The work and ideas of Rudolf Laban, dancer, choreographer and seminal theoretician of movement and dance, have had a profound impact across a range of disciplines. This book explores this impact.

This paper argues that in Christian Wolff’s theory of knowledge, logical regimentation does not take the place of experiential justification, but serves to facilitate the application of empirical information and clearly exhibit its warrant. My argument targets rationalistic interpretations such as R. Lanier Anderson’s. It is common ground in this dispute that making concepts “distinct” issues in the premises on which all deductive justification rests. Against the view that concepts are made distinct only by analysis, which is carried out by (...) the understanding independently of experience, I contend that for Wolff some distinct concepts are arrived at through experience. I emphasize that Wolff countenances empirical methods of obtaining distinct concepts even in mathematics. This striking feature of his view indicates how its empiricist elements can be reconciled with his injunction to follow “mathematical” method. (shrink)

This paper considers Kant's understanding of conceptual representation in light of his view of geometry.

J. H. Lambert proved important results of what we now think of as non-Euclidean geometries, and gave examples of surfaces satisfying their theorems. I use his philosophical views to explain why he did not think the certainty of Euclidean geometry was threatened by the development of what we regard as alternatives to it. Lambert holds that theories other than Euclid's fall prey to skeptical doubt. So despite their satisfiability, for him these theories are not equal to Euclid's in justification. Contrary (...) to recent interpretations, then, Lambert does not conceive of mathematical justification as semantic. According to Lambert, Euclid overcomes doubt by means of postulates. Euclid's theory thus owes its justification not to the existence of the surfaces that satisfy it, but to the postulates according to which these "models" are constructed. To understand Lambert's view of postulates and the doubt they answer, I examine his criticism of Christian Wolff's views. I argue that Lambert's view reflects insight into traditional mathematical practice and has value as a foil for contemporary, model-theoretic, views of justification. (shrink)

In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant's 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional (...) applicability of mathematical concepts. (shrink)

There exists a significant disparity within society between individuals in terms of intelligence. While intelligence varies naturally throughout society, the extent to which this impacts on the life opportunities it affords to each individual is greatly undervalued. Intelligence appears to have a prominent effect over a broad range of social and economic life outcomes. Many key determinants of well-being correlate highly with the results of IQ tests, and other measures of intelligence, and an IQ of 75 is generally accepted as (...) the most important threshold in modern life. The ability to enhance our cognitive capacities offers an exciting opportunity to correct disabling natural variation and inequality in intelligence. Pharmaceutical cognitive enhancers, such as modafinil and methylphenidate, have been shown to have the capacity to enhance cognition in normal, healthy individuals. Perhaps of most relevance is the presence of an ‘inverted U effect’ for most pharmaceutical cognitive enhancers, whereby the degree of enhancement increases as intelligence levels deviate further below the mean. Although enhancement, including cognitive enhancement, has been much debated recently, we argue that there are egalitarian reasons to enhance individuals with low but normal intelligence. Under egalitarianism, cognitive enhancement has the potential to reduce opportunity inequality and contribute to relative income and welfare equality in the lower, normal intelligence subgroup. Cognitive enhancement use is justifiable under prioritarianism through various means of distribution; selective access to the lower, normal intelligence subgroup, universal access, or paradoxically through access primarily to the average and above average intelligence subgroups. Similarly, an aggregate increase in social well-being is achieved through similar means of distribution under utilitarianism. In addition, the use of cognitive enhancement within the lower, normal intelligence subgroup negates, or at the very least minimises, several common objections to cognitive enhancement. Subsequently, this paper demonstrates that there is a compelling case for cognitive enhancement use in individuals with lower, normal intelligence. (shrink)

Controversies in science are an essential feature of scientific practice: defined here as current problems that are unresolved because there are no accepted procedures by which they can be resolved or there are differing assumptions that affect the interpretation of evidence. Although there has been much attention in science education literature addressing socio-scientific and historical controversies in science, less has been paid to the teaching of contemporary scientific controversies. Using semi-structured qualitative interviews with 18 teachers at different career stages in (...) England, we investigated teachers’ social representations of scientific controversies using the discourse of the collective subject. We found a lack of controversy in teachers’ responses. Whilst scientific controversies were seen as an essential feature of how science works, they were not viewed as essential in science education and were represented as a distraction and dealt with informally, outside the planned curriculum and in response to students’ questions. Subject knowledge was considered a barrier. We argue that teaching about carefully selected scientific controversies has the potential to contribute to teachers’ and students’ understandings of science and the nature of science. There are perceived to be few opportunities for teachers to exercise this in the English context. We suggest how the collective subject discourses might be used to open up a discussion about teaching controversies in professional learning situations. Materials to stimulate discussion of scientific controversies could be useful in future curriculum development in science, but these would need to address the barriers of subject knowledge, access to literature and conflict with assessment-related priorities and a perceived need to advocate for trust in science. (shrink)

Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the putting-together in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity is ultimately related to spatial extension. I (...) use this conception of Newton’s project to explain the organization and proofs of the first theorems of mechanics to appear in the Principia. The placementof Kepler’s rule of areas as the first proposition, and the manner in which Newton proves it, appear natural on the supposition that Newton seeks a measure, in the sense of a moveable spatial quantity, of time. I argue that Newton proceeds in this way so that his reasoning can have the ostensive certainty of geometry. (shrink)

In a crucial passage of the second-edition Transcendental Deduction, Kant claims that the concept of motion is central to our understanding of change and temporal order. I show that this seemingly idle claim is really integral to the Deduction, understood as a replacement for Locke’s “physiological” epistemology (cf. A86-7/B119). Béatrice Longuenesse has shown that Kant’s notion of distinctively inner receptivity derives from Locke. To explain the a priori application of concepts such as succession to this mode of sensibility, Kant construes (...) the mind as receptive to its own activity. As Longuenesse understands Kant’s response to Locke, “motion” becomes little more than a metaphor for the action of understanding on inner sense. For Michael Friedman, in contrast, this passage evidences Kant’s deep concern with the foundations of Newtonian science. He reads it as a reference to inertial motion, the standard by which temporal intervals are measured. I show that Longuenesse’s and Friedman’s interpretations are in fact complementary. Both Locke and Kant are deeply concerned with the quantification of time. So Longuenesse is right that §24 is meant to supplant Locke’s account, and Friedman correctly takes it as the foundation of Kant’s account of the application of quantitative concepts to time. Kant aims, specifically, to explain cognition of time as continuous magnitude. However, Longuenesse leaves Kant without an answer to Locke’s challenge that continuous magnitude cannot be understood on the basis of discrete magnitude. And on Friedman’s view Kant’s account of the understanding’s activity presupposes, and thus cannot explain, the achievements of the mathematical sciences (such as the representation of temporal continuity). On my reading, Kant’s key contention is that we must regard the segregation of temporally ordered representation into units as the work of the understanding, rather than (as Locke views it) of sensibility. By giving the understanding this role, Kant succeeds where he takes Locke to fail. I show how the power to unify temporal representation can be ascribed to the understanding on the basis, not of assumed mathematical or scientific knowledge, but of its characterization as the power of judgment. (shrink)

The use of placebo as a control condition in clinical trials of major depressive disorder and anxiety disorders continues to be an area of ethical concern. Typically, opponents of placebo controls argue that they violate the beneficent-based, “best proven diagnostic and therapeutic method” that the original Helsinki Declaration of 1964 famously asserted participants are owed. A more consequentialist, oppositional argument is that participants receiving placebo might suffer enormously by being deprived of their usual medication(s). Nevertheless, recent findings of potential for (...) suicidality in young people treated with antidepressants, along with meta-analyses suggesting that antidepressants add no significant clinical benefit over placebos, warrant a re-evaluation of the arguments against placebo. Furthermore, the nature of placebo treatment in short-term clinical trials is often not well understood, and lack of understanding can foster opposition to it. This paper will show how scientific justifications for placebo use are morally relevant. The fundamental ethical importance of placebo controls is discussed in relation to several aspects of clinical trials, including detection of adverse events, accurate assessment of clinical benefit, advancing understanding of the heterogeneity of depression and anxiety disorders and respecting informed consent requirements. Prohibiting the use of placebo controls is morally concerning in that such prohibitions allow for the possibility of serious adverse public health consequences. Moral worries that research participants receiving placebo are being unduly jeopardised will be shown to be exaggerated, especially in relation to the net benefits for end-users to be gained from the quality of data resulting from using placebo controls. (shrink)

The main goal of part 1 is to challenge the widely held view that Poincaré orders the sciences in a hierarchy of dependence, such that all others presuppose arithmetic. Commentators have suggested that the intuition that grounds the use of induction in arithmetic also underlies the conception of a continuum, that the consistency of geometrical axioms must be proved through arithmetical induction, and that arithmetical induction licenses the supposition that certain operations form a group. I criticize each of these readings. (...) More fully, I argue that the justification Poincaré offers for the use of the group notion in geometry appears to extend to set-theoretic notions that would suffice to put arithmetic on a logical foundation, thus undermining his own case for the necessity of intuition in arithmetic. In part 2, I offer an interpretation of intuition’s role on which it justifies the use of group-theoretic, but not set-theoretic, notions. (shrink)

This book focuses on material culture as a subject of philosophical inquiry and promotes the philosophical study of material culture by articulating some of the central and difficult issues raised by this topic and providing innovative solutions to them, most notably an account of improvised action and a non-intentionalist account of function in material culture. Preston argues that material culture essentially involves activities of production and use; she therefore adopts an action-theoretic foundation for a philosophy of material culture. Part (...) 1 illustrates this foundation through a critique, revision, and extension of existing philosophical theories of action. Part 2 investigates a salient feature of material culture itself—its functionality. A basic account of function in material culture is constructed by revising and extending existing theories of biological function to fit the cultural case. Here the adjustments are for the most part necessitated by special features of function in material culture. These two parts of the project are held together by a trio of overarching themes: the relationship between individual and society, the problem of centralized control, and creativity. (shrink)

Part 1 of this article exposed a tension between Poincaré’s views of arithmetic and geometry and argued that it could not be resolved by taking geometry to depend on arithmetic. Part 2 aims to resolve the tension by supposing not merely that intuition’s role is to justify induction on the natural numbers but rather that it also functions to acquaint us with the unity of orders and structures and show practices to fit or harmonize with experience. I argue that in (...) this manner, intuition serves the epistemological function of warranting generalizations and justifying practices. In particular, it justifies the application of group-theoretic notions in geometry but not the use of set-theoretic notions in arithmetic. (shrink)

Kant’s Mathematical World (KMW) is a strikingly original, richly detailed account of Kant’s philosophy of mathematics as a reckoning with the long-held understa.

Kant’s Metaphysical Foundations of Natural Science (MFNS), published in 1786, has proved difficult to situate in the context of eighteenth-century responses to Newton. One point beyond dispute is that Kant is not satisfied with the “metaphysical foundations” thus far proffered by Newton and his followers. He echoes some familiar Leibnizian criticisms (such as those concerning absolute space) and, in a passage we will examine closely, insists that rejecting “the concept of an original attraction” would put Newton “at variance with himself” (...) (4:515). In light of Kant’s robust defense of the immediacy and universality of gravitational attraction, the overall similarity between his three “mechanical laws” and Newton’s “Axioms, or Laws of Motion” has made it the “standard” view that Kant “intends to justify Newtonian science in general and Newtonian mechanics in particular as stated in” Newton’s laws of motion (Watkins 2019, 89). But it is unclear whether the alternative “foundations” he proposes are for Newton’s theory of motion or something more akin to Leibniz’s physics. Recent scholarship has documented the Leibnizian provenance of Kant’s three laws, and argued for the relevance of later figures strongly influenced by Leibniz. (shrink)

_Review of: Anderson, Abraham, _Kant, Hume, and the Interruption of Dogmatic Slumber_, New York, Oxford University Press, 2020, 180+xxii, 978-0-19-009674-8_.

Not a full treatment of Newton’s scientific method, this book discusses his optical research only in passing (342–43). Its subtitle better indicates its scope: it focuses narrowly on the argument for universal gravitation in Book III of the Principia. The philosophical project is to set out an “ideal of empirical success” realized by the argument. Newton claims his method is to “deduce” propositions “from phenomena.” On Harper’s interpretation Newton’s phenomena are patterns of data, which are used to measure “parameters” by (...) which the theory explains them. An example is Kepler’s Area Rule. Its fit to the data confirms the hypothesis that the force maintaining a body in orbit is directed toward the .. (shrink)

The geometrical results included in De Corpore were intended to demonstrate the power of Hobbes’s approach to philosophy and cement his standing as a mathematician. They were promptly refuted, making his geometry an object of derision. I defend Hobbes’s mathematical program by showing that it addressed important needs and that similar ideas formed the basis of Newton’s calculus. In closing, I consider how placing Hobbes’s geometrical doctrine in its historical setting can further our understanding of his philosophy.

The concept of orthodoxy is not prominent in the thinking of mid-twentiethcentury writers on religion. There are many reasons for this. It is, for instance, always more interesting to challenge accepted traditions than to defend them, and publishers know that radical questioning generally attracts more attention than defence of received ideas. But the task of defending orthodox beliefs is an absolute necessity for the adherents of a revealed religion. It may be unpalatable to have to examine a long succession of (...) ‘reinterpretations’ of Christianity, but it is important, since the new thinkers may often get things badly wrong, and the faithful may be seduced by superficial plausibility or flashy modernity.One can well imagine a person who has found Christianity attractive enough for him to pray and to attend church services occasionally, but whose world-view has been largely formed by the mass media, discovering one of the modern ‘reinterpreters’ of the Christian faith with an enormous feeling of relief. (shrink)

When the tomb of Cangrande della Scala (d. 1329), ruler of Verona, was opened in 1921, it was found to contain an array of silks from Central Asia. These textiles are a reminder of the important links between the Veneto and Eurasian trade around 1300 - l’età di Marco Polo. With the rise of the interconnected Mongol states from the mid-thirteenth century, Venice became a gateway between Europe and the Asian world: people and ideas, as well as materials and objects (...) of value, moved as both commodities and gifts. This essay explores some of the ways that Mongol Eurasia penetrated the collective imagination and material culture of the fourteenth-century Veneto. The goal is to think about the larger context and implications of these links, and Venice’s function within them. What emerges is less a fascination with the exotic than an inclination to absorb new images, stories, materials, and objects into the native cultural models. (shrink)