach. The discussion as a whole is grounded in a number of case studies drawn from the history of quantum physics, and extended to contest recent claims that the explanatory role of certain mathematical structures in scientific practice supports a realist attitude towards them. The overall conclusion is that the effectiveness of mathematics does not seem unreasonable at all once close attention is paid to how it is actually applied in practice. (shrink)

Quantifier variance faces a number of difficulties. In this paper we first formulate the view as holding that the meanings of the quantifiers may vary, and that languages using different quantifiers may be charitably translated into each other. We then object to the view on the basis of four claims: (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier variance is not an (...) ontological doctrine; (iv) quantifier variance is not compatible with charitable translation and as such is internally inconsistent. In light of these troubles, we recommend the dissolution of quantifier variance and suggest that the view be laid to rest. (shrink)

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. (shrink)

We have three goals in this paper. First, we outline an ontology of stance, and explain the role that modes of engagement and styles of reasoning play in the characterization of a stance. Second, we argue that we do enjoy a degree of control over the modes of engagement and styles of reasoning we adopt. Third, we contend that maximizing one’s prospects for change also maximizes one’s rationality.

What things count as individuals, and how do we individuate them? It is a classic philosophical question often tackled from the perspective of analytic metaphysics. This volume proposes that there is another channel by which to approach individuation -- from that of scientific practices. From this perspective, the question then becomes: How do scientists individuate things and, therefore, count them as individuals? This volume collects the work of philosophers of science to engage with this central philosophical conundrum from a new (...) angle, highlighting the crucial topic of experimental individuation and building upon recent, pioneering work in the philosophy of science. An introductory chapter foregrounds the problem of individuation, arguing it should be considered prior to the topic of individuality. The following chapters address individuation and individuality from a variety of perspectives, with prominent themes being the importance of experimentation, individuation as a process, and pluralism in individuation's criteria. Contributions examine individuation in a wide range of sciences, including stem cell biology, particle physics, and community ecology. Other chapters examine the metaphysics of individuation, its bearing on realism/antirealism debates, and interrogate epistemic aspects of individuation in scientific practice. In exploring individuation from the philosophy of biology, physics, and other scientific subjects, this volume ultimately argues for the possibility of several criteria of individuation, upending the tenets of traditional metaphysics. It provides insights for philosophers of science, but also for scientists interested in the conceptual foundations of their work. (shrink)

Based on da Costa's and French's notions of partial structures and pragmatic truth, this paper examines two possible characterizations of the concept of empirical adequacy, one depending on the notion of partial isomorphism, the other on the hierarchy of partial models of phenomena, and both compatible with an empiricist view. These formulations can then be employed to illuminate certain aspects of scientific practice.An empirical theory must single out a specific part of the world, establish reference to that part, and say—by (...) way of contingent, substantial claim about the world—that its models fit that. Now, how exactly can this be done? Bas C. van Fraassen. (shrink)

In this paper, we examine the concept of particle as it appears in quantum field theories, focusing on a puzzling situation regarding this concept. Although quantum ‘particles’ arise from fields, which form the basic ontology of QFT, and thus a certain concept of ‘particle’ is al- ways available, the properties ascribed to such ‘particles’ are not completely in agreement with the mathematical and logical description of such fields, which should be taken as individuals.

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. (shrink)

Philosophers are very fond of making non-factualist claims—claims to the effect that there is no fact of the matter as to whether something is the case. But can these claims be coherently stated in the context of classical logic? Some care is needed here, we argue, otherwise one ends up denying a tautology or embracing a contradiction. In the end, we think there are only two strategies available to someone who wants to be a non-factualist about something, and remain within (...) the province of classical logic. But one of these strategies is rather controversial, and the other requires substantially more work than is often supposed. Being a non-factualist is no easy business, and it may not be the most philosophically perspicuous way to go. (shrink)

An account of scientific representation in terms of partial structures and partial morphisms is further developed. It is argued that the account addresses a variety of difficulties and challenges that have recently been raised against such formal accounts of representation. This allows some useful parallels between representation in science and art to be drawn, particularly with regard to apparently inconsistent representations. These parallels suggest that a unitary account of scientific and artistic representation is possible, and our article can be viewed (...) as laying the groundwork for such an account—although, as we shall acknowledge, significant differences exist between these two forms of representation. (shrink)

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. (shrink)

We offer an overview of some ways of examining the connections between stance and rationality, by surveying recent work on four central topics: the very idea of a stance, the relations between stances and voluntarism, the metaphysics and epistemology that emerge once stances are brought to center stage, and the role that emotions and phenomenology play in the empirical stance.

According to modalism, modality is primitive. In this paper, we examine the implications of this view for modal epistemology, and articulate a modalist account of modal knowledge. First, we discuss a theoretical utility argument used by David Lewis in support of his claim that there is a plurality of concrete worlds. We reject this argument, and show how to dispense with possible worlds altogether. We proceed to account for modal knowledge in modalist terms.

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. (shrink)

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. (shrink)

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. (shrink)

In this paper we examine theoretical utility arguments in metaphysics. While philosophers claim a procedural continuity with science when using such arguments, we argue that examining famous instances from the history of science expose their fundamental flaws. We find that arguments from theoretical utility invoke considerations that are not truth conducive and that justifications for claims that a theory possesses theoretical virtues often assume the truth of the theory such virtues are supposed to support. We conclude that theoretical utility arguments (...) provide no epistemic grounds for metaphysical inquiry. (shrink)

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. (shrink)

In this paper, we compare two theories, modal Meinongianism and object theory, with respect to several issues that have been discussed recently in the literature. In particular, we raise some objections for MM, undermine some of the objections that its defenders raise for OT, and we point out some virtues of the latter with respect to the former.

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. (shrink)

Identity is arguably one of the most fundamental concepts in metaphysics. There are several reasons why this is the case: Identity is presupposed in every conceptual system: without identity, it is unclear that any conceptual system can be formulated. Identity is required to characterize an individual: nothing can be an individual unless it has well-specified identity conditions. Identity cannot be defined: even in systems that allegedly have the resources to define identity. Identity is required for quantification: the intelligibility of quantification (...) presupposes the identity of the objects that are quantified over. These are only four considerations in support of identity's fundamental role. In this paper, I examine and defend them. I then examine a challenge that has been raised against identity's fundamentality: one from the metaphysics of physics—based on a significant interpretation of non-relativist quantum mechanics—according to which certain quantum particles lack identity conditions. After responding to this challenge, I consider the nature of the commitment to identity, and argue that it turns out to be very minimal. In fact, a very deflationary form of metaphysics can accommodate it. In arguing that identity is fundamental, one need not overstep the boundaries of even a very minimal empiricist metaphysics. Or so I argue. (shrink)

Amie Thomasson has articulated a novel conception of ontological debates, defending an easy approach to ontological questions as part of the articulation of a deflationary metaphysical view (Thomasson, 2015). After raising some concerns to the approach, we sketch a neutralist alternative to her ontological framework, offering an even easier way of conducting ontological debates.

In this paper, 1 examine the role of the delta function in Dirac’s formulation of quantum mechanics (QM), and I discuss, more generally, the role of mathematics in theory construction. It has been argued that mathematical theories play an indispensable role in physics, particularly in QM [Colyvan, M. (2001). The inrlispensability of mathematics. Oxford University Press: Oxford]. As I argue here, at least in the case of the delta function, Dirac was very clear about its rlispensability. I first discuss the (...) significance of the delta function in Dirac’s work, and explore the strategy that he devised to overcome its use. l then argue that even if mathematical theories turned out to be indispensable, this wouidn’t justify the commitment to the existence of mathematical entities. In fact, even in successful uses of mathematics, such as in Dirac’s discovery of antimatter, there’s no need to believe in the existence of the corresponding mathematical entities. An interesting picture about the application of mathematics emerges from a careful examination of Dirac’s work. (shrink)

In this work, we focus on a very specific case study: assuming that quantum theories deal with “particles” of some kind, what kind of entity can such particles be? One possible answer, the one we shall examine here, is that they are not the usual kind of object found in daily life: individuals. Rather, we follow a suggestion by Erwin Schrödinger, according to which quantum mechanics poses a revolutionary kind of entity: non-individuals. While physics, as a scientific field, is not (...) concerned with whether entities posited by a specific physical theory are individuals or not, answering this question is part of the quest for a better understanding of physical reality. Here lies, in large measure, the relevance of ontology. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

_Thinking about Science, Reflecting on Art: Bringing Aesthetics and Philosophy of Science togethe_r is the first book to systematically examine the relationship between the philosophy of science and aesthetics. With contributions from leading figures from both fields this edited collection engages with such questions as: Does representation function in the same way in science and in art? What important characteristic do scientific models share with literary fictions? What is the difference between interpretation in the sciences and in the arts? Can (...) there be a science of aesthetics? In what ways can aesthetics and philosophy of science be integrated? Aiming to develop the interconnections between the philosophy of science and the philosophy of art more broadly and more deeply than ever before this volume not only explores scientific representation by comparison with fiction but extends the scope of interaction to include metaphysical and other questions around methodology in mainstream philosophy of science, including the aims of science, the characterisation of scientific understanding, and the nature of observation, as well as drawing detailed comparisons between specific examples in both art and the sciences. (shrink)

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. (shrink)

We advance a framework for an inferential conception of physical laws, addressing the problem of the application of mathematical structures to the relevant structure of physical domains. Physical laws, we argue, express generalizations that work as rules for deriving physically informative inferences about their target systems, hence guiding us in our interaction with various domains. Our analysis of the application of mathematics to the articulation of physical laws follows a threefold scheme. First, we examine the immersion of the relevant structure (...) of physical domains into mathematical structures. Second, we assess the inferential power of laws resulting from the mathematical formalism employed in the immersion step. And third, we provide a suitable physical interpretation for the extant mathematical structures obtained from the inferential step. We demonstrate that a deflationary, empiricist framework for an inferential conception of physical laws delivers both an understanding of the mathematical character of physical laws, and a way of responding to some of the standard philosophical riddles associated with laws. (shrink)

In order to develop an account of scientific rationality, two problems need to be addressed: (i) how to make sense of episodes of theory change in science where the lack of a cumulative development is found, and (ii) how to accommodate cases of scientific change where lack of consistency is involved. In this paper, we sketch a model of scientific rationality that accommodates both problems. We first provide a framework within which it is possible to make sense of scientific revolutions, (...) but which still preserves some (partial) relations between old and new theories. The existence of these relations help to explain why the break between different theories is never too radical as to make it impossible for one to interpret the process in perfectly rational terms. We then defend the view that if scientific theories are taken to be quasi-true, and if the underlying logic is paraconsistent, it's perfectly rational for scientists and mathematicians to entertain inconsistent theories without triviality. As a result, as opposed to what is demanded by traditional approaches to rationality, it's not irrational to entertain inconsistent theories. Finally, we conclude the paper by arguing that the view advanced here provides a new way of thinking about the foundations of science. In particular, it extends in important respects both coherentist and foundationalist approaches to knowledge, without the troubles that plague traditional views of scientific rationality. (shrink)

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 (namely, QED and QCD), 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. (shrink)

A common response to those who question the Law of Non-Contradiction is that it is impossible to debate such a fundamental law of logic. The reasons for this response vary, but what seems to underlie them is the thought that there is a minimal set of logical resources without which rational debate is impossible. This chapter argues that this response is misguided. First, it defends non-apriorism in logic: the view that logic is in the same epistemic boat as other scientific (...) theories. It then offers an account of logical theory change in terms of this epistemology. The LNC is discussed in terms of this account of logical theory change, and it is shown that rational debate over this law can, and does, proceed. Finally, arguments for and against the LNC are discussed, and how and where non-a priori considerations arise in these arguments are illustrated. (shrink)

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. (shrink)

Pyrrhonism involves the inability to defend claims about the unobservable world, or, more generally, about what is really going on beyond the phenomena. As a result, the Pyrrhonist is not engaged in developing a philosophical doctrine, at least in the sense of defending a view about the underlying features of reality. The issue then arises as to whether the Pyrrhonist also has something positive to say about our knowledge of the world, while still keeping Pyrrhonism. In this paper, I develop (...) a positive neo-Pyrrhonist attitude, indicating that we can use this attitude to make sense of important aspects of science and empirical knowledge. To do that, I explore the connection between this revived form of Pyrrhonism and contemporary versions of empiricism, in particular constructive empiricism. Although constructive empiricism is not a form of skepticism, there are important elements in common between constructive empiricism and Pyrrhonism. The resulting form of Pyrrhonism suggests that there is something right about the original stance articulated by Sextus Empiricus, and that suitably formulated it provides an insightful approach to think about empirical knowledge. (shrink)

It is easy to show that in many natural axiomatic formulations of physical and even mathematical theories, there are many superfluous concepts usually assumed as primitive. This happens mainly when these theories are formulated in the language of standard set theories, such as Zermelo–Fraenkel’s. In 1925, John von Neumann created a set theory where sets are definable by means of functions. We provide a reformulation of von Neumann’s set theory and show that it can be used to formulate physical and (...) mathematical theories with a lower number of primitive concepts very naturally. Our basic proposal is to offer a new kind of set-theoretic language that offers advantages with respect to the standard approaches, since it doesn’t introduce dispensable primitive concepts. We show how the proposal works by considering significant physical theories, such as non-relativistic classical particle mechanics and classical field theories, as well as a well-known mathematical theory, namely, group theory. This is a first step of a research program we intend to pursue. (shrink)