Naturalism in Mathematics PENELOPE MADDY, 1997 Oxford, Oxford University Press viii + 254 pp., $CAN91, ISBN 0–19–823573–9 Bohmian Mechanics and Quantum Theory: an Appraisal JAMES T. CUSHING, ARTHUR FINE & SHELDON GOLDSTEIN, 1996 Dordrecht, Kluwer viii + 403, pp., US$159.00, ISBN 0–7923–4028–0 Pragmatism as a Principle and Method of Right Thinking: the 1903 Harvard Lectures on Pragmatism CHARLES SANDERS PEIRCE, 1997 Edited and introduced, with a commentary, by PATRICIA ANN TURRISI Albany, State University of New York Press xi + 305 (...) pp., $26.53 ISBN 0–7914–3265–3 ISBN 0–7914–3266–1. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism (...) follow from the norm, while the characteristic claim of the Objectivist Bayesian follows from the norm along with an extra assumption. Finally, we consider Richard Jeffrey’s proposed generalization of conditionalization. We show not only that his rule cannot be derived from the norm, unless the requirement of Rigidity is imposed from the start, but further that the norm reveals it to be illegitimate. We end by deriving an alternative updating rule for those cases in which Jeffrey’s is usually supposed to apply. (shrink)

David Armstrong once argued that to solve the problem of induction with inference to the best explanation we need an anti-Humean conception of law. Some Humeans have argued that this argument begs the question against Humeanism. In this paper, I propose a new argument for the same conclusion which is not vulnerable to this criticism. In particular, I argue that explanationist approaches to the problem of induction that are combined with Humeanism is internally incoherent.

In this paper, I examine J. Carroll's “Mirror Argument” against the Humean conception of law and H. Beebee's response to this argument. I will first show that Beebee's criticism is quite plausible if it is refined slightly. Then, I will propose a revised version of the Mirror Argument which is immune to criticisms like that of Beebee's. According to the Humean conception of law, I will argue, we should accept the existence of counterfactual dependence relation where there should not be (...) such relation. (shrink)

In this paper I offer a coherentist justification of induction along the lines of a Sellarsian coherence theory. On this coherence theory, a proposition is justified if we can answer all objections raised against it in our social practice of demanding justification and responding to such demands. On the basis of this theory of justification, I argue that we are justified in accepting the uniformity of nature partly because we have no alternative but to accept it for rationally pursuing our (...) epistemic goal. In addition, my coherentist view explains which inductive inferences it is rational to accept. Furthermore, my coherentist view also explains why we can hardly determine a particular numerical value x such that we can draw the conclusion ‘it is rational to accept that p’ from the premise ‘the numerical probability of p is greater than or equal to x’. (shrink)

In this paper, a modest version of the Semantic View is motivated as both tenable and potentially fruitful for philosophy of science. An analysis is proposed in which the Semantic View is characterized by three main claims. For each of these claims, a distinction is made between stronger and more modest interpretations. It is argued that the criticisms recently leveled against the Semantic View hold only under the stronger interpretations of these claims. However, if one only commits to the modest (...) interpretation for all the claims, then the view obtained, the Modest Semantic View, is tenable and fruitful for the philosophy of science. (shrink)

The view that takes laws of nature to be essentially nothing more than descriptions of facts is still rather popular. The present article, on the contrary, defends the claim that the only real motivation for defending a descriptive view of laws—the quest for ontological parsimony—entails too high a price to pay in philosophical terms. It is argued that nomic primitivism, namely the alternative option that takes laws to be primitive fundamental entities in our ontology, is decisively more appealing, since it (...) is the crucial role assigned to laws that makes a scientific theory of natural phenomena a system rather than a list. Finally, the implications that nomic primitivism might have for the issue of the status of the wave function in that particular formulation of quantum mechanics known as Bohmian mechanics are considered. (shrink)

In this paper a simple model in particle dynamics of a well-known supertask is constructed (the supertask was introduced by Max Black some years ago). As a consequence, a new and simple result about creation ex nihilo of particles can be proved compatible with classical dynamics. This result cannot be avoided by imposing boundary conditions at spatial infinity, and therefore is really new in the literature. It follows that there is no reason why even a world of rigid spheres should (...) be eternal, as has been erroneously assumed, especially since the time of Newton. (shrink)

This paper argues that in mathematical practice, conjectures are sometimes confirmed by “Inference to the Best Explanation” as applied to some mathematical evidence. IBE operates in mathematics in the same way as IBE in science. When applied to empirical evidence, IBE sometimes helps to justify the expansion of scientists’ ontological commitments. Analogously, when applied to mathematical evidence, IBE sometimes helps to justify mathematicians' in expanding the range of their ontological commitments. IBE supplements other forms of non-deductive reasoning in mathematics, avoiding (...) obstacles sometimes faced by enumerative induction or hypothetico-deductive reasoning. Both platonist and non-platonist interpretations of mathematics ought to accommodate explanation in mathematics and ought to recognize IBE in mathematics, though these interpretations disagree on the ontological commitments that mathematicians ought to have. This paper offers an inductive account of why mathematical IBE tends to lead to mathematical truths. (shrink)

After reviewing several failed arguments that laws cannot change, I use the laws' special relation to counterfactuals to show how temporary laws would have to differ from eternal but time-dependent laws. Then I argue that temporary laws are impossible and that neither Lewis's nor Armstrong's analyses of law nicely accounts for the laws' immutability. *Received September 2006; revised September 2007. ‡Many thanks to John Roberts and John Carroll for valuable comments on earlier drafts, as well as to several anonymous referees (...) for their good suggestions. †To contact the author, please write to: Department of Philosophy, University of North Carolina, CB #3125, Caldwell Hall, Chapel Hill, NC 27599-3125; e-mail: [email protected]. (shrink)

Why do forces compose according to the parallelogram of forces? This question has been controversial; it is one episode in a longstanding, fundamental dispute regarding which facts are not to be explained dynamically. If the parallelogram law is explained statically, then the laws of statics are separate from and “transcend” the laws of dynamics. Alternatively, if the parallelogram law is explained dynamically, then statical laws become mere corollaries to the dynamical laws. I shall attempt to trace the history of this (...) controversy in order to identify what it would be for one or the other of these rival views to be correct. I shall argue that various familiar accounts of natural law not only make it difficult to see what the point of this dispute could have been, but also improperly foreclose some serious scientific options. I will sketch an alternative account of laws that helps us to understand what this dispute was all about. (shrink)

Constructive empiricism is supposed to offer a positive alternative to scientific realism that dispenses with the need for metaphysics. I first review the terms of the debate before arguing that the standard objections to constructive empiricism are not decisive. I then explain van Fraassen's views on modality and counterfactuals, and argue that, because constructive empiricism recommends on epistemological grounds belief in the empirical adequacy rather than the truth of theories, it requires that there be an objective modal distinction between the (...) observable and the unobservable. This conclusion is incompatible with van Fraassen's empiricism. Finally I explain some further problems for constructive empiricism that arise when we consider modal matters. (shrink)

Abstractvan Fraassen (The empirical stance, 2002) contrasts the empirical stance with the materialist stance. The way he describes them makes both of them attractive, and while opposed they have something in common for both stances are scientific approaches to philosophy. The difference between them reflects their differing conceptions of science itself. Empiricists emphasise fallibilism, verifiability and falsifiability, and also to some extent scepticism and tolerance of novel hypotheses. Materialists regard the theoretical picture of the world as matter in motion as (...) a true and explanatory account and insist on not taking ‘spooky’ entities or processes seriously as potential explanations of phenomena that so far lie outside the scope of successful science. The history of science shows us that both stances have been instrumental in the achievement of progress at various times. It is therefore plausible for a naturalist to suggest that science depends for its success on the dialectic between empiricism and materialism. A truly naturalist approach to philosophy ought then to synthesise them. Call the synthesized empiricist and materialist stances ‘the scientistic stance’. This paper elaborates and defends it. (shrink)

While there are many examples of metaphysical theorising being heuristically and intellectually important in the progress of scientific knowledge, many people wonder how metaphysics not closely informed and inspired by empirical science could lead to rival or even supplementary knowledge about the world. This paper assesses the merits of a popular defence of the a priori methodology of metaphysics that goes as follows. The first task of the metaphysician, like the scientist, is to construct a hypothesis that accounts for the (...) phenomena in question. It is then argued that among the possible metaphysical theories, the empirical evidence underdetermines the right one, just as the empirical evidence underdetermines the right scientific theory. In the latter case it is widely agreed that we must break the underdetermination by appeal to theoretical virtues, and this is just what should be and largely is done in metaphysics. This is part of a more general line of argument that defends metaphysics on the basis of its alleged continuity with highly theoretical science. In what follows metaphysics and theoretical science are compared in order to see whether the above style of defence of a priori metaphysics is successful. (shrink)

The present paper concerns how scientific realism is formulated and defended. It is argued that van Fraassen is fundamentally right that scientific realism requires metaphysics in general, and modality in particular. This is because of several relationships that raise problems for the ontology of scientific realism, namely those between: scientific realism and common sense realism; past and current theories; the sciences of different scales; and the ontologies of the special sciences and fundamental physics. These problems are related. It is argued (...) that ontic structural realism, in the form of the real-patterns account of ontology, offers a unified solution to them all. (shrink)

, I argued that Bas van Fraassen's constructive empiricism was undermined in various ways by his antirealism about modality. Here I offer some comments and responses to the reply to my arguments by Bradley Monton and van Fraassen [2003]. In particular, after making some minor points, I argue that Monton and van Fraassen have not done enough to show that the context dependence of counterfactuals renders their truth conditions non-objective, and I also argue that adopting modal realism does after all (...) undermine the motivation for constructive empiricism. Introduction Underdetermination and epistemic modesty Counterfactual observations Modal realism and constructive empiricism. (shrink)

We are concerned here with how structural properties of language may come to reflect features of the world in which it evolves. As a concrete example, we will consider how a simple term language might evolve to support the principle of indifference over state descriptions in that language. The point is not that one is justified in applying the principle of indifference to state descriptions in natural language. Instead, it is that one should expect a language that has evolved in (...) the context of facilitating successful action to reflect probabilistic features of the world in which it evolved. (shrink)

Van Fraassen's epistemology is forged from two commitments, one to a type of Bayesianism and the other to what he terms voluntarism. Van Fraassen holds that if one is going to follow a rule in belief-revision, it must be a Bayesian rule, but that one does not need to follow a rule in order to be rational. It is argued that van Fraassen's arguments for rejecting non-Bayesian rules is unsound, and that his voluntarism is subject to a fatal dilemma arising (...) from the non-monotonic character of reasoning. (shrink)

I lay out the framework for my theory of sensory imagination in “Imagining as a guide to possibility.” Sensory imagining involves mental imagery , and crucially, in describing the content of imagining, I distinguish between qualitative content and assigned content. Qualitative content derives from the mental image itself; for visual imaginings, it is what is “pictured.” For example, visually imagine the Philadelphia Eagles defeating the Pittsburgh Steelers to win their first Super Bowl. You picture the greenness of the field and (...) the football’s brown oblong shape. Some of what you imagine isn’t explicitly pictured, however. That it is Sunday, that it is the Super Bowl: these facts are assigned. (shrink)

Recently in epistemology a number of authors have mounted Bayesian objections to dogmatism. These objections depend on a Bayesian principle of evidential confirmation: Evidence E confirms hypothesis H just in case Pr(H|E) > Pr(H). I argue using Keynes' and Knight's distinction between risk and uncertainty that the Bayesian principle fails to accommodate the intuitive notion of having no reason to believe. Consider as an example an unfamiliar card game: at first, since you're unfamiliar with the game, you assign credences based (...) on the indifference principle. Later you learn how the game works and discover that the odds dictate you assign the very same credences. Examples like this show that if you initially have no reason to believe H, then intuitively E can give you reason to believe H even though Pr(H|E) ≤ Pr(H). I show that without the principle, the objections to dogmatism fail. (shrink)

Both sides in the debate about scientific realism have argued that their view provides a better account of actual scientific practice. For example, it has been claimed that the practice of theory conjunction presupposes realism, and that scientists' use of multiple and incompatible models presupposes some form of instrumentalism. Assuming that the practices of science are rational, these conclusions cannot both be right. I argue that neither of them is right, and that, in fact, all scientific practices are compatible with (...) both realism and instrumentalism. I also repudiate van Fraassen's argument to the effect that the instrumentalist account of scientific practice is logically weaker, hence better, than the realist account. In the end, there are no scientific practice arguments on the table that support either side of the debate. It is also noted that the deficiencies of van Fraassen's argument are recapitulated in Putnam's miracle argument for realism. My pessimistic assessment of the state of the debate is reminiscent of Arthur Fine's. However, Fine's argument for the ‘natural ontological attitude’ once again repeats the problems of van Fraassen's and Putnam's arguments. (shrink)

The question of the role of theory in the determination of reference of theoretical terms continues to be a controversial one. In the present paper I assess a number of responses to this question (including variations on David Lewis’s appeal to Ramsification), before describing an alternative, epistemically oriented account of the reference-determination of such terms. The paper concludes by discussing some implications of the account for our understanding of both realism and such competitors of realism as constructive empiricism.

An otherwise lawlike generalisation hedged by a ceteris paribus (CP) clause qualifies as a law of nature, if the CP clause can be substituted with a set of conditions derived from the multivariate regression model used to interpret the empirical data in support of the gen- eralisation. Three studies in human biology that use regression analysis are surveyed, showing that standard objections to cashing out CP clauses in this way—based on alleged vagueness, vacuity, or lack of testability—do not apply. CP (...) laws also cannot be said to be simply false due to the indefinitely many conditions not explicitly stated in their associated model: scientific CP clauses imply that these are, given the evidence, not nomically relevant. (shrink)

Knowledge of many facts does not amount to understanding unless one also has a sense of how the facts fit together. This aspect of coherence among scientific observations and theories is usually overlooked in summaries of scientific method, since the emphasis is on justification and verification rather than on understanding. I argue that the inter-theoretic coherence, as the hallmark of understanding, is an essential and informative component of any accurate description of science.

The Standard Model of elementary particle physics distinguishes between fundamental and accidental symmetries. The distinction is not based on empirical features of the symmetry, nor on a metaphysical notion of necessity. A symmetry is fundamental to the extent that other aspects of nature depend on it, and it is recognized as fundamental by its being theoretically well-connected. This paper clarifies the concept of what it is to be fundamental in this sense, and suggests broader implications for the analysis of scientific (...) knowledge. (shrink)

The anti-metaphysical argument against scientific realism is the following: Knowledge of unobservable entities implies metaphysical knowledge; There is no metaphysical knowledge. Therefore, there is no knowledge of unobservable entities. This argument has strangely received little attention in the profuse literature on scientific realism. This paper claims that the AMA is logically more fundamental than both the pessimistic meta-induction and the underdetermination argument. The second and main claim of this paper is that the instrumentalists’ use of AMA is incoherent. The gist (...) of my argument is that experimental knowledge requires minimally metaphysical knowledge, and that minimally metaphysical knowledge—when associated with empirical knowledge—suffices to yield a minimal knowledge of the unobservable. I then examine and reject two possible responses: minimally metaphysical instrumentalism and algebraic instrumentalism. (shrink)

This article criticizes the attempts by Bas van Fraassen and Michael Friedman to address the challenge to rationality posed by the Kuhnian analysis of scientific revolutions. In the paper, I argue that van Fraassen's solution, which invokes a Sartrean theory of emotions to account for radical change, does not amount to justifying rationally the advancement of science but, rather, despite his protestations to the contrary, is an explanation of how change is effected. Friedman's approach, which appeals to philosophical developments at (...) a meta-theoretical level, does not really address the problem of rationality as posed by Kuhn's work. Instead of showing how, despite revolutions, scientific development is, indeed, rational, he gives a transcendental account of rational scientific progress. (shrink)

Ever since Elga presented his famous puzzle of Sleeping Beauty, philosophers have debated between the Thirder and the Halfer positions. In his recent article, Daniel Singer proposes a new position, according to which Beauty ought to assign [0, 1/2] to the coin’s landing heads. For this argument, he exploits the similarity between Elga’s original puzzle and Bovens’s modified one. According to Singer, Beauty ought to assign the same credence to H in both versions of Sleeping Beauty. Since Beauty ought to (...) assign [0, 1/2] to H in Bovens’s version, she ought to assign [0, 1/2] to H in Elga’s original version, too. Let us call this “the Impreciser view.” In this paper, I will contend that Singer’s argument fails. First, he depends on false assumptions in defending his Impreciser view. Second, Bovens’s version of Sleeping Beauty turns out to be underdescribed in an important aspect. If we try to provide a fuller description for it, either Beauty does not have to assign [0, 1/2] to H or the thus complemented version of Bovens’s puzzle will fail to be analogous with Elga’s original one. In either case, Singer’s discussion does not establish his Impreciser view. (shrink)

According to van Fraassen, inference to the best explanation (IBE) is incompatible with Bayesianism. To argue to the contrary, many philosophers have suggested hybrid models of scientific reasoning with both explanationist and probabilistic elements. This paper offers another such model with two novel features. First, its Bayesian component is imprecise. Second, the domain of credence functions can be extended.

Epistemologists have recently debated whether understanding is a species of knowledge. However, because they have offered little in the way of a detailed analysis of understanding, they lack the resources to resolve this issue. In this paper, I propose that S understands why p if and only if S has the non-Gettierised true belief that p, and for some proposition q, S has the non-Gettierised true belief that q is the best available explanation of p, S can correctly explain p (...) with q, and S can identify the features that make q the best explanation of p. On this analysis, understanding is reducible to knowing that p and that q is the best available explanation of p. (shrink)

The underconsideration argument against inference to the best explanation and scientific realism holds that scientists are not warranted in inferring that the best theory is true, because scientists only ever conceive of a small handful of theories at one time, and as a result, they may not have considered a true theory. However, antirealists have not developed a detailed alternative account of why explanatory inference nevertheless appears so central to scientific practice. In this paper, I provide new defences against some (...) recent objections to the underconsideration argument, while also developing an account of explanatory inference that both survives these criticisms and does not entail realism. (shrink)

Das Buch verschafft einen Überblick über die neuere Willensfreiheitsdebatte, wobei es auch die Konsequenzen der Hirnforschung für das Freiheitsproblem erörtert. Ferner entwickelt der Autor eine eigene Position, die er 'fähigkeitsbasierten Libertarismus' nennt. Er widerspricht dem breiten philosophischen Konsens, dass jedenfalls eine Art von Freiheit mit einem naturwissenschaftlichen Weltbild unverträglich sei, nämlich die Fähigkeit, sich unter gegebenen Bedingungen so oder anders zu entscheiden. Im Buch wird argumentiert, dass der libertarischen Freiheitsauffassung, die wir im Alltag alle teilen, bei näherer Betrachtung keine Tatschen (...) entgegenstehen, sondern nur philosophische Doktrinen. Zwar können wir durch unser Handeln keine Naturgesetze abändern und sind auch keine ersten Beweger, aber für ein So-oder-Anderskönnen bedarf es dessen nicht. (shrink)

Virtually all philosophers of science have construed fundamental theories as descriptions of entities, properties, and/or structures. Call this the “descriptive-ontological” view. I argue that this view is incorrect, at least insofar as physical theories are concerned. I propose a novel construal of theories that I call the “prescriptive-dynamical” view. The central tenet of this view, roughly put, is that the _essential_ content of fundamental physical theories is a _prescription for interfacing with natural systems and translating local data into compact theoretical (...) language_. The descriptive-ontological aspects of theories, if any, are taken as _inessential_ content on this view: they do not contribute to the predictive success of the theory. Rather than describing _what is there_, the essence of a physical theory is to tell us _what to do_ when interfacing with a physical system. (shrink)

This paper explores varieties of scientific structuralism. Central to our investigation is the notion of `shared structure'. We begin with a description of mathematical structuralism and use this to point out analogies and disanalogies with scientific structuralism. Our particular focus is the semantic structuralist's attempt to use the notion of shared structure to account for the theory-world connection, this use being crucially important to both the contemporary structural empiricist and realist. We show why minimal scientific structuralism is, at the very (...) least, a powerful methodological standpoint. Our investigation also makes explicit what more must be added to this minimal structuralist position in order to address the theory-world connection, namely, an account of representation. (shrink)

It is shown that Lewis’ ontological doctrine of Humean supervenience incorporates at its foundation the so-called separability principle of classical physics. In view of the systematic violation of the latter within quantum mechanics, the claim that contemporary physical science may posit non-supervenient relations beyond the spatiotemporal ones is reinforced on a foundational basis concerning constraints on the state representation of physical systems. Depending on the mode of assignment of states to quantum systems — unit state vectors versus statistical density operators (...) — we distinguish between strongly and weakly non-Humean, non-supervenient relations. It is demonstrated that in either case, the relations of quantum entanglement constitute prototypical examples of irreducible physical relations that do not supervene upon a spatiotemporal arrangement of Humean qualities, weakening, thereby, the thesis of Humean supervenience. In this respect, the status of Lewis’ recombination principle is examined, whereas his conception of lawhood is critically investigated. It is concluded that the assumption of ontological reductionism, as expressed in Lewis’ Humean doctrine, cannot be regarded as a reliable code of the nature of the physical world and its contents. It is proposed instead that due to the undeniable existence of non-supervenient relations, a metaphysic of relations of a moderate kind ought to be acknowledged as an indispensable part of our understanding of the natural world at a fundamental level. (shrink)

Epistemic theories of objective chance hold that chances are idealised epistemic probabilities of some sort. After giving a brief history of this approach to objective chance, I argue for a particular version of this view, that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. The main argument for this view is the demonstration that it entails all of the commonly-accepted properties of chance. For example, this analysis entails that chances (...) supervene on the physical facts, that the chance function is an expert probability, that the existence of stable frequencies results from invariant chances in repeated experiments, and that chances are probably close to long-run relative frequencies in repeated experiments. Despite these virtues, epistemic approaches to chance have been neglected in recent decades, on account of their conflict with accepted views about closely related topics such as causation, laws of nature, and epistemic probability. However, existing views on these topics are also very problematic, and I believe that the epistemic view of chance is a key piece of this puzzle that, once in place, allows all the other pieces to fit together into a new and coherent way. I also respond to some criticisms of the epistemic theory that I favour. (shrink)

In criminal trials, judges or jurors have to decide whether the facts described in the indictment are proven beyond a reasonable doubt. However, these decision-makers cannot always imagine every relevant sequence of events—there may be unconceived alternatives. The possibility of unconceived alternatives is an overlooked source of reasonable doubt. I argue that decision-makers should not consider the defendant’s guilt proven if they have good reasons to believe that plausible, unconceived scenarios exist. I explore this thesis through the lens of the (...) two most influential accounts of rational criminal proof—Bayesian and explanation-based approaches. I draw on related ideas from the philosophy of science to show why and when unconceived alternatives lead to reasonable doubt on either account. (shrink)

Explanationist accounts of rational legal proof view trials as a competition between explanations. Such accounts are often criticized for being underdeveloped. One question in need of further attention is when guilt is proven beyond a reasonable doubt in criminal trials. This article defends an inference to the best explanation -based approach on which guilt is only established BARD if the best guilt explanation in a case is substantially more plausible than any innocence explanation, and there is no good reason to (...) presume that we have overlooked evidence or alternative explanations that could realistically have exonerated the defendant. This is a comparative account, which I argue is better suited for arriving at accurate verdicts than the non-comparative ‘no plausible alternative’ account that many explanationists tacitly assume. Furthermore, this account is not susceptible to the most important arguments against IBE in criminal trials or to arguments against other, non-explanationist interpretations of the BARD standard. I use a case study to illustrate how this account provides meaningful guidance for decision makers in criminal trials. (shrink)

From a point of view like de Finetti's, what is the judgmental reality underlying the objectivistic claim that a physical magnitude X determines the objective probability that a hypothesis H is true? When you have definite conditional judgmental probabilities for H given the various unknown values of X, a plausible answer is sufficiency, i.e., invariance of those conditional probabilities as your probability distribution over the values of X varies. A different answer, in terms of conditional exchangeability, is offered for use (...) when such definite conditional probabilities are absent. (shrink)

Scientific practice involves two kinds of induction. In one, generalizations are drawn about the states of a particular system of variables. In the other, generalizations are drawn across systems in a class. We can discern two questions of correctness about both kinds of induction: what distinguishes those systems and classes of system that are ‘projectible’ in Goodman’s sense from those that are not, and what are the methods by which we are able to identify kinds that are likely to be (...) projectible? In answer to the first question, numerous theories of ‘natural kinds’ have been advanced, but none has satisfactorily addressed both questions simultaneously. I propose a shift in perspective. Both essentialist and cluster property theories have traditionally characterized kinds directly in terms of the causally salient properties their members possess. Instead, we should focus on ‘dynamical symmetries’, transformations of a system to which the causal structure of that system is indifferent. I suggest that to be a member of natural kind it is necessary and sufficient to possess a particular collection of dynamical symmetries. I show that membership in such a kind is in turn necessary and sufficient for the presence of the sort of causal structure that accounts for success in both kinds of induction, thus demonstrating that has been answered satisfactorily. More dramatically, I demonstrate that this new theory of ‘dynamical kinds’ provides an answer to with methodological implications concerning the discovery of projectible kinds. (shrink)

Scientists routinely solve the problem of supplementing one’s store of variables with new theoretical posits that can explain the previously inexplicable. The banality of success at this task obscures a remarkable fact. Generating hypotheses that contain novel variables and accurately project over a limited amount of additional data is so difficult—the space of possibilities so vast—that succeeding through guesswork is overwhelmingly unlikely despite a very large number of attempts. And yet scientists do generate hypotheses of this sort in very few (...) tries. I argue that this poses a dilemma: either the long history of scientific success is a miracle, or there exists at least one method or algorithm for generating novel hypotheses with at least limited projectibility on the basis of what’s available to the scientist at a time, namely a set of observations, the history of past conjectures, and some prior theoretical commitments. In other words, either ordinary scientific success is miraculous or there exists a logic of discovery at the heart of actual scientific method. (shrink)

The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are often seen as part of (...) the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence. (shrink)