I argue on the basis of an example, Fourier theory applied to the problem of vibration, that Field's program for nominalizing science is unlikely to succeed generally, since no nominalistic variant will provide us with the kind of physical insight into the phenomena that the standard theory supplies. Consideration of the same example also shows, I argue, that some of the motivation for mathematical fictionalism, particularly the alleged problem of cognitive access, is more apparent than real.
In this paper I argue three things: (1) that the interactionist view underlying Benacerraf's (1973) challenge to mathematical beliefs renders inexplicable the reliability of most of our beliefs in physics; (2) that examples from mathematical physics suggest that we should view reliability differently; and (3) that abstract mathematical considerations are indispensable to explanations of the reliability of our beliefs.
SummaryBenacerraf challenges us to account for the reliability of our mathematical beliefs given that there appear to be no natural connections between mathematical believers and mathematical ontology. In this paper I try to do two things. I argue that the interactionist view underlying this challenge renders inexplicable not only the reliability of our mathematical beliefs, construed either platonistically or naturalistically , but also the reliability of most of our beliefs in physics. I attempt to counter Benacerraf's challenge by sketching an (...) alternative conception of reliability explanations which renders explicable the reliability of our beliefs in physics and in mathematics but in which mathematical and formal considerations themselves play a central role. My main thesis is that abstract objects do not strike us, but that this is irrelevant to the reliability of our mathematical and physical beliefs. (shrink)
Scientific Realism and Antirealism Debates about scientific realism concern the extent to which we are entitled to hope or believe that science will tell us what the world is really like. Realists tend to be optimistic; antirealists do not. To a first approximation, scientific realism is the view that well-confirmed scientific theories are approximately true; … Continue reading Scientific Realism and Antirealism →.
Book Information Knowledge, Cause, and Abstract Objects: Causal Objections to Platonism. Knowledge, Cause, and Abstract Objects: Causal Objections to Platonism Colin Cheyne , Dordrecht: Kluwer Academic Publishers , 2001 , xvi + 236 , £55 ( cloth ) By Colin Cheyne. Dordrecht: Kluwer Academic Publishers. Pp. xvi + 236. £55.
Most science requires applied mathematics. This truism underlies the Quine-Putnam indispensability argument: we cannot be mathematical nominalists without rejecting whole swaths of good science that are seamlessly linked with mathematics. One style of response accepts the challenge head-on and attempts to show how to do science without mathematics. There is some consensus that the response fails because the nominalistic apparatus deployed either is not extendible to all of mathematical physics or is merely a deft reconstrual equivalent to standard mathematics. A (...) second style of response denies that indispensability entails realism: when we mathematize a physical problem we treat its physical content as if it were the mathematical representation; provided the two are sufficiently similar, we can use the mathematics to draw conclusions about the physics; even if we cannot represent physical facts without mathematical tools, as-if-fictionalism is reasonable. In this paper I argue that uses of mathematics in science reach deeper than is appreciated by this second response and, indeed, in the more general literature. More specifically, our confidence that we can use the mathematics to draw conclusions about the physics itself depends on mathematics. If the mathematical premises we employ in concluding that a certain application is trustworthy are false, we may lack a justification for supposing that the application will reliably lead us from correct input to correct output. For example, solutions to many physical problems require the determination of a function satisfying a differential equation. Sometimes the existence of a solution for initial value problems can be established directly; where direct methods fail, the existence of a solution must be established indirectly, generally by constructing a sequence of functions that converges to a limit function that satisfies the initial value problem. Moreover, the solution often cannot be evaluated by analytic methods, and scientists must rely on finite element numerical methods to approximate the solution. Mathematical analysis of errors provides further useful information governing the choice of approximation method and of the step size and number of elements needed for the approximation to reach a desired precision. Mathematical physicists rely on the background mathematical theories presupposed in proving the existence of the solutions and approximating them. It is difficult to see how they could do this while adding the fictionalist disclaimer, “But, you know, I don’t believe any of the mathematics I’m using”. It is difficult to see how a fictionalist pursuing the second strategy can account for the soundness of mathematical reasoning in mathematical physics and elsewhere in the sciences. The paper will fill out this argument by appeal to examples and attempt to make clear how mathematics is indispensable to understanding – and thus underwriting our confidence in – applications that would otherwise be shaky approximations and idealizations and how this role is difficult to square with fictionalism. (shrink)
According to externalism, reference is a relation between uses of an expression and features of the environment. Moreover, the reference relation is normative , and the referential relata of our expressions are explanatory of successful language use. This paper largely agrees with the broad conception underlying externalism: it is what people do with words that makes them have the references they have, and the world constrains what people can successfully do with words. However, the paper strongly disagrees with the details (...) . A centrally important feature of what people do with words is how they use them in inferential contexts. When due attention is given to the reference-determining role played by inferential properties of expressions, I argue, we arrive at a more satisfactory account of semantic norms and explanations. Much of the argument is based on a detailed look at the language of chemical classification used in the late 19th century. (shrink)
In this paper I discuss lessons that metaphysicians might learn from Duhem. Given Duhem’s well known antipathy to metaphysics, you will likely think that this is a fairly inauspicious beginning with a predictable ending: i.e., physics is one thing, metaphysics another, and never the twain shall meet. If you will bear with me, however, I hope to persuade you differently. On the contrary, I will argue, Duhem was both a common sense and metaphysical realist, his nuanced views about the relationship (...) between physics and metaphysics are poorly understood, and properly understood contain important lessons for contemporary metaphysics. I’ll spend most of the paper rehabilitating Duhem and finish with some lessons for metaphysicians. (shrink)
It is commonly presupposed that all instances of the deflationary reference schema ‘F’ applies to x if and only if x is ‘are correct. This paper argues, mainly on the basis of concrete example, that we have little reason to be confident about this presupposition: our tendency to believe the instances is based on local successes that may not be globally extendible. There is a problem of semantic projection, Ii argue, and standard accounts that would resolve or dissolve the problem (...) are problematic. (shrink)
Most science requires applied mathematics. This truism underlies the Quine-Putnam indispensability argument: we cannot be mathematical nominalists without rejecting whole swaths of good science that are seamlessly linked with mathematics. One style of response (e.g. Field’s program) accepts the challenge head-on and attempts to show how to do science without mathematics. There is some consensus that the response fails because the nominalistic apparatus deployed either is not extendible to all of mathematical physics or is merely a deft reconstrual equivalent to (...) standard mathematics. A second style of response (suggested, e.g., by Balaguer and Maddy) denies that indispensability entails realism: when we mathematize a physical problem we treat its physical content as if it were the mathematical representation; provided the two are sufficiently similar, we can use the mathematics to draw conclusions about the physics; even if we cannot represent physical facts without mathematical tools, as-if-fictionalism is reasonable. In this paper I argue that uses of mathematics in science reach deeper than is appreciated by this second response and, indeed, in the more general literature. More specifically, our confidence that we can use the mathematics to draw conclusions about the physics itself depends on mathematics. If the mathematical premises we employ in concluding that a certain application is trustworthy are false, we may lack a justification for supposing that the application will reliably lead us from correct input to correct output. For example, solutions to many physical problems require the determination of a function satisfying a differential equation. Sometimes (e.g., if the differential equation is linear) the existence of a solution for initial value problems can be established directly; where direct methods fail, the existence of a solution must be established indirectly, generally by constructing a sequence of functions that converges to a limit function that satisfies the initial value problem. Moreover, the solution often cannot be evaluated by analytic methods, and scientists must rely on finite element numerical methods to approximate the solution. Mathematical analysis of errors provides further useful information governing the choice of approximation method and of the step size and number of elements needed for the approximation to reach a desired precision. Mathematical physicists rely on the background mathematical theories (e.g., theory of differential equations) presupposed in proving the existence of the solutions and approximating them. It is difficult to see how they could do this while adding the fictionalist disclaimer, “But, you know, I don’t believe any of the mathematics I’m using”. It is difficult to see how a fictionalist pursuing the second strategy can account for the soundness of mathematical reasoning in mathematical physics and elsewhere in the sciences. The paper will fill out this argument by appeal to examples and attempt to make clear (a) how mathematics is indispensable to understanding – and thus underwriting our confidence in – applications that would otherwise be shaky approximations and idealizations and (b) how this role is difficult to square with fictionalism. (shrink)
In this book physicist Roland Omnès addresses some big questions in philosophy of mathematics. Anyone who reflects on the history and practice of mathematics and the sciences, especially physics, will naturally be struck by some remarkable coincidences. First, often newly developed mathematics was not well understood. But its successful applications and its agreement with intuitive representations of reality promoted confidence in its correctness even absent clear foundations . Later, this confidence is vindicated when a proper setting for the concepts and (...) techniques is discovered . Second, often mathematical concepts designed for one purpose later turn out to have pervasive applications that could not have been imagined by the original practitioners. Third, many of the most important results obtained in physics since the late nineteenth century were driven by the search for precise, comprehensive, consistent theoretical frameworks: the sequence special relativity, general relativity, relativistic quantum mechanics, string theory can be seen as one that increases comprehensiveness by consistent unification. The fundamental theoretical work has little to do with empirical investigation and a lot to do with mathematical and conceptual investigation of invariances and symmetries. Fourth, mathematical principles guarantee existence principles needed by physics . Such coincidences naturally invite questions: Why is confidence in the consistency of a successful piece of mathematics so often vindicated? Why does mathematics turn out to be so comprehensive and fruitful in unexpected …. (shrink)
Scientific Realism and Antirealism Debates about scientific realism concern the extent to which we are entitled to hope or believe that science will tell us what the world is really like. Realists tend to be optimistic; antirealists do not. To a first approximation, scientific realism is the view that well-confirmed scientific theories are approximately true; … Continue reading Scientific Realism and Antirealism →.
Russell’s views about the proper logical and epistemological treatment of names conspired to lead him to set aside considerations that support the claim that names are not definite descriptions. Though he appreciated those considerations, he famously argued that ordinary names are truncated definite descriptions. Nevertheless, his appreciation of the distinctive semantic behavior of ordinary names combined with his view that acquaintance comes in degrees led him to attempt to secure a semantically privileged status for ordinary names: only special kinds of (...) descriptions can go proxy for ordinary names “used as names”. The paper attempts to tell this story, filling in gaps where Russell doesn’t provide sufficient elaboration, and to draw some general conclusions about acquaintance-based approaches to names and singular thoughts. (shrink)
In this book, Michael Arbib, a researcher in artificial intelligence and brain theory, joins forces with Mary Hesse, a philosopher of science, to present an integrated account of how humans 'construct' reality through interaction with the social and physical world around them. The book is a major expansion of the Gifford Lectures delivered by the authors at the University of Edinburgh in the autumn of 1983. The authors reconcile a theory of the individual's construction of reality as a network (...) of schemas 'in the head' with an account of the social construction of language, science, ideology and religion to provide an integrated schema-theoretic view of human knowledge. The authors still find scope for lively debate, particularly in their discussion of free will and of the reality of God. The book integrates an accessible exposition of background information with a cumulative marshalling of evidence to address fundamental questions concerning human action in the world and the nature of ultimate reality. (shrink)
This paper deals with Ludwik Fleck’s theory of thought styles and Michael Polanyi’s theory of tacit knowledge. Though both concepts have been very influential for science studies in general, and both have been subject to numerous interpretations, their accounts have, somewhat surprisingly, hardly been comparatively analyzed. Both Fleck and Polanyi relied on the physiology and psychology of the senses in order to show that scientific knowledge follows less the path of logical principles than the path of accepting or rejecting (...) specific conventions, where these may be psychologically or sociologically grounded. It is my aim to show that similarities and differences between Fleck and Polanyi are to be seen in the specific historical and political context in which they worked. Both authors, I shall argue, emphasized the relevance of perception in close connection to their respective understanding of science, freedom, and democracy. (shrink)
In the Trolley Case, as devised by Philippa Foot and modified by Judith Jarvis Thomson, a runaway trolley is headed down a main track and will hit and kill five unless you divert it onto a side track, where it will hit and kill one.
In various areas of Anglo-American law, legal liability turns on causation. In torts and contracts, we are each liable only for those harms we have caused by the actions that breach our legal duties. Such doctrines explicitly make causation an element of liability. In criminal law, sometimes the causal element for liability is equally explicit, as when a statute makes punishable any act that has “ caused … abuse to the child….” More often, the causal element in criminal liability is (...) more implicit, as when criminal statutes prohibit killings, maimings, rapings, burnings, etc. Such causally complex action verbs are correctly applied only to defendants who have caused death, caused disfigurement, caused penetration, caused fire damage, etc. (shrink)
Freud justified his extensive theorizing about dreams by the observation that they were “the royal road” to something much more general: namely, our unconscious mental life. The current preoccupation with the theory of excuse in criminal law scholarship can be given a similar justification, for the excuses are the royal road to theories of responsibility generally. The thought is that if we understand why we excuse in certain situations but not others, we will have also gained a much more general (...) insight into the nature of responsibility itself. Nowhere has this thought been more evident than in the century-old focus of criminal law theoreticians on the excuse of insanity, a focus that could not be justified by the importance of the excuse itself. In this paper I wish to isolate two theories of excuse, each of which instantiates its own distinctive theory of responsibility. One is what I shall call the choice theory of excuse, according to which one is excused for the doing of a wrongful action because and only because at the moment of such action's performance, one did not have sufficient capacity or opportunity to make the choice to do otherwise. Such a choice theory of excuse instantiates a more general theory of responsibility, according to which we are responsible for wrongs we freely choose to do, and not responsible for wrongs we lacked the freedom to avoid doing. The second I shall call the character theory of excuse, according to which one is excused for the doing of a wrongful action because and only because such action is not determined by those enduring attributes of ourselves we call our characters. (shrink)
A plea: If you're going to propose a Bayesian framework for updating self-locating degrees of belief, please read this piece first. I've tried to survey all the extant formalisms, group them by their general approach, then describe challenges faced by every formalism employing a given approach. Hopefully this survey will prevent further instances of authors' re-inventing updating rules already proposed elsewhere in the literature.
The arguments for redistribution of wealth, and for prohibiting certain transactions such as price-gouging, both are based in mistaken conceptions of exchange. This paper proposes a neologism, “euvoluntary” exchange, meaning both that the exchange is truly voluntary and that it benefits both parties to the transaction. The argument has two parts: First, all euvoluntary exchanges should be permitted, and there is no justification for redistribution of wealth if disparities result only from euvoluntary exchanges. Second, even exchanges that are not euvoluntary (...) should generally be permitted, because access to market exchange may be the only means by which people in desperate circumstances can improve their position. (shrink)
Michael Walzer is currently at the School of Social Science, Institute for Advanced Study, in Princeton, New Jersey. Professor Walzer has written Just and Unjust Wars; The Revolution of the Saints and has edited Toward A Global Civil Society. In this interview, he discusses some of the current concerns about education, political theory and the current state of the art of toleration, and acceptance and accommodation of different racial, ethnic, social and minority groups. He has published extensively and his (...) work has been translated in several other languages. In this interview, he responds to questions about his work, his writings and his current concerns. (shrink)
Largely due to the popular allegation that contemporary science has uncovered indeterminism in the deepest known levels of physical reality, the debate as to whether humans have moral freedom, the sort of freedom on which moral responsibility depends, has put aside to some extent the traditional worry over whether determinism is true. As I argue in this paper, however, there are powerful proofs for both chronological determinism and necessitarianism, forms of determinism that pose the most penetrative threat to human moral (...) freedom. My ultimate hope is to show that, despite the robust case against human moral freedom that can be made without even relying on them, chronological determinism and necessitarianism should be regarded with renewed urgency. (shrink)
This article focusses on corporate attitudes to stakeholder environmental pressures in Argentina. It uses a cross section survey of 505 CEOs of Argentinean firms to gather information on environmental attitudes and a stakeholder theory framework to design and interpret the statistical analyses. It is underpinned by theoretical and empirical findings in the literature on stakeholder management, targeting in particular studies that deal with corporate social responsibility (CSR) in Latin America. Its general aim is to gain a deeper empirical understanding of (...) the coherence between managers' perceptions of stakeholder pressures and the importance they are given in corporate CSR strategies through an empirical investigation of environmental management (EM) decisions. In doing so, it uncovers general differences in the way firms perceive and treat groups of stakeholders. It also detects variations across firms, observing that some are typically proactive in their response to stakeholder pressures whilst others are less responsive. Profiling the various stakeholder networks and the corporate response strategies in this way encourages the development of stakeholder-focussed policies and corporate strategies that emphasise communications, awareness and a clear sense of direction. It concludes that CSR appears to be more effective in the protection of the environment than previously reported. Although this study focusses on EM in Argentina, the findings are more generally applicable. (shrink)
