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)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (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)

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)

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 traditional formulation of the indispensability argument for the existence of mathematical entities (IA) has been criticised due to its reliance on confirmational holism. Recently a formulation of IA that works without appeal to confirmational holism has been defended. This recent formulation is meant to be superior to the traditional formulation in virtue of it not being subject to the kind of criticism that pertains to confirmational holism. I shall argue that a proponent of the version of IA that works (...) without appeal to confirmational holism will struggle to answer a challenge readily answered by proponents of a version of IA that does appeal to confirmational holism. This challenge is to explain why mathematics applied in falsified scientific theories is not considered to be falsified along with the rest of the theory. In cases where mathematics seemingly ought to be falsified it is saved from falsification, by a so called 'Euclidean rescue'. I consider a range of possible answers to this challenge and conclude that each answer fails. (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.

Modern-day heirs of the Cartesian revolution have been fascinated by the thought that one could utilize certain hypotheses – that one is dreaming, deceived by an evil demon, or a brain in a vat – to argue at one fell swoop that one does not know, is not justified in believing, or ought not believe most if not all of what one currently believes about the world. A good part of the interest and mystique of these discussions arises from the (...) contention that the seeds of such arguments lie in our ordinary epistemic practices, so that external world skepticism can arise “from within”. But is this contention correct? I doubt it. Taking skepticism seriously requires that we address this question head on. To do so, I will approach skeptical arguments from a certain vantage point. I will try to stand, as far as possible, with both feet squarely in ordinary life. I will start out with all of our ordinary commitments about what is the case, about what we know or have reason to believe, about when someone knows, is justified, or has good reason to believe something, and about how one should proceed in deciding what to believe. My question, then, will be this. From within that vantage point can I somehow be moved in a reasonable way to accept the conclusion that I know far less about the world around me than I thought, or that epistemically speaking, I really ought not believe much of what I have believed about the world around me? In order for such movement to take place, I will have to find reason from within my ordinary standpoint to discount or reject much of what I ordinarily accept. And of course, that reason will have to come from some.. (shrink)

This paper considers Maddy’s strategy for naturalising mathematics in the context of Quine’s scientific naturalism. The aim of this proposal is to account for the acceptability of mathematics on scientific grounds without committing to revisionism about mathematical practice entailed by the Quine-Putnam indispensability argument. It has been argued that Maddy’s mathematical naturalism makes inconsistent assumptions on the role of mathematics in scientific explanations to the effect that it cannot distinguish mathematics from pseudo-science. I shall clarify Maddy’s arguments and show that (...) the objection can be overcome. I shall then reformulate a novel version of the objection and consider a possible answer, and I shall conclude that mathematical naturalism does not ultimately provide a viable strategy for accommodating an anti-revisionary stance on mathematics within a Quinean naturalist framework. (shrink)

In this paper, I use the cases of intuitionistic arithmetic with Church’s thesis, intuitionistic analysis, and smooth infinitesimal analysis to argue for a sort of pluralism or relativism about logic. The thesis is that logic is relative to a structure. There are classical structures, intuitionistic structures, and (possibly) paraconsistent structures. Each such structure is a legitimate branch of mathematics, and there does not seem to be an interesting logic that is common to all of them. One main theme of my (...) ante rem structuralism is that any coherent axiomatization describes a structure, or a class of structures. If one weakens the logic, then more axiomatizations become coherent. (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)

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.

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.

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)

I argue that the most popular versions of naturalism imply nominalism in philosophy of mathematics. In particular, there is a conflict in Quine's philosophy between naturalism and realism in mathematics. The argument starts from a consequence of naturalism on the nature of human cognitive subjects, physicalism about cognitive subjects, and concludes that this implies a version of nominalism, which I will carefully characterize. The indispensability of classical mathematics for the sciences and semantic/confirmation holism does not affect the argument. The disquotational (...) theory of reference and truth is discussed but rejected. This argument differs from the Benacerrafian arguments against realism, because it does not rely on any specific assumption about the nature of knowledge or reference. It differs from the popular objections to the indispensability argument for realism as well, because it can admit both indispensability and holism. This argument motivates a new, radically naturalistic and nominalistic approach to philosophy of mathematics. (shrink)

This paper examines the relevance of philosophical work on consciousness to its scientific study. Of particular concern is the debate over whether consciousness can be naturalized, which is typically taken to have consequences for the prospects for its scientific investigation. It is not at all clear that philosophers of consciousness have properly identified and evaluated the assumptions about scientific activity made by both naturalization and anti- naturalization projects. I argue that there is good reason to think that some of the (...) assumptions about physicalism and explanation made by the parties to the debate are open to serious doubt. Thus this paper is an invitation for those inquiring into whether consciousness can be naturalized to more carefully consider the expected payoff of such efforts. (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)

A new reading of G.E. Moore's ‘Proof of an External World’ is offered, on which the Proof is understood as a unique and essential part of an anti-sceptical strategy that Moore worked out early in his career and developed in various forms, from 1909 until his death in 1958. I begin by ignoring the Proof and by developing a reading of Moore's broader response to scepticism. The bulk of the article is then devoted to understanding what role the Proof plays (...) in Moore's strategy, and how that role is played. (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)

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)

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)

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)

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)

In an attempt to address some long-standing issues of epistemology, Hilary Kornblith proposes that knowledge is a natural kind the identification of which is the unique responsibility of one particular science: cognitive ethology. As Kornblith sees it, the natural kind thus picked out is knowledge as construed by reliabilism. Yet the claim that cognitive ethology has this special role has not convinced all critics. The present article argues that knowledge plays a causal and explanatory role within many of our more (...) fruitful current theories, diverging from the reliabilist conception even in disciplines that are closely related to cognitive ethology, and thus still dealing with knowledge as a natural as opposed to a social phenomenon, where special attention will be given to cognitive neuroscience. However, rather than discarding the natural kind approach altogether, it is argued that many of Kornblith’s insights can in fact be preserved within a framework that is both naturalist and pluralist. (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)

Reply in Book Symposium on James Ladyman, Don Ross: 'Everything must go: metaphysics naturalized', Oxford: Oxford University Press, 2007.

I discuss the applicability of mathematics via a detailed case study involving a family of mathematical concepts known as ‘fractional derivatives.’ Certain formulations of the mystery of applied mathematics would lead one to believe that there ought to be a mystery about the applicability of fractional derivatives. I argue, however, that there is no clear mystery about their applicability. Thus, via this case study, I think that one can come to see more clearly why certain formulations of the mystery of (...) applied mathematics are not convincing. (shrink)

A standard interpretation of Hume’s naturalism is that it paved the way for a scientistic and ‘disenchanted’ conception of the world. My aim in this paper is to show that this is a restrictive reading of Hume, and it obscures a different and profitable interpretation of what Humean naturalism amounts to. The standard interpretation implies that Hume’s ‘science of human nature’ was a reductive investigation into our psychology. But, as Hume explains, the subject matter of this science is not restricted (...) to introspectively accessible mental content and incorporates our social nature and interpersonal experience. Illuminating the science of human nature has implications for how we understand what Hume means by ‘experience’ and thus how we understand the context of his epistemological investigations. I examine these in turn and argue overall that Hume’s naturalism and his science of man do not simply anticipate a disenchanted conception of the world. (shrink)

Arthur Fine presented the Natural Ontological Attitude as a third alternative between scientific realism and anti-realism by identifying a core position contained in both and rejecting any philosophical addition to this core. At first, Fine’s proposal was understood as offering a doxastic middle ground between believing in the truth of a theory and believing in its empirical adequacy. In this reading, NOA was widely disregarded after Alan Musgrave’s criticisms of it, which characterized Fine’s proposal as a form of realism. After (...) that, NOA was reinterpreted as a local variety of realism focused in changing the attitude used to settle the scientific realism debate, by rejecting global philosophies with an approach external to science, and by considering only the scientific evidence with a contextualist mood. Although this reading clarifies how to understand NOA, there is still no consensus about what is Fine’s argument to support it. I organize the four main interpretations of Fine’s defense and point their main flaws. Finally, I develop some clarifications about NOA in order to solve the flaws of the preceding interpretations, defending that NOA is based upon a prevalence of the epistemic values actually used in scientific practice. (shrink)

The subject of this paper is Malebranche’s relation to Descartes on the question of method. Using recent commentary as a springboard, it examines whether Malebranche advances a nonpsychologistic account of method, in contrast to the psychologism typically thought to characterize the Cartesian view. I explore this question with respect to two issues of central importance to method generally: doubt and free will. My argument is that, despite superficial differences of emphasis, Descartes and Malebranche adopt positions on doubt and free will (...) that effectively ensure that their respective accounts of method aresubstantially the same. (shrink)

Intellectualism is the claim that practical knowledge or ‘know-how’ is a kind of propositional knowledge. The debate over Intellectualism has appealed to two different kinds of evidence, semantic and scientific. This paper concerns the relationship between Intellectualist arguments based on truth-conditional semantics of practical knowledge ascriptions, and anti-Intellectualist arguments based on cognitive science and propositional representation. The first half of the paper argues that the anti-Intellectualist argument from cognitive science rests on a naturalistic approach to metaphysics: its proponents assume that (...) findings from cognitive science provide evidence about the nature of mental states. We demonstrate that this fact has been overlooked in the ensuing debate, resulting in inconsistency and confusion. Defenders of the semantic approach to Intellectualism engage with the argument from cognitive science in a way that implicitly endorses this naturalistic metaphysics, and even rely on it to claim that cognitive science support Intellectualism. In the course of their arguments, however, they also reject that scientific findings can have metaphysical import. We argue that this situation is preventing productive debate about Intellectualism, which would benefit from both sides being more transparent about their metaphilosophical assumptions. (shrink)

This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science (...) and ethics on one side and a case study from philosophy of mathematics on the other. We argue that empirically informed philosophy of mathematics is different from the rest in a way that encourages a Freeway explorer approach, because intuitions about mathematical objects are often unavailable for non-mathematicians. This consideration is supported by a case study in set theory. (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)

In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.

Penelope Maddy advances a purportedly naturalistic account of mathematical methodology which might be taken to answer the question 'What justifies axioms of set theory?' I argue that her account fails both to adequately answer this question and to be naturalistic. Further, the way in which it fails to answer the question deprives it of an analog to one of the chief attractions of naturalism. Naturalism is attractive to naturalists and nonnaturalists alike because it explains the reliability of scientific practice. Maddy's (...) account, on the other hand, appears to be unable to similarly explain the reliability of mathematical practice without violating one of its central tenets. (shrink)

Any movement worth its salt has a creation myth. Analytic metaphysics is no exception. According to legend, it was born from the clash of two titans. On the one side, was the anti-metaphysical Logi...

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)

Traditional theories of how children learn the positive integers start from infants' abilities in detecting the quantity of physical objects. Our target article examined this view and found no plausible accounts of such development. Most of our commentators appear to agree that no adequate developmental theory is presently available, but they attempt to hold onto a role for early enumeration. Although some defend the traditional theories, others introduce new basic quantitative abilities, new methods of transformation, or new types of end (...) states. A survey of these proposals, however, shows that they do not succeed in bridging the gap to knowledge of the integers. We suggest that a better theory depends on starting with primitives that are inherently structural and mathematical. (shrink)

This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) those that are more readily available for mathematico-scientific use. (shrink)

Yet, he also says that it is philosophically indeterminate which criterion for what exists is correct. Nominalism is the view that certain objects ( i.e ., abstract objects) do not exist, and not the view that it is philosophically indeterminate whether or not they do. I resolve the dilemma that Azzouni's claims pose: Azzouni is a non-factualist about what exists, but he is a factualist about which criterion for what exists our community of speakers has adopted. It is in the (...) latter sense only that Azzouni can call himself a nominalist. My thanks to Jody Azzouni and to an anonymous referee for helpful suggestions. CiteULike Connotea Del.icio.us What's this? (shrink)

This paper reassesses the criticism of the Lucas-Penrose anti-mechanist argument, based on Gödel’s incompleteness theorems, as formulated by Krajewski : this argument only works with the additional extra-formal assumption that “the human mind is consistent”. Krajewski argues that this assumption cannot be formalized, and therefore that the anti-mechanist argument – which requires the formalization of the whole reasoning process – fails to establish that the human mind is not mechanistic. A similar situation occurs with a corollary to the argument, that (...) the human mind allegedly outperforms machines, because although there is no exhaustive formal definition of natural numbers, mathematicians can successfully work with natural numbers. Again, the corollary requires an extra-formal assumption: “PA is complete” or “the set of all natural numbers exists”. I agree that extra-formal assumptions are necessary in order to validate the anti-mechanist argument and its corollary, and that those assumptions are problematic. However, I argue that formalization is possible and the problem is instead the circularity of reasoning that they cause. The human mind does not prove its own consistency, and outperforms the machine, simply by making the assumption “I am consistent”. Starting from the analysis of circularity, I propose a way of thinking about the interplay between informal and formal in mathematics. (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)

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)

Philosophers of science have often favoured reductive approaches to how-possibly explanation. This article identifies three alternative conceptions making how-possibly explanation an interesting phenomenon in its own right. The first variety approaches “how possibly X?” by showing that X is not epistemically impossible. This can sometimes be achieved by removing misunderstandings concerning the implications of one’s current belief system but involves characteristically a modification of this belief system so that acceptance of X does not result in contradiction. The second variety offers (...) a potential how-explanation of X. It is usually followed by a range of further potential how-explanations of the same phenomenon. In recent literature the factual claims implied by the second variety have been downplayed whereas the heuristic role of mapping the space of conceptual possibilities has been emphasized. I will focus especially on this truth-bracketing sense of potentiality when looking closer at the second variety in the paper. The third variety has attracted less interest. It presents a partial how-explanation of X. Typically it aims to establish the existence of a mechanism by which X could be and was generated. The third conception stands out as the natural alternative for the advocate of ontic how-possibly explanations. This article transfers Salmon’s view that explanation-concepts can be broadly divided into epistemic, modal, and ontic to the context of how-possibly explanations. Moreover, it is argued that each of the three above-mentioned varieties of how-possibly explanation occurs in science. To recognize this may be especially relevant for philosophers. We are often misled by the promises of various why-explanation accounts, and seem to have forgotten nearly everything about the diversity of how-possibly explanations. (shrink)

This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand (...) Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century. (shrink)

We see no grounds for insisting that, because the concept natural number is abstract, its foundations must be innate. It is possible to specify domain general learning processes that feed into more abstract concepts of numerical infinity. By neglecting the messiness of children's slow acquisition of arithmetical concepts, Rips et al. present an idealized, unnecessarily insular, view of number development.