The history of the Euclidean Steiner tree problem, which is the problem of constructing a shortest possible network interconnecting a set of given points in the Euclidean plane, goes back to Gergonne in the early nineteenth century. We present a detailed account of the mathematical contributions of some of the earliest papers on the Euclidean Steiner tree problem. Furthermore, we link these initial contributions with results from the recent literature on the problem.

A principle that many have found attractive is one that goes by the name “'Ought' Implies 'Can'.” According to this principle, one morally ought to do something only if one can do it. This essay has two goals: to show that the principle is false and to undermine the motivations that have been offered for it. Toward the end, a proposal about moral obligation according to which something like a restricted version of 'Ought' Implies 'Can' is true is floated. Though (...) no full-fledged argument for this proposal is offered, that it fits with a rather natural and intuitive picture of the structure of morality and seems to explain certain salient features of the debate over whether the principle is true, goes some way toward recommending it. (shrink)

First published in 1975, this is a book of general intellectual interest about the role of the university in contemporary society and that of university teachers in relation to their subjects, their students, and their wider political commitments. Alan Montefiore offers preliminary analyses of the family of concepts most often invoked in discussions of these problems, taking the central dispute to be between those who hold a 'liberal' view of the university and those who regard this notion as illusory, dishonest (...) or undesirable. Six academics, representing, discuss issues of substantive conflict in light of Montefiore's initial distinctions. The volume is of particular interest to students of political and social philosophy, and political and educational theory. It is also intended for a wider readership among those who care about the political status of the universities and recognize the importance and difficulty of the problems involved in this. (shrink)

This article proposes a reading of Michel de Certeau’s TheWriting of History which derives an understanding of the concept of practice as authoritative to the establishment and development of Enlightenment rationality. It is seen as a new form of legitimation established in the redeployment of religious ‘formalities’ in early modernity, supportive of the ostensible deliverance of the projects of reason.Subversive of its moral and ideological operations and geneses, this is an understanding of practice whose subject is the state. Practice, as (...) de Certeau advances it, led to the development of a concept of education productive of a regulatory ambit of social utility, and the student as both a figure of the utile and its moral postulate.This article thematizes the authoritative formality of the concept of practice in its hegemonic origins from early modernity to the thought of Karl Marx. It provides a needed supplement to Marx’s still provocative contribution to a persistent counternarrative, one which elides,and thus reinforces, significant prior,and no less persistent, functions of the concept of practice as here elaborated from de Certeau’s TheWriting of History. (shrink)

This is a revised and updated edition of Graham Nerlich's classic book The Shape of Space. It develops a metaphysical account of space which treats it as a real and concrete entity. In particular, it shows that the shape of space plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like causal explanation, Professor Nerlich prepares the ground for philosophical argument, and, using a number of novel examples, investigates how different spaces would (...) affect perception differently. This leads naturally to conventionalism as a non-realist metaphysics of space, an account which Professor Nerlich criticises, rejecting its Kantian and positivistic roots along with Reichenbach's famous claim that even the topology of space is conventional. He concludes that there is, in fact, no problem of underdetermination for this aspect of spacetime theories, and offers an extensive discussion of the relativity of motion. (shrink)

One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing (...) a general conception of conditionality that may unify the three given conceptions. (shrink)

Why should a Bayesian bother performing an experiment, one the result of which might well upset his own favored credence function? The Ramsey-Good theorem provides a decision theoretic answer. Provided you base your decision on expected utility, and the the experiment is cost-free, performing the experiment and then choosing has at least as much expected utility as choosing without further ado. Furthermore, doing the experiment is strictly preferable just in case at least one possible outcome of the experiment could alter (...) your choice of options. That is, you should pursue the information just in case it could make a difference to what you do. The problem remains, however, why one should do an experiment when nothing of much practical consequence hangs in the balance. One possibility here is to invoke the pure cognitive utility of states. It is shown that one constraint on cognitive value (what I call cogency) guarantees the value of learning: from a cognitive point of view you are justified in performing an experiment if the outcome of the experiment could make a different to what you think. A bonus of the basic framework is that it provides a new decision theoretic argument for the rationality of conditionalization. (shrink)

In this paper, I start by showing that sorites paradoxes are inclosure paradoxes. That is, they fit the Inclosure Scheme which characterizes the paradoxes of self-reference. Given that sorites and self-referential paradoxes are of the same kind, they should have the same kind of solution. The rest of the paper investigates what a dialetheic solution to sorites paradoxes is like, connections with a dialetheic solution to the self-referential paradoxes, and related issues—especially so called "higher order" vagueness.

The paper argues for realism in quantum mechanics. Specifically, the formalism of quantum mechanics should be understood as giving a complete description of quantum situations. When it is understood in this way, traditional primary properties of matter can be seen as similar to traditional secondary properties, though at a different level.

We have seen that proofs of soundness of (Boolean) DS, EFQ and of ABS — and hence the legitimation of these inferences — can be achieved only be appealing to the very form of reasoning in question. But this by no means implies that we have to fall back on classical reasoning willy-nilly. Many logical theories can provide the relevant boot-strapping. Decision between them has, therefore, to be made on other grounds. The grounds include the many criteria familiar from the (...) philosophy of science: theoretical integrity (e.g., paucity of ad hoc hypotheses), adequacy to the data (explaining the data of inference —all inferences, not just those chosen from consistent domains!) and so on. This paper has not attempted to address these issues in general. All it demonstrates is that the charge that a dialetheist solution to the semantic paradoxes can be maintained only by making some intelligible notion ineffable cannot be made to stick. The dialetheist has a coherent position, endorsing the T-scheme, but rejecting DS, EFQ (even Boolean DS and EFQ) and ABS. And any argument to the effect that the relevant notions are both ineffable and intelligible begs the question. The case against consistent “solutions” to the semantic paradoxes therefore remains intact. (shrink)

This paper asks and examines the question “who are you?” In doing so it embarks across the conceptual terrain of subjectivity, passing through five different regions. First is the subject and otherness, in which are considered Arendtian notions of the “who” of the individual in the appearing world. Next is the relation between the “I” and the “you” in systems of recognition, and how those systems are creations and expressions of social normativity. This is followed by the idea of the (...) sovereignty of the self as a reaction to its dislocation within systems of recognition. Sovereignty as such is viewed through the thought of Jacques Derrida and Hannah Arendt. With Foucault, the authors approach the question of social normativity as a frame rather than a constraint by which the self is stylized. The fourth section of the paper then explores self-questioning as a means of explicit or intentional self-stylization. Contrasting the “mere liberation” of thinking in Arendt’s thought with broader understandings of freedom, the fifth section relates Arendt’s conception of the miraculous with Derrida’s of the event. The paper’s trajectory returns in conclusion to the implications of its course for the initial question of who one is, particularly with respect to the teaching subject. (shrink)

In this paper I will review the developments in the foundations of mathematics in the last 150 years in such a way as to show that they have delivered something of a rather different kind: mathematical pluralism.

Towards Non-Being develops an account of the semantics of intentional predicates and operators. The account appeals to objects, both existent and non-existent, and worlds, both possible and impossible. This paper formulates replies to a number of the more interesting objections to the semantics that have been proposed since the book was published.

The paper establishes the general structure of the inconsistent models of arithmetic of [7]. It is shown that such models are constituted by a sequence of nuclei. The nuclei fall into three segments: the first contains improper nuclei: the second contains proper nuclei with linear chromosomes: the third contains proper nuclei with cyclical chromosomes. The nuclei have periods which are inherited up the ordering. It is also shown that the improper nuclei can have the order type of any ordinal, of (...) the rationals, or of any other order type that can be embedded in the rationals in a certain way. (shrink)

The paper establishes the general structure of the inconsistent models of arithmetic of [7]. It is shown that such models are constituted by a sequence of nuclei. The nuclei fall into three segments: the first contains improper nuclei: the second contains proper nuclei with linear chromosomes: the third contains proper nuclei with cyclical chromosomes. The nuclei have periods which are inherited up the ordering. It is also shown that the improper nuclei can have the order type of any ordinal. of (...) the nationals. or of any other order type that can be embedded in the rationals in a certain way. (shrink)

The Internet: A Philosophical Inquiry offers the first concise and accessible exploration of the issues which arise as we enter further into the world of Cyberspace.

This paper articulates Sylvan's theory of mathematical objects as non-existent, by improving (arguably) his treatment of the Characterisation Postulate. It then defends the theory against a number of natural objections, including one according to which the account is just platonism in disguise.

Relationships of physical resemblance to personality similarity and social affiliation have generated considerable discussion among behavioral science researchers. A “twin-like” experimental design explores associations among resemblance in appearance, the Big Five personality traits, self-esteem, and social attraction within an evolutionary framework. The Personality for Professionals Inventory, NEO/NEO-FFI-3, Rosenberg Self-Esteem Scale, and a Social Relationship Survey were variously completed by 45 U-LA pairs, identified from the “I’m Not a Look-Alike” project, Mentorn Media, and personal referrals. The mean U-LA intraclass correlations were (...) negligible for all Big Five personality traits on the PfPI and NEO/NEO-FFI-3. In contrast, mean ri values of.53 and.15 for monozygotic and dizygotic reared-apart twins, respectively, have been reported for these personality measures. The U-LA self-esteem correlation was also below the correlations reported for MZ and DZ reared-together twins. Finally, far fewer U-LAs expressed close social relationships than MZA and DZA twins. The present study extends earlier findings indicating that appearance is not meaningfully related to personality similarity and social relatedness. The criticism that MZ twins are alike in personality because their matched looks invite similar treatment by others is refuted. A more judicious interpretation is reactive genotype-environment correlation, namely that MZ twins’ similar personalities evoke similar reactions from others. MZ twins’ close social relations most likely derive from their perceptions of genetically based within-pair similarities that are lacking in U-LAs. (shrink)

Standard sorites paradoxes can always be put into a simple canonical form, employing the sole inference modus ponens. For example, consider the following paradox. Take a continuum of colours going from red to blue, and let a1,..., am be a sequence of segments of this continuum such that each segment is phenomenologically indistinguishable in colour from its immediate neighbours. Let Fx be the predicate ‘x is red’. Then the untrue conclusion Fam can be inferred from the premises Fa0 and Fan (...) → Fan + 1. (shrink)

I consider it a 'must read'"—Kathleen Marie Higgins, Philosophy East and West "An excellent introduction to the broad ranging reception of Nietzsche among Asian thinkers."—James R. Watson, Canadian Philosophical Review "The essays in ...

A number of different theories of truthlikeness have been proposed, but most can be classified into one of two different main programmes: the probability-content programme and the likeness programme.1 In Brink and Heidema [1987] we are offered a further proposal, with the attraction of some novelty. I argue that while the heuristic path taken by the authors is rather remote from what they call ‘the well-worn paths’,2 in fact their point of arrival is rather closer to existing proposals within the (...) likeness approach than might at first appear. It is the purpose of this note to outline the logical connections and to assess the reasons which have been offered in favour of the new proposal. (shrink)

Dialetheists concerning the paradoxes of self-refrence have often argued that the phenomeonon provides a choice between inconsistency and expressive incompleteness, and that inconsistency is the correct choice. In a recent paper 75: 573-84), JC Beall attacks this argument. This paper analyses his arguments, and argues that his paper simply provides a new spin on matters well known.

Towards NonBeing (Priest, 2005) gives a noneist account of the semantics of intentional operators and predicates. The semantics for intentional operators are modelled on those for the , is given and assessed.

This article takes an autobiographical approach to the development of practical theology as a discipline over the past 30 years, with particular attention to my own context of the United Kingdom. The unfolding of my own intellectual story in relation to key issues within the wider academic discourse provides an opportunity to reflect on some of the predominant themes and trends: past, present and future. Changing nomenclature, from 'pastoral studies' to 'practical theology', indicates how the discipline has moved from regarding (...) itself as the application of theory into practice, into a more performative and inductive epistemology. This emphasis continues to the present day and foregrounds the significance of the human context and the realities of lived experience, including narrative and autobiography. Whilst the methodological conundrums of relating experience to tradition and theory to practice continue, further challenges are beckoning, including religious pluralism, and so the article closes by surveying the prospects for a multicultural practical theology. (shrink)

What, if anything, is religious or spiritual delusion? What does religious delusion reveal about the difference between good and bad spirituality? 'The Abraham Dilemma' is the first book written by a philosopher on the topic of religious delusion - on the disorder's causes, contents, consequences, diagnosis and treatment.

In the year 1308, Cardinal Giacomo Colonna was a tremendously busy man. He had returned to Rome only a few years earlier in the aftermath of a devastating papal war waged against his family by Boniface VIII. The papal court had been absent from the city for years, leaving an administrative void in Rome as it established itself first in Poitiers, then in Avignon from 1308 under the leadership of the Gascon pope Clement V. In 1306 Giacomo was fully reinstated (...) to the cardinalate, and set about rebuilding his family's fortunes and reputation, as well as a number of the city's churches. He commissioned a new mosaic facade for the basilica of Santa Maria Maggiore, and in 1308 he oversaw repairs... (shrink)

Erin Murphy-Graham draws on more than a decade of qualitative research to examine the experiences of Juanita and eighteen other women who participated in the SAT program.

The word ‘logic’ has many senses. Here we will understand it as meaning an account of what follows from what and why. With contemporary methodology, logic in this sense – though it may not always have been thought of in this way – is a branch of applied mathematics. This has various implications for how one understands a number of issues concerning validity. In this paper I will explain this perspective of logic, and explore some of its consequences with respect (...) to the notion of logical form. (shrink)

This chapter presents a different and complementary take on the nature of realism and antirealism, one which has a clearer application to value when our journey is almost over than it would have here just as we embark. It argues that realism can be characterized as the affirmation of three important logical gaps. First, there is the gap between appearance and reality — the logical gap which constitutes the possibility of illusion or distortion. Second, there is the gap between reality (...) and belief — the logical gap which constitutes the possibility of error. Third, there is the gap between appearance and belief — the logical gap which constitutes the possibility of incoherence between percept and concept. Various versions of antirealism try to close these gaps, thereby handily blocking the possibility of a certain kind of shortcoming. (shrink)