The present paper discusses different approaches to metaphysics and defends a specific, non-deflationary approach that nevertheless qualifies as scientifically-grounded and, consequently, as acceptable from the naturalistic viewpoint. By critically assessing some recent work on science and metaphysics, we argue that such a sophisticated form of naturalism, which preserves the autonomy of metaphysics as an a priori enterprise yet pays due attention to the indications coming from our best science, is not only workable but recommended.

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...) development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

I argue that a common philosophical approach to the interpretation of physical theories—particularly quantum field theories—has led philosophers astray. It has driven many to declare the quantum field theories employed by practicing physicists, so-called ‘effective field theories’, to be unfit for philosophical interpretation. In particular, such theories have been deemed unable to support a realist interpretation. I argue that these claims are mistaken: attending to the manner in which these theories are employed in physical practice, I show that interpreting effective (...) field theories yields a robust foundation for a more refined approach to scientific realism in the context of quantum field theory. The paper concludes by briefly sketching some general morals for interpretive practice in the philosophy of physics. (shrink)

While anti-exceptionalism about logic is now a popular topic within the philosophy of logic, there’s still a lack of clarity over what the proposal amounts to. currently, it is most common to conceive of AEL as the proposal that logic is continuous with the sciences. Yet, as we show here, this conception of AEL is unhelpful due to both its lack of precision, and its distortion of the current debates. Rather, AEL is better understood as the rejection of certain traditional (...) properties of logic. The picture that results is not of one singular position, but rather a cluster of often connected positions with distinct motivations, understood in terms of their rejection of clusters of the various traditional properties. In order to show the fruitfulness of this new conception of AEL, we distinguish between two prominent versions of the position, metaphysical and epistemological AEL, and show how the two positions need not stand or fall together. (shrink)

During the past few decades, a radical shift has occurred in how philosophers conceive of the relation between science and philosophy. A great number of analytic philosophers have adopted what is commonly called a ‘naturalistic’ approach, arguing that their inquiries ought to be in some sense continuous with science. Where early analytic philosophers often relied on a sharp distinction between science and philosophy—the former an empirical discipline concerned with fact, the latter an a priori discipline concerned with meaning—philosophers today largely (...) follow Willard Van Orman Quine (1908-2000) in his seminal rejection of this distinction. -/- This book offers a comprehensive study of Quine’s naturalism. Building on Quine’s published corpus as well as thousands of unpublished letters, notes, lectures, papers, proposals, and annotations from the Quine archives, this book aims to reconstruct both the nature (chapters 2-4) and the development (chapter 5-7) of his naturalism. As such, this book aims to contribute to the rapidly developing historiography of analytic philosophy, and to provide a better, historically informed, understanding of what is philosophically at stake in the contemporary naturalistic turn. (shrink)

Philosophy of science appears caught in what Einstein (1933) called the ‘eternal antithesis between the two inseparable components of our knowledge – the empirical and the rational’ (p. 271). It wants to employ metaphysical speculation, but impressed with the methods of the subject it studies, it fears overreaching. Philosophy of science thus tries to walk a fine line between scientifically grounded metaphysics and its more speculative cousins. Here I try to draft some of the contour of this boundary.

Scientific realism and anti-realism are most frequently discussed as global theses: theses that apply equally well across the board to all the various sciences. Against this status quo I defend the localist alternative, a methodological stance on scientific realism that approaches debates on realism at the level of individual sciences, rather than at science itself. After identifying the localist view, I provide a number of arguments in its defense, drawing on the diversity and disunity found in the sciences, as well (...) as problems with other approaches (such as basing realism debates on the aim of science). I also show how the view is already at work, explicitly or implicitly, in the work of several philosophers of science. After meeting the objections that localism collapses either into globalism or hyperlocalism, I conclude by sketching what sorts of impacts localism can have in the philosophy of science. (shrink)

Many philosophers think all abstract objects are causally inert. Here, focusing on novels, I argue that some abstracta are causally efficacious. First, I defend a straightforward argument for this view. Second, I outline an account of object causation—an account of how objects cause effects. This account further supports the view that some abstracta are causally efficacious.

Recent work on the hole argument in general relativity by Weatherall has drawn attention to the neglected concept of models’ representational capacities. I argue for several theses about the structure of these capacities, including that they should be understood not as many-to-one relations from models to the world, but in general as many-to-many relations constrained by the models’ isomorphisms. I then compare these ideas with a recent argument by Belot for the claim that some isometries “generate new possibilities” in general (...) relativity. Philosophical orthodoxy, by contrast, denies this. Properly understanding the role of representational capacities, I argue, reveals how Belot’s rejection of orthodoxy does not go far enough, and makes better sense of our practices in theorizing about spacetime. (shrink)

First, I answer the controversial question ’What is scientific realism?’ with extensive reference to the varied accounts of the position in the literature. Second, I provide an overview of the key developments in the debate concerning scientific realism over the past decade. Third, I provide a summary of the other contributions to this special issue.

Logical realism is a view about the metaphysical status of logic. Common to most if not all the views captured by the label ‘logical realism’ is that logical facts are mind- and language-independent. But that does not tell us anything about the nature of logical facts or about our epistemic access to them. The goal of this paper is to outline and systematize the different ways that logical realism could be entertained and to examine some of the challenges that these (...) views face. It will be suggested that logical realism is best understood as a metaphysical view about the logical structure of the world, but this raises an important question: does logical realism collapse into standard metaphysical realism? It will be argued that this result can be accommodated, even if it cannot be altogether avoided. (shrink)

According to Ole Hjortland, Timothy Williamson, Graham Priest, and others, anti-exceptionalism about logic is the view that logic “isn’t special”, but is continuous with the sciences. Logic is revisable, and its truths are neither analytic nor a priori. And logical theories are revised on the same grounds as scientific theories are. What isn’t special, we argue, is anti-exceptionalism about logic. Anti-exceptionalists disagree with one another regarding what logic and, indeed, anti-exceptionalism are, and they are at odds with naturalist philosophers of (...) logic, who may have seemed like natural allies. Moreover, those internal battles concern well-trodden philosophical issues, and there is no hint as to how they are to be resolved on broadly scientific grounds. We close by looking at three of the founders of logic who may have seemed like obvious enemies of anti-exceptionalism—Aristotle, Frege, and Carnap—and conclude that none of their positions is clearly at odds with at least some of the main themes of anti-exceptionalism. We submit that, at least at present, anti-exceptionalism is too vague or underspecified to characterize a coherent conception of logic, one that stands opposed to more traditional approaches. (shrink)

This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against determinacy and discuss a particularly popular approach (...) to resolving indeterminacy, before offering some brief closing reflections. We believe our discussion poses a serious challenge for most philosophical theories of mathematics, since it puts considerable pressure on all views that accept a non-trivial amount of determinacy for even basic arithmetic. (shrink)

Argues that truth, moral right, political right, and aesthetic value may be understood as arising out of a naturalist account of humanity, if naturalism is rightly conceived.

Anti-exceptionalism about logic is the thesis that logic is not special. In this paper, I consider, and reject, a challenge to this thesis. According to this challenge, there are basic logical principles, and part of what makes such principles basic is that they are epistemically exceptional. Thus, according to this challenge, the existence of basic logical principles provides reason to reject anti-exceptionalism about logic. I argue that this challenge fails, and that the exceptionalist positions motivated by it are thus unfounded. (...) I make this case by disambiguating two senses of ‘basic’ and showing that, once this disambiguation is taken into account, the best reason we have for thinking that there are basic principles actually implies that those principles do not require a special epistemology. Consequently, the existence of basic logical principles provides reason to accept, rather than reject, anti-exceptionalism concerning the epistemology of logic. I conclude by explaining how an abductivist, anti-exceptionalist approach to the epistemology of logic can accommodate the notion of basic logical principles. (shrink)

According to Ian Hacking’s Entity Realism, unobservable entities that scientists carefully manipulate to study other phenomena are real. Although Hacking presents his case in an intuitive, attractive, and persuasive way, his argument remains elusive. I present five possible readings of Hacking’s argument: a no-miracle argument, an indispensability argument, a transcendental argument, a Vichian argument, and a non-argument. I elucidate Hacking’s argument according to each reading, and review their strengths, their weaknesses, and their compatibility with each other.

The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. Apart (...) from considering rigour of proof as a fixture, I discuss fixed models, invariant notions and fixed information about objects across theories. There are other fixtures, but it is enough to start with these. (shrink)

The story of how Perrin’s experimental work established the reality of atoms and molecules has been a staple in (realist) philosophy of science writings (Wesley Salmon, Clark Glymour, Peter Achinstein, Penelope Maddy, …). I’ll argue that how this story is told distorts both what the work was and its significance, and draw morals for the understanding of how theories can be or fail to be empirically grounded.

I argue that scientific realism, insofar as it is only committed to those scientific posits of which we have causal knowledge, is immune to Kyle Stanford’s argument from unconceived alternatives. This causal strategy is shown not to repeat the shortcomings of previous realist responses to Stanford’s argument. Furthermore, I show that the notion of causal knowledge underlying it can be made sufficiently precise by means of conceptual tools recently introduced into the debate on scientific realism. Finally, I apply this strategy (...) to the case of Jean Perrin’s experimental work on the atomic hypothesis, disputing Stanford’s claim that the problem of unconceived alternatives invalidates a realist interpretation of this historical episode. 1 Stanford’s Argument from Unconceived Alternatives2 Previous Attempts to Undermine the Problem of Unconceived Alternatives2.1 The plausibility of unconceived alternatives2.2 The distinctness of unconceived alternatives2.3 The induction from past to present3 Causal Knowledge as a Criterion for the Realist3.1 How Chakravartty’s proposal differs from earlier causal strategies3.2 Causal realism and the detection/auxiliary distinction4 Causal Realism, Unconceived Alternatives, and the Atomic Hypothesis4.1 Perrin and the philosophers: some initial observations4.2 Roush and Stanford on Perrin4.3 From Brownian motion to the reality of atoms4.4 What we know about atoms5 Conclusion. (shrink)

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...) from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas. (shrink)

In set theory, a maximality principle is a principle that asserts some maximality property of the universe of sets or some part thereof. Set theorists have formulated a variety of maximality principles in order to settle statements left undecided by current standard set theory. In addition, philosophers of mathematics have explored maximality principles whilst attempting to prove categoricity theorems for set theory or providing criteria for selecting foundational theories. This article reviews recent work concerned with the formulation, investigation and justification (...) of maximality principles. (shrink)

In science and everyday life, we often infer that something is true because it would explain some set of facts better than any other hypothesis we can think of. But what if we have reason to believe that there is a better way to explain these facts that we just haven't thought of? Wouldn't that undermine our warrant for believing the best available explanation? Many philosophers have assumed that we can solve such underconsideration problems by stipulating that a hypothesis should (...) not only be 'the best' explanation available; rather, it should also be 'good enough'. Unfortunately, however, the only current suggestion for what it might mean to say that an explanation is 'good enough' is, well, not good enough. This paper aims to provide a better account of what is required for an explanatory hypothesis to be considered 'good enough'. In brief, the account holds that a `good enough' hypothesis is one that has gone through a process that I call explanatory consolidation, in which accumulating evidence and failed attempts to formulate better alternatives gradually make it more plausible that the explanation we currently have is better than any other that could be formulated. (shrink)

Contemporary science seems to be caught in a strange predicament. On the one hand, it holds a firm and reasonable commitment to a healthy naturalistic methodology, according to which explanations of natural phenomena should never overstep the limits of the natural itself. On the other hand, contemporary science is also inextricably and now inevitably dependent on ever more complex technologies, especially Information and Communication Technologies, which it exploits as well as fosters. Yet such technologies are increasingly “artificialising” or “denaturalising” the (...) world, human experiences and interactions, as well as what qualifies as real. So the search for the ultimate explanation of the natural seems to rely upon, and promote, the development of the artificial, seen here as an instantiation of the non-natural. In this article, I would like to try and find a way out of this apparently strange predicament. I shall argue that the naturalisation of our knowledge of the world is either philosophically trivial, or mistaken. First, I shall distinguish between different kinds of naturalism. Second, I shall remind the reader that the kinds of naturalism that are justified today need to be protected and supported pragmatically, but they are no longer very interesting conceptually. We know how to win the argument. We just have to keep winning it. Whereas the kind of naturalism that is still interesting today is now in need of revision in order to remain acceptable. Such a kind of naturalism may be revised on the basis of a realistic philosophy of information, according to which knowing is a constructive activity, through which we do not merely represent the phenomena we investigate passively, but create more or less correct informational models of them, proactively and interactively. I shall conclude that the natural is in itself artefactual, and that the information revolution is disclosing a tension not between the natural and the non-natural, but a deeper one between a user’s and a producer’s interpretation of knowledge. The outcome is a philosophical view of knowledge and science in the information age that may be called constructionist and a revival of philosophy as a classic, foundationalist enterprise. (shrink)

Contrary to common views that philosophy is extraneous to cognitive science, this paper argues that philosophy has a crucial role to play in cognitive science with respect to generality and normativity. General questions include the nature of theories and explanations, the role of computer simulation in cognitive theorizing, and the relations among the different fields of cognitive science. Normative questions include whether human thinking should be Bayesian, whether decision making should maximize expected utility, and how norms should be established. These (...) kinds of general and normative questions make philosophical reflection an important part of progress in cognitive science. Philosophy operates best, however, not with a priori reasoning or conceptual analysis, but rather with empirically informed reflection on a wide range of findings in cognitive science. (shrink)

According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, (...) I outline a different approach, which circumvents these problems by dispensing with the priority or dependence relation altogether. Along the way, I show how this approach enables the mathematical structuralist to defuse an objection recently raised against her view. (shrink)

If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case (...) with respect to the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way, namely, by deduction from basic principles. The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. Therefore philosophers have accorded special attention to ontological and epistemological questions concerning mathematics. (shrink)

Abstract: This paper is an attempt to identify and to suggest reasons to reject those assumptions about the nature and scope of perceptual knowledge that appear to make an unacceptable scepticism the only strictly defensible answer to the philosophical problem of knowledge of the world in general. The suggestion is that our knowing things about the world around us by perception can be satisfactorily explained only if we can be understood to sometimes perceive that such-and-such is so, where what we (...) perceive to be so is the very state of the world that we thereby know to be so. This is not proposed as a better answer to the philosophical problem, but as a way of seeing how that problem as traditionally understood could not really present a threat to anyone who can think about the world at all. (shrink)

Epistemologists and philosophers of mind both ask questions about belief. Epistemologists ask normative questions about belief—which beliefs ought we to have? Philosophers of mind ask metaphysical questions about belief—what are beliefs, and what does it take to have them? While these issues might seem independent of one another, there is potential for an interesting sort of conflict: the epistemologist might think we ought to have beliefs that, according to the philosopher of mind, it is impossible to have. This essay argues (...) that this conflict does arise and that it creates problems for traditional skeptical views in epistemology. In particular, it argues that on certain popular views about the nature of belief, it is impossible to adopt the near-global agnosticism recommended by the skeptical epistemologist. On other plausible views, it is possible only in special circumstances, and this limitation undermines skeptical epistemological claims. The only views about the nature of belief on which there are no metaphysical hurdles to adopting the agnosticism recommended by the skeptic are views that face powerful objections—objections that are completely independent of antiskeptical epistemological considerations. (shrink)

In this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well-defined form of language or linguistic framework we please. A linguistic framework defines framework-internal standards of correct reasoning that guide us in our first-order scientific pursuits. The choice of a linguistic framework, on the other hand, is an ‘external’ question to be settled on pragmatic grounds and so not (...) itself constrained by these standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance. (shrink)

Realists about science tend to hold that our scientific theories aim for the truth, that our successful theories are at least partly true, and that the entities referred to by the theoretical terms of these theories exist. Antirealists about science deny one or more of these claims. A sizable minority of philosophers of science prefers not to take sides: they believe the realism debate to be fundamentally mistaken and seek to abstain from it altogether. In analogy with other realism debates (...) I will call these philosophers quietists. In the philosophy of science quietism often takes a somewhat peculiar form, which I will call naturalistic quietism. In this paper I will characterize Maddy’s Second Philosophy as a form of naturalistic quietism, and show what the costs for making it feasible are. (shrink)

My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, or in (...) social arrangements, governments, power structures, or some such thing, but I resist the full force of this way of thinking, clinging to the old school notion that we have gradually learned more about the world over time, that our opinions on these matters have improved, and that seeing how we reached the point we now occupy may help us avoid falling back into old philosophies that are now no longer viable. In that spirit, it seems to me that once we focus on the general question of how mathematics relates to science, one observation is immediate: the march of the centuries has produced an amusing reversal of philosophical fortunes. Let me begin there. In the beginning, that is, in Plato, mathematical knowledge was sharply distinguished from ordinary perceptual belief about the world. According to Plato’s metaphysics, mathematics is the study of eternal and unchanging abstract Forms,1 while science is uncertain and changeable opinion about the world of mere becoming. Indeed, in Plato’s lights, of the two, only mathematics deserves to be called ‘knowledge’ at all! Of course if sense perception cannot give us knowledge, if mathematics is not about perceivable things, then Plato owes us an account of how we ordinary humans achieve this wonderful insight into the properties of the abstract world of Forms. Plato’s answer is that we do not actually acquire mathematical knowledge at all; rather, we recollect it from a time before birth, when our souls, unencumbered by physical bodies, were free to commune with the Forms, and not just the mathematical ones, either – also Truth, Beauty, Justice, the Good, and so on.2 Whatever appeal this position may have held for the ancient Greeks, it will not begin to satisfy a contemporary, scientifically minded philosopher.. (shrink)

While Saunders Mac Lane studied for his D.Phil in Göttingen, he heard David Hilbert's weekly lectures on philosophy, talked philosophy with Hermann Weyl, and studied it with Moritz Geiger. Their philosophies and Emmy Noether's algebra all influenced his conception of category theory, which has become the working structure theory of mathematics. His practice has constantly affirmed that a proper large-scale organization for mathematics is the most efficient path to valuable specific results—while he sees that the question of which results are (...) valuable has an ineliminable philosophic aspect. His philosophy relies on the ideas of truth and existence he studied in Göttingen. His career is a case study relating naturalism in philosophy of mathematics to philosophy as it naturally arises in mathematics. Introduction Structures and Morphisms Varieties of Structuralism Göttingen Logic: Mac Lane's Dissertation Emmy Noether Natural Transformations Grothendieck: Toposes and Universes Lawvere and Foundations Truth and Existence Naturalism Austere Forms of Beauty. (shrink)

Sherri Roush ([2005]) and I ([2001], [2006]) have each argued independently that the most significant challenge to scientific realism arises from our inability to consider the full range of serious alternatives to a given hypothesis we seek to test, but we diverge significantly concerning the range of cases in which this problem becomes acute. Here I argue against Roush's further suggestion that the atomic hypothesis represents a case in which scientific ingenuity has enabled us to overcome the problem, showing how (...) her general strategy is undermined by evidence I have already offered in support of what I have called the 'problem of unconceived alternatives'. I then go on to show why her strategy will not generally (if ever) allow us to formulate and test exhaustive spaces of hypotheses in cases of fundamental scientific theorizing. (shrink)

Idealized scientific representations result from employing claims that we take to be false. It is not surprising, then, that idealizations are a prime example of allegedly inconsistent scientific representations. I argue that the claim that an idealization requires inconsistent beliefs is often incorrect and that it turns out that a more mathematical perspective allows us to understand how the idealization can be interpreted consistently. The main example discussed is the claim that models of ocean waves typically involve the false assumption (...) that the ocean is infinitely deep. While it is true that the variable associated with depth is often taken to infinity in the representation of ocean waves, I explain how this mathematical transformation of the original equations does not require the belief that the ocean being modeled is infinitely deep. More generally, as a mathematical representation is manipulated, some of its components are decoupled from their original physical interpretation. (shrink)

In this paper, I describe some strategies for teaching an introductory philosophy of science course to Science, Technology, Engineering, and Mathematics (STEM) students, with reference to my own experience teaching a philosophy of science course in the Fall of 2020. The most important strategy that I advocate is what I call the “Second Philosophy” approach, according to which instructors ought to emphasize that the problems that concern philosophers of science are not manufactured and imposed by philosophers from the outside, but (...) rather are ones that arise internally, during the practice of science itself. To justify this approach, I appeal to considerations from both educational research and the epistemology of testimony. In addition, I defend some distinctive learning goals that philosophy of science instructors ought to adopt when teaching STEM students, which include rectifying empirically well-documented shortcomings in students’ conceptions of the “scientific method” and the “nature of science.” Although my primary focus will be on teaching philosophy of science to STEM students, much of what I propose can be applied to non-philosophy majors generally. Ultimately, as I argue, a successful philosophy of science course for non-philosophy majors must be one that advances a student’s science education. The strategies that I describe and defend here are aimed at precisely that end. (shrink)

Thought experiments have been influential in philosophy at least since Plato, and they have contributed to science at least since Galileo. Some of this influence is appropriate, because thought experiments can have legitimate roles in generating and clarifying hypotheses, as well as in identifying problems in competing hypotheses. I will argue, however, that philosophers have often overestimated the significance of thought experiments by supposing that they can provide evidence that supports the acceptance of beliefs. Accepting hypotheses merely on the basis (...) of thinking about them constitutes a kind of epistemic hubris with many negative consequences, including the acquisition of false beliefs and the blocking of .. (shrink)

Contemporary philosophy’s three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion’s share of the attention, so we concentrate on this. Ontological and epistemological naturalism in the philosophy of mathematics are discussed more briefly in section (...) 6. (shrink)

Quine's argument for a naturalized epistemology is routinely perceived as an argument from despair: traditional epistemology must be abandoned because all attempts to deduce our scientific theories from sense experience have failed. In this paper, I will show that this picture is historically inaccurate and that Quine's argument against first philosophy is considerably stronger and subtler than the standard conception suggests. For Quine, the first philosopher's quest for foundations is inherently incoherent; the very idea of a self-sufficient sense datum language (...) is a mistake, there is no science-independent perspective from which to validate science. I will argue that a great deal of the confusion surrounding Quine's argument is prompted by certain phrases in his seminal ‘Epistemology Naturalized’. Scrutinizing Quine's work both before and after the latter paper provides a better key to understanding his remarkable views about the epistemological relation between theory and evidence. (shrink)

In this introduction we discuss the motivation behind the workshop “Towards a New Epistemology of Mathematics” of which this special issue constitutes the proceedings. We elaborate on historical and empirical aspects of the desired new epistemology, connect it to the public image of mathematics, and give a summary and an introduction to the contributions to this issue.

An extensive exploration of the special properties of ‘exist’ is here undertaken. Two of several results are: Denying that `exist’ has associated with it a set of necessary and sufficient conditions has seemed to a number of philosophers to imply metaphysical nihilism . This is because it has seemed that without such conditions the target domain of `existence’ is arbitrarily open. I show this is wrong. Second, my analysis sheds light on the puzzling question of what we are asking when (...) we ask of something, `Does it exist?’ and mean that question in an ontically relevant way. (shrink)

Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...) be crucial, and show how one may provide responses to Maddy's concerns based on a careful analysis of 'multiverse practice'. (shrink)

In comparing classical and non-classical solutions to the semantic paradoxes arguments relying on strength have been influential. In this paper I argue that non-classical solutions should preserve the proof-theoretic strength of classical solutions. Leitgeb’s logic of HYPE is then presented as an interesting possibility to strengthen FDE with a suitable conditional. It is shown that HYPE allows for a non-classical Kripkean theory of truth, called KFL, that is strong enough for the relevant purposes and has additional attractive properties.

A theory of truth is language-transcendent if it ascribes truth conditions to truth-bearers that are not expressible in our natural language; a theory is language-immanent if it is not language-transcendent. In this paper, I argue for the following theses. Whether the correct theory of truth is language-transcendent or language-immanent will have significant consequences for general philosophy. Prima facie, a language-transcendent theory is preferable. However, language-transcendent theories tend to require substantive metaphysical commitments concerning truth. Deflationist theories are particularly interesting in this (...) context. I argue that, if deflationism is to remain consistent with its motivations, then it must opt for a language-immanent conception of truth. (shrink)

Simon’s bounded rationality , the first scientific research program to seriously take the cognitive limitations of decision makers into account, has often been conflated with his more restricted concept of satisficing—choosing an alternative that meets or exceeds specified criteria, but that is not guaranteed to be unique or in any sense “the best.” Proponents of optimization often dismiss bounded rationality out of hand with the following “hallway syllogism” : bounded rationality “boils down to” satisficing; satisficing is “simply” a theory of (...) search for alternatives that takes into account the costs of computation. Hence, bounded rationality is “just a minor tweak” on optimal search theory. (shrink)

This book intends to show that radical naturalism, nominalism and strict finitism account for the applications of classical mathematics in current scientific theories. The applied mathematical theories developed in the book include the basics of calculus, metric space theory, complex analysis, Lebesgue integration, Hilbert spaces, and semi-Riemann geometry. The fact that so much applied mathematics can be developed within such a weak, strictly finitistic system, is surprising in itself. It also shows that the applications of those classical theories to the (...) finite physical world can be translated into the applications of strict finitism, which demonstrates the applicability of those classical theories without assuming the literal truth of those theories or the reality of infinity. Both professional researchers and students of philosophy of mathematics will benefit greatly from reading this book. (shrink)

This paper develops and defends a coherentist account of reasons. I develop three core ideas for this defense: a distinction between basic reasons and noninferential justification, the plausibility of the neglected argument against first philosophy, and an emergent account of reasons. These three ideas form the backbone for a credible coherentist view of reasons. I work toward this account by formulating and explaining the basic reasons dilemma. This dilemma reveals a wavering attitude that coherentists have had toward basic reasons. More (...) importantly, the basic reasons dilemma focuses our attention on the central problems that afflict coherentist views of basic beliefs. By reflecting on the basic reasons dilemma, I formulate three desiderata that any viable coherentist account of basic beliefs must satisfy. I argue that the account on offer satisfies these desiderata. (shrink)