In Metaphysics A, Aristotle offers some objections to Plato’s theory of Forms to the effect that Plato’s Forms would not be explanatory in the right way, and seems to suggest that they might even make the explanatory project worse. One interesting historical puzzle is whether Aristotle can avoid these same objections to his own theory of universals. The concerns Aristotle raises are, I think, cousins of contemporary concerns about the usefulness and explanatoriness of abstract objects, some of which have recently (...) been receiving attention in the philosophy of mathematics. After discussing Aristotle’s objections and their contemporary cousins, the paper discusses some of the main available lines of response to these sorts of challenges, before concluding with an examination of whether these responses could assist Plato or Aristotle in responding to these challenges. (shrink)

This paper aims to clarify some conceptual aspects of decoherence that seem largely overlooked in the recent literature. In particular, I want to stress that decoherence theory, in the standard framework, is rather silent with respect to the description of (sub)systems and associated dynamics. Also, the selection of position basis for classical objects is more problematic than usually thought: while, on the one hand, decoherence offers a pragmatic-oriented solution to this problem, on the other hand, this can hardly be seen (...) as a genuine ontological explanation of why the classical world is position-based. This is not to say that decoherence is not useful to the foundations of quantum mechanics; on the contrary, it is a formidable weapon, as it accounts for a realistic description of quantum systems. That powerful description, however, becomes manifest when decoherence theory itself is interpreted in a realist framework of quantum mechanics. (shrink)

The philosophical problem that stems from the successful application of mathematics in the empirical sciences has recently attracted growing interest within philosophers of mathematics and philosophers of science. Nevertheless, little attention has been devoted to the converse applicability issue of how physical considerations find successful application in mathematics. In this article, focusing on some case studies, I address the latter issue and argue that some successful applications of physics to mathematics essentially depend on the use of conservation principles. I conclude (...) with a short discussion of how the successful interplay between conservation principles and mathematics can be accounted for. (shrink)

In a paper titled, “The Unreasonable Effectiveness of Mathematics”, published 20 years after Wigner’s seminal paper, the mathematician Richard W. Hamming discussed what he took to be Wigner’s problem of Unreasonable Effectiveness and offered some partial explanations for this phenomenon. Whether Hamming succeeds in his explanations as answers to Wigner’s puzzle is addressed by other scholars in recent years I, on the other hand, raise a more fundamental question: does Hamming succeed in raising the same question (...) as Wigner? The answer is no. My goal is to show that Hamming’s reading misses Wigner’s highly original formulation of the problem.Through a close and contextual reading of Wigner’s work, as I will show, we are led in new directions in addressing and solving the applicability problem. (shrink)

The attempts of theoretically solving the famous puzzle-dictum of physicist Eugene Wigner regarding the “unreasonable” effectiveness of mathematics as a problem of analytical philosophy, started at the end of the 19th century, are yet far from coming out with an acceptable theoretical solution. The theories developed for explaining the empirical “miracle” of applied mathematics vary in nature, foundation and solution, from denying the existence of a genuine problem to structural theories with an advanced level of mathematical formalism. Despite (...) this variation, methodologically fundamental questions like “Which is the adequate theoretical framework for solving Wigner’s conjecture?” and “Can the logico-mathematical formalism solve it and is it entitled to do it?” did not receive answers yet. The problem of the applicability of mathematics in the physical reality has been treated unitarily in some sense, with respect to the semantic-conceptual use of the constitutive terms, within both the structural and non-structural theories. This unity (of consistency) applied to both the referred objects and concepts per se and the aims of the investigations. For being able to make an objective study of the possible alternatives of the existent theories, a foundational approach of them is needed, including through semantic-conceptual distinctions which to weaken the unity of consistency. (shrink)

The fact that the same equations or mathematical models reappear in the descriptions of what are otherwise disparate physical systems can be seen as yet another manifestation of Wigner's “unreasonable effectiveness of mathematics.” James Clerk Maxwell famously exploited such formal similarities in what he called the “method of physical analogy.” Both Maxwell and Hermann von Helmholtz appealed to the physical analogies between electromagnetism and hydrodynamics in their development of these theories. I argue that a closer historical examination of (...) the different ways in which Maxwell and Helmholtz each deployed this analogy gives further insight into debates about the representational and explanatory power of mathematical models. (shrink)

Computers provide tools suprisingly effective in analyzing physical processes. The interaction of analytical and computer methods of physical research has been synergistic. Examples are given of the conceptual advances which have been spurred by the interaction of computer and classical analysis. It is argued that a new age in physical research is beginning and that the power of computer tools has scarcely been tapped.

Prologue. It is evident from the title that this is a philosophical discussion. I shall not apologize for the philosophy, though I am well aware that most scientists, engineers, and mathematicians have little regard for it; instead, I shall give this short prologue to justify the approach.

Many mathematicians, physicists, and philosophers have suggested that the fact that mathematics—an a priori discipline informed substantially by aesthetic considerations—can be applied to natural science is mysterious. This paper sharpens and responds to a challenge to this effect. I argue that the aesthetic considerations used to evaluate and motivate mathematics are much more closely connected with the physical world than one might presume, and (with reference to case-studies within Galois theory and probabilistic number theory) show that they are correlated with (...) generally recognized theoretical virtues, such as explanatory depth, unifying power, fruitfulness, and importance. (shrink)

I present a reconstruction of Eugene Wigner’s argument for the claim that mathematics is ‘unreasonable effective’, together with six objections to its soundness. I show that these objections are weaker than usually thought, and I sketch a new objection.

This book explores the persistence of Pythagorean ideas in theoretical physics. It shows that the Pythagorean position is both philosophically deep and scientifically interesting. However, it does not endorse pure Pythagoreanism; rather, it defends the thesis that mind and mathematical structure are the grounds of reality. The book begins by examining Wigner's paper on the unreasonable effectiveness of mathematics in the natural sciences. It argues that, whilst many issues surrounding the applicability of mathematics disappear upon examination, there are (...) some core issues to do with the effectiveness of mathematics in fundamental physics which remain. The core issues are the existence of the laws of nature and our minds ability to fathom them, the use of formal mathematics in discovering things about the quantum world, the fact that deep mathematics is needed to describe fundamental physics, and the asymptotic nature of the quest for knowledge. These issues are the focus of the book. The author seeks to explain them within a metaphysical framework that takes mind and mathematical structure as its fundamental principles. The framework - called quantum monadology - combines ideas from Leibnizian monadology, set theory, and consistent histories quantum theory. (shrink)

The point of departure for this article is Werner Heisenberg’s remark, made in 1929: “It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which seems entirely (...) adequate for the treatment of atomic processes.” The cost of this discovery, at least in Heisenberg’s and related interpretations of quantum mechanics, is that, in contrast to classical mechanics, the mathematical scheme in question no longer offers a description, even an idealized one, of quantum objects and processes. This scheme only enables predictions, in general, probabilistic in character, of the outcomes of quantum experiments. As a result, a new type of the relationships between mathematics and physics is established, which, in the language of Eugene Wigner adopted in my title, indeed makes the effectiveness of mathematics unreasonable in quantum but, as I shall explain, not in classical physics. The article discusses these new relationships between mathematics and physics in quantum theory and their implications for theoretical physics—past, present, and future. (shrink)

The process of theory development in physics is a very complex one. The best scientists sometimes proceed on the basis of their physical intuition, ignoring serious conceptual or mathematical objections well known to them at the time.The results soon justify their actions: but the removal of these objections is often not possible for a very long time. Four examples are presented: Newton, Schrödinger, Dirac, Dyson. Some thoughts on this “unreasonableness≓ are offered.

A famous essay by Wigner is reexamined in view of more recent developments around its topic, together with some remarks on the metaphysical character of its main question about mathematics and natural sciences.

In his influential 1960 paper ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’, Eugene P. Wigner raises the question of why something that was developed without concern for empirical facts—mathematics—should turn out to be so powerful in explaining facts about the natural world. Recent philosophy of science has developed ‘Wigner’s puzzle’ in two different directions: First, in relation to the supposed indispensability of mathematical facts to particular scientific explanations and, secondly, in connection with the idea that aesthetic (...) criteria track theoretical desiderata such as empirical success. An important aspect of Wigner’s article has, however, been overlooked in these debates: his worries about the underdetermination of physical theories by mathematical frameworks. The present paper argues that, by restoring this aspect of Wigner’s argument to its proper place, Wigner’s puzzle may become an instructive case study for the teaching of core issues in the philosophy of science and its history. (shrink)

ABSTRACTIn 1960, Eugene P. Wigner shared his observation of the unreasonable effectiveness of mathematics in formulating regularities in nature. Later, Jean Piaget recognized the functioning of the...

How and why, historian of science Lily Kay asks, did the ‘biological problem of DNA-based protein synthesis’ come to be represented ‘as an information code and a writing technology?’ What sort of metaphor was ‘code’ for these bio-geneticists? One whose run-away expansion, Derrida noted in Of Grammatology (1967), urgently required philosophical justification. Yet, 60 years later, there is still fundamental disagreement about its meaning and epistemic status. If the metaphor lacks ontological purchase, what accounts for its effectiveness? If, on (...) the other hand, scriptural metaphors get at the common root of culture and biology, what do we now mean by ‘code’? In this article, I trace several influential accounts of the metaphor’s effectiveness—making explicit the opposing notions of ‘code’ that animate them—and argue that each is too limited. Greater attention to the metaphoricity of ‘code’ yields a more philosophically productive and critical account of the metaphor of code. (shrink)

Much mainstream analytic epistemology is built around a sceptical treatment of modality which descends from Hume. The roots of this scepticism are argued to lie in Hume’s (nominalist) theory of perception, which is excavated, studied and compared with the very different (realist) theory of perception developed by Peirce. It is argued that Peirce’s theory not only enables a considerably more nuanced and effective epistemology, it also (unlike Hume’s theory) does justice to what happens when we appreciate a proof in mathematics.

Biometrics has done damage with levels of R or p or Student’s t. The damage widened with Ronald A. Fisher’s victory in the 1920s and 1930s in devising mechanical methods of “testing,” against methods of common sense and scientific impact, “oomph.” The scale along which one would measure oomph is particularly clear in biomedical sciences: life or death. Cardiovascular epidemiology, to take one example, combines with gusto the “fallacy of the transposed conditional” and what we call the “sizeless stare” of (...) statistical significance. Some medical editors have battled against the 5% philosophy, as did, for example, Kenneth Rothman, the founder of Epidemiology. And decades ago a sensible few in education, ecology, and sociology initiated a “significance test controversy.” But, grantors, journal referees, and tenure committees in the statistical sciences had faith that probability spaces can substitute for scientific judgment. A finding of p <.05 is deemed to be “better” for variable X than p <.11 for variable Y. It is not. It depends on the oomph of X and Y—the effect size, size judged in the light of how much it matters for scientific or clinical purposes. In 1995 a Cancer Trialists’ Collaborative Group, for example, came to a rare consensus on effect size: 10 different studies had agreed that a certain drug for treating prostate cancer can increase patient survival by 12%. An 11th study published in the New England Journal in 1998 dismissed the drug. The dismissal was based on a t-test, not on what William Gosset had called, against Ronald A. Fisher’s machinery, “real” error. (shrink)

Philosophy & Social Criticism, Volume 48, Issue 9, Page 1226-1246, November 2022. In this study, we claim that political liberalism, despite harsh criticism, is still the best option available for providing a just and stable society. However, we maintain that political liberalism needs to be revised so as to be justifiable from the perspective of not only the “reasonable” in a Rawlsian sense but also the ones whom Rawls labels as “unreasonable.” To support our claim, going beyond Rawls’s original (...) account, we unpack the concept of unreasonableness and identify three different subsets that we label as the “partially reasonable,” the “non-reasonable,” and the “unreasonable.” We argue that both the “fully” reasonable and the “partially reasonable” would be included into the constituency of public justification; more specifically, we claim that the latter would support liberal institutions out of their reasons: we define these reasons as mutually intelligible reasons and claim that they allow to acknowledge the importance of a convergence approach to public justification. As for the “non-reasonable” and “unreasonable,” we claim that they cannot be included in the constituency of public justification, but they nonetheless could be compliant with liberal institutions if political liberalism offers them some reasons to comply: here, we claim that political liberalism should include them through engagement and propose reasoning from conjecture as an effecting way of offering reasons for compliance. In particular, we claim that through reasoning from conjecture, the “non-reasonable” could find conciliatory reasons to comply with liberal institutions on a stable base. With regard to the “unreasonable” in the strict sense, we claim that through reasoning from conjecture, their unreasonableness could be contained and they could find reasons—even if just self-interested—for complying with liberal institutions rather than defying them. In our discussion, we consider the different subsets not as “frozen” but as dynamic and open to change, and we aim to propose a more complex and multilayered approach to inclusion that would be able to include a wider set of people. To strengthen our argument, we show that the need for a wider public justification and for broader inclusion in liberal societies is grounded in respect for persons both as equal persons and as particular individuals. In particular, we claim that individuals’ values, ends, commitments, and affiliations activate demands of respect and can strengthen the commitment to the liberal–democratic order. Through a reformulation of the role of respect in liberal societies, we also show a kind of social and communitarian dimension that, we claim, is fully compatible with political liberalism and opens it up to “civic friendship” and “social solidarity,” which are constitutive elements for the development of a sense of justice and for the realization of a just and stable society. (shrink)

Philosophy & Social Criticism, Volume 48, Issue 9, Page 1226-1246, November 2022. In this study, we claim that political liberalism, despite harsh criticism, is still the best option available for providing a just and stable society. However, we maintain that political liberalism needs to be revised so as to be justifiable from the perspective of not only the “reasonable” in a Rawlsian sense but also the ones whom Rawls labels as “unreasonable.” To support our claim, going beyond Rawls’s original (...) account, we unpack the concept of unreasonableness and identify three different subsets that we label as the “partially reasonable,” the “non-reasonable,” and the “unreasonable.” We argue that both the “fully” reasonable and the “partially reasonable” would be included into the constituency of public justification; more specifically, we claim that the latter would support liberal institutions out of their reasons: we define these reasons as mutually intelligible reasons and claim that they allow to acknowledge the importance of a convergence approach to public justification. As for the “non-reasonable” and “unreasonable,” we claim that they cannot be included in the constituency of public justification, but they nonetheless could be compliant with liberal institutions if political liberalism offers them some reasons to comply: here, we claim that political liberalism should include them through engagement and propose reasoning from conjecture as an effecting way of offering reasons for compliance. In particular, we claim that through reasoning from conjecture, the “non-reasonable” could find conciliatory reasons to comply with liberal institutions on a stable base. With regard to the “unreasonable” in the strict sense, we claim that through reasoning from conjecture, their unreasonableness could be contained and they could find reasons—even if just self-interested—for complying with liberal institutions rather than defying them. In our discussion, we consider the different subsets not as “frozen” but as dynamic and open to change, and we aim to propose a more complex and multilayered approach to inclusion that would be able to include a wider set of people. To strengthen our argument, we show that the need for a wider public justification and for broader inclusion in liberal societies is grounded in respect for persons both as equal persons and as particular individuals. In particular, we claim that individuals’ values, ends, commitments, and affiliations activate demands of respect and can strengthen the commitment to the liberal–democratic order. Through a reformulation of the role of respect in liberal societies, we also show a kind of social and communitarian dimension that, we claim, is fully compatible with political liberalism and opens it up to “civic friendship” and “social solidarity,” which are constitutive elements for the development of a sense of justice and for the realization of a just and stable society. (shrink)

Out of my normal context, and separated from my usual reference groups, perhaps I need first of all to explain the background from which I speak. As a developmental psychologist whose main research interests are to do with child rearing in the various social environments in which it takes place, I have been particularly concerned with the long-term dialogues that go on between parents and children, in the course of which they commonly come to certain understandings about their mutual tolerances (...) and intolerances, and learn to live together with some regard to these limits. I stress the intersubjective nature of these understandings because I take it as axiomatic that children bring up their parents in the course of parents bringing up their children, even though parents are more powerful in physical terms and marginally more powerful in psychological terms. Secondly, as a child psychologist working clinically with parents and handicapped or problem children, I am also interested in another kind of dialogue: that which takes place between parents and professionals with the child as focus. I am concerned to find ways of making this dialogue as effective as possible, in particular by recognising the differences that inform parental and professional approaches to our common focus, and then using these differences to enable a complementary partnership that builds upon the advantages of each. (shrink)

Effective altruism (EA) is a movement devoted to the idea of doing good in the most effective way possible. EA has been the target of a number of critiques. In this article, I focus on one prominent critique: that EA fails to acknowledge the importance of institutional change. One version of this critique claims that EA relies on an overly individualistic approach to ethics. Defenders of EA have objected that this charge either fails to identify a problem with EA's core (...) idea that each of us should do the most good we can, or makes unreasonable claims about what we should do. However, I argue that we can understand the critique in a way that is well motivated, and that can avoid these objections. (shrink)

A key and continuing concern within the pragma-dialectical theory of argumentation is how to account for effective persuasion disciplined by dialectical rationality. Currently, van Eemeren and Houtlosser offer one response to this concern in the form of strategic manoeuvring. This paper offers a prior/passing theory of communicative interaction as a supplement to the strategic manoeuvring approach. Our use of a prior/passing model investigates how a difference of opinion can be resolved while both dialectic obligations of reasonableness and rhetorical ambitions of (...) argumentative success are simultaneously accommodated. The paper explores the model with particular reference to the pragma-dialectical rules of critical discussion, strategic manoeuvring and fallacious reasoning. (shrink)

Much recent philosophy of physics has investigated the process of symmetry breaking. Here, I critically assess the alleged symmetry restoration at the fundamental scale. I draw attention to the contingency that gauge symmetries exhibit, that is, the fact that they have been chosen from an infinite space of possibilities. I appeal to this feature of group theory to argue that any metaphysical account of fundamental laws that expects symmetry restoration up to the fundamental level is not fully satisfactory. This is (...) a symmetry argument in line with Curie’s first principle. Further, I argue that this same feature of group theory helps to explain the ‘unreasonable’ effectiveness of mathematics in physics, and that it reduces the philosophical significance that has been attributed to the objectivity of gauge symmetries. (shrink)

We argue that E. Wigner’s well-known claim that mathematics is unreasonably effective in physics is only one side of the hill. The other side is the surprising insufficiency of present-day mathematics to capture the uniformities that arise in science outside physics. We describe roughly what the situation is in the areas of everyday reasoning, theory of meaning and vagueness. We make also the point that mathematics, as we know it today, founded on the concept of set, need not be a (...) conceptually final and closed system, but only a stage in a developing subject. (shrink)

Wigner famously referred to the `unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics, I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa's partial structures programme.

In 1960, E. P. Wigner, a joint winner of the 1963 Nobel Prize for Physics, published a paper titled On the Unreasonable Effectiveness of Mathematics in the Natural Sciences [61]. This paper can be construed as an examination and affirmation of Galileo's tenet that “The book of nature is written in the language of mathematics”. To this effect, Wigner presented a large number of examples that demonstrate the effectiveness of mathematics in accurately describing physical phenomena. Wigner viewed (...) these examples as illustrations of what he called the empirical law of epistemology, which asserts that the mathematical formulation of the laws of nature is both appropriate and accurate, and that mathematics is actually the correct language for formulating the laws of nature. At the same time, Wigner pointed out that the reasons for the success of mathematics in the natural sciences are not completely understood; in fact, he went as far as asserting that “… the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.”. (shrink)

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates (...) and implements a strategy to show that the applicability of mathematics is very reasonable indeed. I distinguish three forms of the problem of the applicability of mathematics, and focus on one I call the problem of uncanny accuracy: Given that the construction and manipulation of mathematical representations is pervaded by uncertainty, error, approximation, and idealization, how can their apparently uncanny accuracy be explained? I argue that this question has found no satisfactory answer because our rational reconstruction of scientific practice has not involved tools rich enough to capture the logic of mathematical modelling. Thus, I characterize a general schema of mathematical analysis of real systems, focusing on the selection of modelling assumptions, on the construction of model equations, and on the extraction of information, in order to address contextually determinate questions on some behaviour of interest. A concept of selective accuracy is developed to explain the way in which qualitative and quantitative solutions should be utilized to understand systems. The qualitative methods rely on asymptotic methods and on sensitivity analysis, whereas the quantitative methods are best understood using backward error analysis. The basic underpinning of this perspective is readily understandable across scientific fields, and it thereby provides a view of mathematical tractability readily interpretable in the broader context of mathematical modelling. In addition, this perspective is used to discuss the nature of theories, the role of scaling, and the epistemological and semantic aspects of experimentation. In conclusion, we argue for a method of local and global conceptual analysis that goes beyond the reach of the tools standardly used to capture the logic of science; on their basis, the applicability of mathematics finds itself demystified. (shrink)

Contributors to the debate on ethical rationing bring with them assumptions about the proper role of moral theories in practical discourse, which seem reasonable, realistic and pragmatic. These assumptions function to define the remit of bioethical discourse and to determine conceptions of proper methodology and causal reasoning in the area. However well intentioned, the desire to be realistic in this sense may lead us to judge the adequacy of a theory precisely with reference to its ability to deliver apparently determinate (...) answers to questions that strike most practitioners and patients as morally arbitrary. By providing ethical solutions that work given the world as it is, work in clinical ethics may serve to endorse or protect from scrutiny the very structures that need to change if real moral progress is to be possible. Such work can help to foster the illusion that fundamentally arbitrary decisions are ‘grounded’ in objective, impartial reasoning, bestowing academic credibility on policies and processes, making it subsequently harder for others to criticise those processes. As theorists, we need to reflect on our political role and how best to foster virtuous, critical practice, if we are to avoid making contributions to the debate that not only do no good, but may even be harmful. A recent debate in this journal illustrates these issues effectively. (shrink)

Originally proposed by John Rawls, the idea of reasoning from conjecture is popular among the proponents of political liberalism in normative political theory. Reasoning from conjecture consists in discussing with fellow citizens who are attracted to illiberal and antidemocratic ideas by focusing on their religious or otherwise comprehensive doctrines, attempting to convince them that such doctrines actually call for loyalty to liberal democracy. Our goal is to criticise reasoning from conjecture as a tool aimed at persuasion and, in turn, at (...) improving the stability of liberal democratic institutions. To pursue this goal, we use as case study real-world efforts to counter-radicalise at-risk Muslim citizens, which, at first glance, reasoning from conjecture seems well-placed to contribute to. This case study helps us to argue that the supporters of reasoning from conjecture over-intellectualise opposition to liberal democracy and what societies can do to counter it. Specifically, they (i) underestimate how few members of society can effectively perform reasoning from conjecture; (ii) overlook that the burdens of judgement, a key notion for political liberals, highlight how dim the prospects of reasoning from conjecture are and (iii) do not pay attention to the causes of religious persons’ opposition to liberal democracy. However, not everything is lost for political liberals, provided that they redirect attention to different and under-researched resources contained in Rawls’s theory. In closing, we briefly explain how such resources are much better placed than reasoning from conjecture to provide guidance relative to counter-radicalisation in societies (i) populated by persons who do not generally hold anything close to a fully worked out and internally consistent comprehensive doctrine and (ii) where political institutions should take responsibility for at least part of the existing alienation from liberal democratic values. (shrink)

The world appears causal in the sense that the result of a measurement may depend on the past history of the observed system, but not on what the experimenter will do with the system after the measurement. This raises the question whether noncausality at a macroscopic level would necessarily lead to an “unreasonable” world. The study of a model world with axiomatically well-specified properties shows that noncausal systems can be discussed in a logically consistent manner so that noncausality might (...) well exist in the real world as a weak, but so far overlooked, effect. (shrink)

In this article, responding to assertions that the principle of double effect has no place in legal analysis, I explore the overlap between double effect and negligence analysis. In both, questions of culpability arise in situations where a person acts with no intent to cause harm but where reasonable foreseeability of unintended harm exists. Under both analyses, the determination of whether such conduct is permissible involves a reasonability test that balances that foreseeable harm against the good intended by the actor's (...) conduct. In both, absent a finding that the foreseeable harm is unreasonable in light of that intended good, no liability will be imposed upon the actor. Even conceding, however, such general similarity between double effect and negligence analysis - disagreement over the proper interpretation of the reasonability criterion at play in negligence poses an additional challenge for the attempt to correlate negligence with double effect. Economic efficiency interpretations of negligence, for example, purportedly based on the Learned Hand Formula and the RESTATEMENT (SECOND) OF THE LAW OF TORTS, propose that culpability depends upon a utilitarian balancing of good effects of conduct (utility) versus its harmful foreseeable consequences (magnitude of risk of injury). Based on such an interpretation of negligence, however, contrasts between actors' states of mind, and normative differences between kinds of goods and harms, ultimately fade into the background and become irrelevant as essential conditions for properly assessing liability. This article elaborates and defends the view that double effect analysis lies at the heart of negligence theory. Part I elucidates in more detail the principle of double effect and describes its prima facie operation in negligence analysis. Part II considers and rejects the economic efficiency interpretation that has been offered as a theory of negligence, overcoming the challenge that such an interpretation presents for the effort to locate double effect analysis in the law. Part III illustrates and confirms the overlap between double effect and negligence by consideration of a series of case applications. The Article proposes that the weighing of conflicting values in double effect analysis and negligence is not achieved - as proposed by law and economics theory with respect to negligence - by imposing a consequentialist-utilitarian reduction of all value to a single concept of good and eliminating the relevance of traditional state of mind distinctions between intention and foreseeability. Instead, each mode of analysis recognizes that distinct culpability determinations flow naturally and plausibly from an appreciation of the traditional legal distinctions made between various types of goods and harms, and upon whether such goods and harms come about as result of an actor's intention or mere foreseeability. Keywords: Double effect, negligence, intention, foreseeability, choice, law and economics, utilitarianism, consequentialism, weighing of values. (shrink)

Unreasonable expectations about the nature and character of scientific knowledge support the widespread political assumption that predictive scientific assessments are a necessary precursor to environmental decision making. All too often, the practical outcome of this assumption is that scientific uncertainty becomes a ready-made dodge for what is in reality just a difficult political decision. Interdisciplinary assessments necessary to address complex environmental policy issues invariably result in findings that are inherently contestable, especially when applied in the unrestrained realm of partisan (...) politics. In this article, the authors argue that predictive scientific assessments are inherently limited in the extent to which they can guide policy development and that rigorous scientific assessments can be much more valuable in the role of ex post policy evaluation than they can in the context of ex ante policy formulation. (shrink)

In my reply to Wertheimer and Miller's paper on coercive offers and payment for research participation1 I claim that ‘… it's not unreasonable to suppose that there is another normative aspect to these cases, over and above the voluntariness of consent. While the parents of children at Willowbrook and the millionaire's mistress might have given consent that was voluntary and informed, they are still wronged by taking up this offer…’2 Furthermore, nowhere in my paper on surgical castration do I (...) claim that coercive offers invalidate consent,3 and I suggest that Bomann-Larsen has come closest to cashing this out correctly with her idea that ‘the wrongness of these coercive offers has more to do with the wilful creation of choices that take advantage of others vulnerabilities…’.4 So, it is puzzling that they object to my analysis of coercion and castration because coercive offers are not readily unpacked as a problem with consent. …. (shrink)

Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce several notions of symmetry in mathematics and explain how they can also be used in resolving different problems in the philosophy of mathematics. We use symmetry to discuss the objectivity of mathematics, the role of mathematical objects, the unreasonable (...) class='Hi'>effectiveness of mathematics and the relationship of mathematics to physics. (shrink)

Anthropology diffracted : originary humanicity -- Just figures?: forensic clairvoyance, mathematics, and the language question -- Enumerating language : "The unreasonable effectiveness of mathematics" -- Natural convers(at)ions : or, what if culture was really nature all along? -- (Con)founding "the human" : rethinking the incest taboo -- Culpability and the double-cross : Irigaray with Merleau-Ponty.

Mathematics may seem unreasonably effective in the natural sciences, in particular in physics. In this essay, I argue that this judgment can be attributed, at least in part, to selection effects. In support of this central claim, I offer four elements. The first element is that we are creatures that evolved within this Universe, and that our pattern finding abilities are selected by this very environment. The second element is that our mathematics—although not fully constrained by the natural world—is strongly (...) inspired by our perception of it. Related to this, the third element finds fault with the usual assessment of the efficiency of mathematics: our focus on the rare successes leaves us blind to the ubiquitous failures. The fourth element is that the act of applying mathematics provides many more degrees of freedom than those internal to mathematics. This final element will be illustrated by the usage of ‘infinitesimals’ in the context of mathematics and that of physics. In 1960, Wigner wrote an article on this topic [4] and many later authors have echoed his assessment that the success of mathematics in physics is a mystery. At the end of this essay, I will revisit Wigner and three earlier replies that harmonize with my own view. I will also explore some of Einstein’s ideas that are connected to this. But first, I briefly expose my views of science and mathematics, since these form the canvass of my central claim. (shrink)

How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? What has been called 'the unreasonable effectiveness of mathematics' sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character, whereas others have pointed to the range of structures that mathematics offers. Otavio Bueno and Steven French offer a middle way, which focuses on the moves that have to (...) be made in both the mathematics and the relevant physics in order to bring the two into appropriate relation. This relation can be captured via the inferential conception of the applicability of mathematics, which is formulated in terms of immersion, inference, and interpretation. In particular, the roles of idealisations and of surplus structure in science and mathematics respectively are brought to the fore and captured via an approach to models and theories that emphasize the partiality of the available information: the partial structures approach. The discussion as a whole is grounded in a number of case studies drawn from the history of quantum physics, and extended to contest recent claims that the explanatory role of certain mathematical structures in scientific practice supports a realist attitude towards them. The overall conclusion is that the effectiveness of mathematics does not seem unreasonable at all once close attention is paid to how it is actually applied in practice. (shrink)

Attempts at solving what has been labeled as Eugene Wigner’s puzzle of applicability of mathematics are still far from arriving at an acceptable solution. The accounts developed to explain the “miracle” of applied mathematics vary in nature, foundation, and solution, from denying the existence of a genuine problem to designing structural theories based on mathematical formalism. Despite this variation, all investigations treated the problem in a unitary way with respect to the target, pointing to one or two ‘why’ or ‘how’ (...) questions to be answered. In this paper, I argue that two analyses, a semantic analysis ab initio and a metatheoretical analysis starting from the types of unreasonableness involved in this problem, will establish the interdisciplinary character of the problem and reveal many more targets, which may be addressed with different methodologies. In order to address objectively the philosophical problem of applicability of mathematics, a foundational revision of the problem is needed. (shrink)

In his seminal 1960 paper, the physicist Eugene Wigner formulated the question of the applicability of mathematics in physics in a way nobody had before. This formulation has been entirely overlooked due to an exclusive concern with solving Wigner’s problem and explaining the effectiveness of mathematics in the natural sciences, in one way or another. Many have attempted to attribute Wigner’s unjustified conclusion—that mathematics is unreasonably effective in the natural sciences—to his formalist views on mathematics. My goal is to (...) show that this reading misses out on Wigner’s highly original formulation of the problem which is presented throughout his body of work in physics as well as in philosophy. This formulation, as I will show, leads us in a new direction in solving the applicability problem. (shrink)

This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...) does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is. The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishment of a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies. (shrink)