Cases where analogy has played a significant role in the formation of a new scientific concept are well-documented. Yet, how is it that genuinely new representations can be constructed from existing representations? It is argued that the process of ‘generic modeling’ enables abstraction of features common to both the domain of the source of the analogy and of the target phenomena. The analysis focuses on James Clerk Maxwell's construction of the electromagnetic field concept. The mathematical representation Maxwell constructed turned out (...) to be a system of abstract laws that when applied to electromagnetic systems yield laws of a dynamical system that will not map back onto the mechanicals domains used in their construction. (shrink)

Cases where analogy has played a significant role in the formation of a new scientific concept are well-documented. Yet, how is it that genuinely new representations can be constructed from existing representations? It is argued that the process of ‘generic modeling’ enables abstraction of features common to both the domain of the source of the analogy and of the target phenomena. The analysis focuses on James Clerk Maxwell's construction of the electromagnetic field concept. The mathematical representation Maxwell constructed turned out (...) to be a system of abstract laws that when applied to electromagnetic systems yield laws of a dynamical system that will not map back onto the mechanicals domains used in their construction. (shrink)

Appeals to some thesis of underdetermination, to the idea that scientific theories and hypotheses are not entailed by the evidence that supports them, are common in feminist philosophy of science. These appeals seek to understand and explain how androcentrism and other problematic approaches to gender have found their way into good science, as well as the reverse – how feminist approaches to gender and science that are also value-laden, can contribute to good science. Focusing on W.V. Quine’s positions on holism (...) and underdetermination, I argue that although Quine’s general thesis of holism does not entail his thesis of global underdetermination, his account of and arguments for moderate holism entail a localized and generalizable underdetermination, which I call moderate underdetermination. This moderate underdetermination is not transient or true of only some theories and hypotheses. Rather, it is a permanent state of affairs that characterizes all reasonably inclusive theories and hypotheses, however much evidence for them accumulates. I contend that Quine’s moderate holism entails the most robust and defensible argument for localized underdetermination, and that feminists would do well to appeal to it in arguing that values inform good science. (shrink)

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.

During the 19th century atomism was a controversial issue in chemistry. It is an oversimplification to dismiss the critics' arguments as all falling under the general positivist view that what can't be seen can't be. The more interesting lines of argument either questioned whether any coherent notion of an atom had ever been formulated or questioned whether atoms were ever really given any explanatory role. At what point, and for what reasons, did atomistic hypotheses begin to explain anything in chemistry? (...) It is argued that 19th-century atomic accounts of constant proportions and isomerism had little to offer, whereas a non-atomic explanation of chemical combination was developed. Not until the turn of the century did atomism begin to do serious explanatory work in chemistry. (shrink)

I criticize the treatment of natural kinds as some sort of object, advocated in a recent paper by Alexander Bird. The arguments he gives for regimenting an illustrative statement featuring chemical kinds in his preferred manner are not conclusive, and his criticisms of an alternative strategy involving universally quantified sentences fail. This is important because of the widespread but poorly supported assumption that expressions of natural kinds should be treated as singular referring terms.

In a recent critique of the doctrine of emergentism championed by its classic advocates up to C. D. Broad, Jaegwon Kim (Philosophical Studies 63:31–47, 1999) challenges their view about its applicability to the sciences and proposes a new account of how the opposing notion of reduction should be understood. Kim is critical of the classic conception advanced by Nagel and uses his new account in his criticism of emergentism. I question his claims about the successful reduction achieved in the sciences (...) and argue that his new account has not improved on Nagel’s and that the critique of emergentism he bases on it is question-begging in important respects. (shrink)

Nancy Cartwright has drawn attention to how explanations are actually given in mathematical sciences. She argues that these procedures support an antirealist thesis that fundamental explanatory laws are not true. Moreover, she claims to be be essentially following Duhem's line of thought in developing this thesis. Without wishing to detract from the importance of her observations, it is suggested that they do not necessarily require the antirealist thesis. The antirealist interpretation of Duhem is also disputed. It is argued that Duhemian (...) points, often understood antirealistically, bear a realist construal, and that antirealist interpretations of Duhem typically run into problems of consistency or of reducing his position to absurdity. (shrink)

Somatic cell count is a diagnostic test of milk for mastitis in cows. Its specificity and sensitivity are less than 1.0, making test results uncertain. I discuss epistemological problems of the test such as underdetermination, undercalibration and underdiscrimination, in the solution of which biomedical and economic factors may play a role. Diagnostics of the SCC should be considered as an epistemological network, functioning in a network in which farmers, veterinarians, epidemiologists and milk industry shift their position following biomedical, technological and (...) economic changes, which is described as an actor-network to understand how human and non-human agents in mastitis may be associated. (shrink)

On the basis of the Suppes–Sneed structuralview of scientific theories, we take a freshlook at the concept of refutability,which was famously proposed by K.R. Popper in 1934 as a criterion for the demarcation of scientific theories from non-scientific ones, e.g., pseudo-scientificand metaphysical theories. By way of an introduction we argue that a clash between Popper and his critics on whether scientific theories are, in fact, refutablecan be partly explained by the fact Popper and his criticsascribed different meanings to the term (...) theoryThen we narrow our attention to one particular theory,namely quantum mechanics, in order to elucidate general matters discussed. We prove that quantum mechanics is irrefutable in a rather straightforward sense, but argue that it is refutable in a more sophisticated sense, which incorporates someobservations obtained by looking closely at the practiceof physics. We shall locate exactly where non-rigourous elements enter the evaluation of a scientific theory – thismakes us see clearly how fruitful mathematics isfor the philosophy of science. (shrink)

This is an attempt to take a look at chemistry from the point of view of practical realism. Besides its social–historical and normative aspects, the latter involves a direct reference to experimental research. According to Edward Caldin chemistry depends on our being able to isolate pure substances with reproducible properties. Thus, the very basis of chemistry is practical. Even the laws of chemistry are not stable but are subject to correction. At the same time, these statements do not necessarily make (...) Edward Caldin a predecessor of practical realism. The latter has other predecessors, like Rom Harré’s policy realism or Sami Pihlström’s pragmatic realism. Chemistry is an experimental science. The experiment is a purposeful and critically theory-guided constructive, manipulative, material interference with nature according to Rein Vihalemm, the founder of practical realism. Chemistry is physics-like science but just partly so. This is an important point in the context of the current paper. (shrink)

Having offered the “argument from bad lot”, Bas van Fraassen has raised an important criticism on the Inference to the Best Explanation (IBE) and challenged scientific realism. Regardless of scientific realism, and given the reliance of today's scientific methods on IBE, this criticism poses a deeper threat to the validity of scientific enquiry. In this article, we will try to provide a way to deal with this threat, according to the structure of the scientific community. Some structural features of the (...) contemporary scientific community have caused the scientific enquiry to be limited to the science derived from the Western tradition and deprived it of the theoretical opportunities of various traditions. The main claim of this article is that paying attention to different traditions together to produce science is a good way to expand scientific enquiry and deal with the mentioned threat. In the first section, we will depict how the argument from bad lot threatens the validity of scientific enquiry. In the second section, we discuss the close relationship between science and tradition, and then examine the status of this relationship in the contemporary scientific society. The final section is devoted to proposing the idea of pluralism regarding the use of the theoretical opportunities of different traditions in scientific enquiry, as a proposed solution to counter this threat. (shrink)

Should judgments of beauty play a guiding role in theoretical science even if beauty is not a sign of truth? In this paper I argue that they should in certain cases. If we analyze the rationality of theoretical pursuit using decision theory, a theory’s beauty can influence the utilities of the various options confronting the researcher. After considering the views of Pierre Duhem and Thomas Kuhn on aesthetics in science, I suggest that because we value freedom of inquiry we rightly (...) allow scientists some choice in how they value aesthetic properties of theories and thus some freedom to use beauty to guide their research program. (shrink)

This paper is an examination of evidential holism, a prominent position in epistemology and the philosophy of science which claims that experiments only ever confirm or refute entire theories. The position is historically associated with W.V. Quine, and it is at once both popular and notorious, as well as being largely under-described. But even though there’s no univocal statement of what holism is or what it does, philosophers have nevertheless made substantial assumptions about its content and its truth. Moreover they (...) have drawn controversial and important conclusions from these assumptions. In this paper I distinguish three types of evidential holism and argue that the most oft-cited and controversial thesis is entirely unmotivated. The other two theses are much overlooked, but are well-motivated and free from controversial implications. (shrink)

Evidential holism begins with something like the claim that “it is only jointly as a theory that scientific statements imply their observable consequences.” This is the holistic claim that Elliott Sober tells us is an “unexceptional observation”. But variations on this “unexceptional” claim feature as a premise in a series of controversial arguments for radical conclusions, such as that there is no analytic or synthetic distinction that the meaning of a sentence cannot be understood without understanding the whole language of (...) which it is a part and that all knowledge is empirical knowledge. This paper is a survey of what evidential holism is, how plausible it is, and what consequences it has. Section 1 will distinguish a range of different holistic claims, Sections 2 and 3 explore how well motivated they are and how they relate to one another, and Section 4 returns to the arguments listed above and uses the distinctions from the previous sections to identify holism's role in each case. (shrink)

The relationship between Peircean abduction and the modern notion of Inference to the Best Explanation is a matter of dispute. Some philosophers, such as Harman :88–95, 1965) and Lipton, claim that abduction and IBE are virtually the same. Others, however, hold that they are quite different :503, 1998; Minnameier in Erkenntnis 60:75–105, 2004) and there is no link between them :419–442, 2009). In this paper, I argue that neither of these views is correct. I show that abduction and IBE have (...) important similarities as well as differences. Moreover, by bringing a historical perspective to the study of the relationship between abduction and IBE—a perspective that is lacking in the literature—I show that their differences can be well understood in terms of two historic developments in the history of philosophy of science: first, Reichenbach’s distinction between the context of discovery and the context of justification—and the consequent jettisoning of the context of discovery from philosophy of science—and second, underdetermination of theory by data. (shrink)

Scientific ideas neither arise nor develop in a vacuum. They are always nutured against a background of prior, partially conflicting ideas. Systemic hypothesistesting is the problem of testing scientific hypotheses relative to various systems of background knowledge. This paper shows how the problem of systemic hypothesis-testing (Sys HT) can be systematically expressed as a constrained maximimization problem. It is also shown how the error of the third kind (E III) is fundamental to the theory of Sys HT.The error of the (...) third kind is defined as the probability of having solved the ‘wrong’ problem when one should have solved the ‘right’ problem. This paper shows howE III can be given both a systematic as well as a systemic treatment. Sys HT gives rise to a whole host of new decision problems, puzzles, and paradoxes. (shrink)

Is rhetoric just a new and trendy way toépater les bourgeois?Unfortunately, I think that the newfound interest of some economists in rhetoric, and particularly Donald McCloskey in his new book and subsequent responses to critics, gives that impression. After economists have worked so hard for the past five decades to learn their sums, differential calculus, real analysis, and topology, it is a fair bet that one could easily hector them about their woeful ignorance of the conjugation of Latin verbs or (...) Aristotle's Six Elements of Tragedy. Moreover, it has certainly become an academic cliché that economists write as gracefully and felicitously as a hundred monkeys chained to broken typewriters. The fact that economists still trot out Keynes's prose in their defense is itself an index of the inarticulate desperation of an inarticulate profession. (shrink)

The ArgumentWhile there has been muchattention given to experiment in modern science studies, there has been astoundingly little concern spared over the practice ofquanitataivemeasurment.Thus myths about the unreasonable effectiveness of mathematice in science still abound. This paper presents: An explicit mathematical model of the stabilization of quantitative constants in a mathematical science to rival older Bayesian and classical accounts;a framework for writing a history of pracitces with regard to treatment of quantitative measurement erroe; resourece for the comparative sociology of differing (...) discipliness in this regard;and a prolegonmena to a critique of orthodox economics and accounting theories. The key to all these diverse themes is the realization that no one individual alone is capable of fixing the magnitude of a quantitative error estimate, and therefore the social construction of error must be given a more precise meaning, an therefore the social construction of error must be given a more precise menaing, and that this occurs through the istrumentality of meta-analysis. (shrink)

Scientific consensus is widely deferred to in public debates as a social indicator of the existence of knowledge. However, it is far from clear that such deference to consensus is always justified. The existence of agreement in a community of researchers is a contingent fact, and researchers may reach a consensus for all kinds of reasons, such as fighting a common foe or sharing a common bias. Scientific consensus, by itself, does not necessarily indicate the existence of shared knowledge among (...) the members of the consensus community. I address the question of under what conditions it is likely that a consensus is in fact knowledge based. I argue that a consensus is likely to be knowledge based when knowledge is the best explanation of the consensus, and I identify three conditions—social calibration, apparent consilience of evidence, and social diversity, for knowledge being the best explanation of a consensus. (shrink)

This paper is a detailed critical study of Adolf Grünbaum's work on the Duhemian thesis. I show that (a) Grünbaum's geometrical counterexample to the (D1) subthesis is unsuccessful, even with minimal claims made for what the counterexample is supposed to show, and (b) the (D2) subthesis is not a reasonable one (and cannot correctly be attributed to Duhem). The paper concludes with an argument about the relation between the Duhemian thesis, concerning component hypotheses of a scientific theory, and the view (...) that it is impossible to falsify entire theories conclusively. (shrink)

It is commonly argued that values “fill the logical gap” of underdetermination of theory by evidence, namely, values affect our choice between two or more theories that fit the same evidence. The underdetermination model, however, does not exhaust the roles values play in evidential reasoning. I introduce WAVE – a novel account of the logical relations between values and evidence. WAVE states that values influence evidential reasoning by adjusting evidential weights. I argue that the weight-adjusting role of values is distinct (...) from their underdetermination gap-filling role. Values adjust weights in three ways. First, values affect our trust in the testimony of others. Second, values influence the evidential thresholds required for justified epistemic judgments. Third, values influence the relative weight of a certain type of evidence within a body of multimodal discordant evidence. WAVE explains, from an epistemic perspective, rather than psychological, how smokers, for example, can find the same evidence about the dangers of smoking less persuasive than non-smokers. WAVE allows for a wider effect of values on our accepted scientific theories and beliefs than the effect for which the underdetermination model allows alone; therefore, science studies scholars must consider WAVE in their research and analysis of evidential case studies. (shrink)

Summary In the methodology of science, intersubjectivity is usually associated with replicability of experimental results. A related, judicial conception of objectivity as impartiality has it that a theory or judgment is objective if it covers all the relevant angles of the object or phenomenon in question, ensuring that the latter is not ephemeral and the concepts referring to them are valid. Based on the assumption that in the social sciences, the researcher is also a participant, an alternative view was conceived, (...) according to the notion that intersubjectivity rests on either sharing of a lifeworld and its associated practices or on empathy, or on some form of direct social cognition. My aim in this paper is to bring some elements of the Gestalt theory – and more specifically, Rudolf Arnheim’s (1988) adapted model of field dynamics – to bear on the problematic of intersubjectivity. The proposed model suggests that intersubjectivity is a dynamic phenomenon, best described as a product of two vectors: a vector describing a movement across the circumference combined with a vector describing the movement from the center to the circumference. While the first vector corresponds to impartiality, the second represents the tension between cognitive distancing and direct experience. Overall, it is argued that intersubjectivity cannot be divorced from either subjectivity or objectivity and it amounts to skillful navigation within different frames of reference. (shrink)

In "Why Feynman Diagrams Represent", I argued that Feynman diagrams have two distinct functions: they are both calculational devices, developed to keep track of the long mathematical expressions of quantum electrodynamics,1 and they are pictorial representations. This challenges the common view that FDs are calculational devices alone and that it is misleading, if not an outright error, to think of them as pictorial. Following Kendall Walton's account of representation, I drew out what it means to think of FDs as pictures, (...) which in turn explained why FDs represent. However, my defence conceded an important point: not all of... (shrink)

This multifaceted essay emerges from a host of sources within diverse academic settings. Its central thesis is guided by physicist John A. Wheeler's thoughts on the quantum enigma. Wheeler concludes, following Niels Bohr, that we are co-participants within the universal self-organizing process. This notion merges with concepts from Peirce's process philosophy, Eastern thought, issues of topology, and border theory in cultural studies and social science, while surrounding itself with such key terms as complementarity, interdependence, interrelatedness, vagueness, generality, incompleteness, inconsistency, and (...) mestizaje. Ultimately, a sense of semiosic process pervades in light of combined homogenous and hetergenous tendencies. (shrink)

In the early eighties, philosophers of science came to the conviction that discovery and creativity form an integral part of scientific rationality. Ever since, the?positivists? have been criticised for their neglect of these topics. It is the aim of this paper to show that the positivists' approach to scientific discovery is not only much richer than is commonly recognized, but that they even defended an important thesis which some of the `friends of discovery' seem to have forgotten. Contrary to what (...) is generally accepted, I shall also show that there is no reason at all why the positivists should have ignored discovery. (shrink)

Rolston (1988) argues that in order to act ethically in the environment, moral agents must assume that their actions are potentially harmful, and then strive to prove otherwise before implementing that action. In order to determine whether or not an action in the environment is harmful requires the tools of applied epistemology in order to act in accord with Rolston’s ethical prescription. This link between ethics and epistemology demands a closer look at the relationship between confirmation theory, particularly notions of (...) plausibility, in the philosophy of science and environmental ethics. Upon taking this look, I conclude that, at least logically, we are no better off assuming that actions are maximally risky (Rolston) than when we assume minimal risk. “Our vulnerability to error is greatest not from the things that we include in the model, but from the prophecies we leave out entirely.” Francis Bretherton “What is the main epistemic problem concerning science? I take it that it is the explication of how we compare and evaluate theories, as a basis either for theory acceptance or for practical action.” Bas van Fraassen “We face two kinds of ethical difficulties. One is where we know what ought to be done but not how to get the company to do it. The other is where we do not know what is right. We do not know the facts, or how to weigh the facts, especially statistical ones. We do not know the probabilities for development of future technologies. We do not know how to attach values to facts, or how to trade this good off against that one.” Holmes Rolston. (shrink)

A rationalist and realist model of scientific revolutions will be constructed by reference to two categories of criteria of theory-evaluation, denominated indicators of truth and of beauty. Whereas indicators of truth are formulateda priori and thus unite science in the pursuit of verisimilitude, aesthetic criteria are inductive constructs which lag behind the progression of theories in truthlikeness. Revolutions occur when the evaluative divergence between the two categories of criteria proves too wide to be recomposed or overlooked. This model of revolutions (...) depends upon a substantial new treatment of aesthetic criteria in science with which much of the paper will therefore be occupied. (shrink)

Although explanation is widely regarded as an important concept in the study of rational inquiry, it remains largely unexplored outside the philosophy of science. This, I believe, is not due to oversight as much as to institutional resistance. In analytic philosophy it is basic that epistemic rationality is a function of justification and that justification is a function of argument. Explanation, however, is not argument nor is belief justification its function. I argue here that the task of incorporating explanation into (...) the theory of rational inquiry poses a serious challenge to our basic concept of epistemic rationality as well as the a priori method of inquiry that still lies at the heart of analytic philosophy. Specifically, it pushes us toward a much stronger form of naturalism than is generally thought necessary, one in which argument and explanation are recognized as distinct and equally fundamental cognitive processes whose dynamic relationship is one of the central issues in the theory of rationality. (shrink)

In this three-part paper, my concern is to expound and defend a conception of science, close to Einstein's, which I call aim-oriented empiricism. I argue that aim-oriented empiricsim has the following virtues. (i) It solve the problem of induction; (ii) it provides decisive reasons for rejecting van Fraassen's brilliantly defended but intuitively implausible constructive empiricism; (iii) it solves the problem of verisimilitude, the problem of explicating what it can mean to speak of scientific progress given that science advances from one (...) false theory to another; (iv) it enables us to hold that appropriate scientific theories, even though false, can nevertheless legitimately be interpreted realistically, as providing us with genuine , even if only approximate, knowledge of unobservable physical entities; (v) it provies science with a rational, even though fallible and non-mechanical, method for the discovery of fundamental new theories in physics. In the third part of the paper I show that Einstein made essential use of aim-oriented empiricism in scientific practice in developing special and general relativity. I conclude by considering to what extent Einstein came explicitly to advocate aim-oriented empiricism in his later years. (shrink)

This paper considers objections to Popper's views on scientific method. It is argued that criticism of Popper's views, developed by Kuhn, Feyerabend, and Lakatos, are not too damaging, although they do require that Popper's views be modified somewhat. It is argued that a much more serious criticism is that Popper has failed to provide us with any reason for holding that the methodological rules he advocates give us a better hope of realizing the aims of science than any other set (...) of rules. Consequently, Popper cannot adequately explain why we should value scientific theories more than other sorts of theories ; which in turn means that Popper fails to solve adequately his fundamental problem, namely the problem of demarcation. It is suggested that in order to get around this difficulty we need to take the search for explanations as a fundamental aim of science. (shrink)

It is thirty years since the last major reforms of science education. many believe that it is time for reappraisal of these earlier curricula, and for the renewal of science education-its content, aims, methods. also, and importantly, there is a renewed interest in the preparation of science teachers. this essay is a contribution to that task.

The present article offers an introductory vision to the political philosophy of science. The political philosophy of science is a new field of study where the philosophy of science and political philosophy converge. We will see the main contents of this field. We will also note that it depends on the construction of a model of rationality where science and politics can meet each other. Finally, the article tries to outline such a model of rationality. In order to do so, (...) we will review the relationship between Karl Popper’s scientific and political philosophy. I suggest to read Popper’s critical rationalism in terms of a kind of prudential rationality. (shrink)

I begin by distinguishing two notions of model, the notion of a truth-making structure and the notion of a mathematical model (in one specific sense). I then argue that although the models of the semantic view have often been taken to be both truth-making structures and mathematical models, this is in part due to a failure to distinguish between two ways of truth-making; in fact, the talk of truth-making is best excised from the view altogether. The result is a version (...) of the semantic view which is better supported by the direct evidence offered for it, better equipped to achieve its avowed aims, and, I think, closer to the intentions of the original proponents of the view in many ways, despite some of their own declarations to the contrary. (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)

I reject the widely held view that Duhem's 1906 book La Théorie physique is a statement of instrumentalistic conventionalism, motivated by the scientific crisis at the end of the nineteenth century. By considering Duhem's historical context I show that his epistemological views were already formed before the crisis occured; that he consistently supported general thermodynamics against the new atomism; and that he rejected the epistemological views of the latter's philosophical supporters. In particular I show that Duhem rejected Poincaré's account of (...) scientific language, Le Roy's view that laws are definitions, and the conventionalist's use of simplicity as the criterion of theory choice. Duhem regarded most theory choices as decidable on empirical grounds, but made historical context the main determining factor in scientific change. (shrink)

There are two ways that we might respond to the underdetermination of theory by data. One response, which we can call the agnostic response, is to suspend judgment: "Where scientific standards cannot guide us, we should believe nothing". Another response, which we can call the fideist response, is to believe whatever we would like to believe: "If science cannot speak to the question, then we may believe anything without science ever contradicting us". C.S. Peirce recognized these options and suggested evading (...) the dilemma. It is a Logical Maxim, he suggests, that there could be no genuine underdetermination. This is no longer a viable option in the wake of developments in modern physics, so we must face the dilemma head on. The agnostic and fideist responses to underdetermination represent fundamentally different epistemic viewpoints. Nevertheless, the choice between them is not an unresolvable struggle between incommensurable worldviews. There are legitimate considerations tugging in each direction. Given the balance of these considerations, there should be a modest presumption of agnosticism. This may conflict with Peirce's Logical Maxim, but it preserves all that we can preserve of the Peircean motivation. (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)

Many philosophers and statisticians argue that risk assessors are morally obligated to evaluate the probabilities and consequences of methodological error, and to base their decisions of whether to adopt a given parameter value, model, or hypothesis on those considerations. This argument is couched within the rubric of null hypothesis testing, which I suggest is a poor descriptive and normative model for risk assessment. Risk regulation is not primarily concerned with evaluating the probability of data conditional upon the null hypothesis, but (...) rather with measuring risks, estimating the consequences of available courses of action and inaction, formally characterising uncertainty, and deciding what to do based upon explicit values and decision criteria. In turn, I defend an ideal of value-neutrality, whereby the core inferential tasks of risk assessment – such as weighing evidence, estimating parameters, and model selection – should be guided by the aim of correspondence to reality. This is not to say that value-judgments be damned, but rather that they should be accounted for within a structured approach to decision analysis, rather than embedded within risk assessment in an informal manner. (shrink)

The axiological tenet of scientific realism, “science seeks true theories,” is generally taken to rest on a corollary epistemological tenet, “we can justifiably believe that our successful theories achieve (or approximate) that aim.” While important debates have centered on, and have led to the refinement of, the epistemological tenet, the axiological tenet has suffered from neglect. I offer what I consider to be needed refinements to the axiological postulate. After showing an intimate relation between the refined postulate and ten theoretical (...) desiderata, I argue that the axiological postulate does not depend on its epistemological counterpart; epistemic humility can accompany us in the quest for truth. Upon contrasting my axiological postulate against the two dominant non-realist alternatives and the standard realist postulate, I contend that its explanatory and justificatory virtues render it, among the axiologies considered, the richest account of the scientific enterprise. (shrink)