Jeremy Bentham was a British philosopher, jurist, and social reformer. He is regarded as the founder of modern utilitarianism.

David Hume, Adam Smith, Jeremy Bentham and John Stuart Mill are often viewed as contributors to or participants in a common tradition of thought roughly characterized as ‘the liberal tradition’ or the tradition of ‘bourgeois ideology’. This view, however useful it may be for polemical or proselytizing purposes, is in some important respects historiographically unsound. This is not to deny the importance of asking what twentieth-century liberals or conservatives might find in the works of, say, David Hume to support their (...) respective ideological persuasions. It is only to insist that attempts to use selected arguments, or parts of arguments, from great eighteenth-century thinkers to shore up twentieth-century programmatic political positions must be categorically distinguished from attempts to understand what Hume, Smith, Bentham or Mill actually meant, or could imaginably have meant, to say. (shrink)

Through his views on perspectivism and the will to power, Nietzsche indirectly influences many current discourses on identity. This article places these themes in the broader context of Nietzsche’s thought. Firstly, it is indicated how difficult it is to speak of someone’s identity by showing how many ‘Nietzsches’ appear in his writings, notebooks and letters and the accounts of his contemporaries. Such comparative readings, although they may cast new light on Nietzsche’s philosophy, are rare in Nietzsche scholarship. Next, his views (...) on identity are briefly explored, paying attention to his rejection of the centred subject, equality and morality and his view on hierarchy, creativity and power struggles. Finally, it is argued that Nietzsche confronts our discourses on identity with challenges regarding the ubiquity of power struggles, the role of ressentiment, the possibility of communication across boundaries, the importance of the individual and the problem of affirmation. Contribution: Discourses on identity, although fashionable, are often confusing. Instead of offering solutions, this article uses Nietzsche’s life and philosophy to identify some causes of confusion and indicates where crucial decisions regarding our presuppositions have to be taken. Its aim was not to produce knowledge but, in line with Nietzsche’s practice, to ‘produce ignorance’, to question the terms we use confidently, without fully considering their meaning or implications. (shrink)

Preparatory Principles is not a linear text in the conventional sense, but consists of a series of short passages on a variety of topics, whose themes are summarised in marginal headings. The material constitutes a philosophical commonplace book, compiled by Bentham in the mid-1770s, in which he worked out the foundational ideas for his new science of legislation. He then drew on this material when composing such works as A Fragment on Government and An Introduction to the Principles of Morals (...) and Legislation. Inspired by such figures as John Locke and Claude Adrien Helvetius, Bentham developed an original ontological and epistemological basis for legal terminology, with the aim of replacing the traditional terminology of English law with that of universal jurisprudence. The work that dominates the text, in that Bentham returns to it time and time again in order to offer criticism of it, is William Blackstone's Commentaries on the Laws of England. While unorganized and fragmentary, the material in Preparatory Principles constitutes a remarkable record of the evolving ideas of a major legal philosopher at a formative stage of his career. (shrink)

Modules in ethics have become astonishingly popular at the University of the Western Cape. This could reflect students’ concern about morality, but the saying by Lafargue in Tao te ching in the title suggests that moral discourse flourishes when moral behaviour is languishing. This article reflects on some 15 years of teaching ethical theory to third-year students. Three trends are identified: Students’ responses to the theories are unpredictable and surprising. Nietzsche and Kant are very popular, although some modern ‘contextual’ theories (...) draw less support. Students who can be extremely moralistic in class are sometimes amoral in their practices and offhand pronouncements. Students are hampered by their poor conceptual skills and rely excessively on memorising. The last two trends raise questions about our teaching of ethics and the ethics of our teaching. Although many students embrace character-based theories, to some ‘a good character’ apparently means ‘what makes me feel good about myself’ and to others ‘what makes me look good to my group’. Thus, they effectively embrace either individual relativism or group relativism, which is understandable when theories are presented without the backing of at least a rudimentary philosophical anthropology. Questions of indoctrination become acute in the teaching of ethics. Are we, in the name of moral formation, teaching students to parrot current dogmas presented without arguments? If so, our practice may be both morally dubious and counterproductive. The best students rebel against such manipulation. The article calls for more reflection on how and to what ends we teach ethics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Cambridge Companion to Wittgenstein ed. by Hans Sluga, David G. SternDouglas G. WinbladHans Sluga and David G. Stern, editors. The Cambridge Companion to Wittgenstein. Cambridge: Cambridge University Press, 1996. Pp. ix + 509. Cloth, $59.95. Paper, $18.95.There is a disconcerting lack of agreement about how to interpret Wittgenstein’s texts. The introduction and fourteen essays in this book are cases in point. Stern claims that the phenomenon is (...) due largely to the fact that Wittgenstein’s writings call for a radical change in philosophical sensibility, a change to which there continues to be considerable resistance. He also notes that most of Wittgenstein’s posthumous publications are the result of massive editorial interventions, and that much of his work remains unpublished. The electronic edition of the entire Nachlass, Stern argues, will reveal that Wittgenstein’s writings as a whole constitute a highly interconnected network of remarks—a hypertext. In a similar vein, Sluga suggests that Wittgenstein’s philosophical trajectory reflects the larger cultural shift in this century from modernism to postmodernism. The postmodern, hypertextual aspect of Wittgenstein’s thinking is nowhere better embodied here than in Cavell’s reflections on the importance of context in deciding whether some behavior counts as language use. Cavell’s remarks reproduce and comment on his own lectures on the opening sections of Philosophical Investigations, sections he reads as a commentary on a passage in Augustine.A closely related theme in the essays concerns the status of Wittgenstein’s attempt to avoid replacing older philosophical theories with new ones. Garver maintains that Wittgenstein’s notion of grammar provides a powerful rebuke to speculative or scientific metaphysics, but not to descriptive metaphysics. Glock argues in turn that Wittgenstein’s distinction between grammatical and empirical propositions does not fall prey to Quine’s attack on analyticity. One wonders whether this distinction is purely descriptive. And even if one grants Glock’s claim that grammatical rules are unfalsifiable, how does one decide whether a particular remark about these rules is mistaken? We cannot pass judgment on what for Garver is Wittgenstein’s genuinely critical enterprise without addressing these issues.Doing so also requires us to assess Wittgenstein’s closely related treatment of rule following. Stroud rejects Kripke’s account of this material, claiming that what the relevant passages actually show is that that no explanation of how language in general—and meaning and normativity in particular—is possible. Stroud holds that this conclusion can be felt as dissatisfying. But is it a theoretical conclusion? And why not find it liberating, as Wittgenstein apparently did?Fogelin also emphasizes Wittgenstein’s antitheoretical animus, taking issue with Dummett’s view that Wittgenstein is advancing a use theory of meaning and an antirealist philosophy of mathematics. Like Fogelin, Gerrard challenges Dummett’s view of Wittgenstein’s treatment of mathematics, insisting that for Wittgenstein, truth is not a matter of human agreement. But Gerrard does not tell us what Wittgenstein believes truth is. The question whether there is anything he thinks it is deserves further attention.Some contributors impute to the later Wittgenstein what are clearly theoretical [End Page 643] stances. Bloor argues that what he takes to be Wittgenstein’s linguistic idealism arises from certain sociological assumptions. And Kober attributes a “collective-linguistic idealism” to Wittgenstein on the grounds that the latter thinks that the truth conditions of a sentence depend on, or are part of, its utterance conditions. But, as several of the other essays make clear, it is debatable whether Wittgenstein would agree.A few authors discuss in detail the nature of philosophical theorizing in the early Wittgenstein. Summerfield offers an interpretation of what she takes to be the theory of representation in the Tractatus. She allows, however, that Wittgenstein tells us that one cannot represent the connection between a name and its referent. Ricketts, on the other hand, stresses that the so-called picture theory appears to imply that there can be no such theory. Yet his reading does not abandon the conception of truth as agreement with reality. It is unclear to me that this conception survives the implosion of the text as a whole. Why not kick the entire ladder away... (shrink)

This paper examines naturalized epistemology's prospects for dealing with Cartesian skepticism and the traditional problem of induction. It is argued that Quine's approach fails to satisfy the skeptic who does not already embrace some version of scientific method. In addition, it is argued that Goldman's reliabilism enables one to address these issues empirically only if one rejects the view that if we are capable of confirming an empirical hypothesis, we are also capable of disconfirming it. The article ends with a (...) negative appraisal of the role relevant alternatives play in Goldman's account, particularly with regard to second order knowledge. (shrink)

The Jewish leftist lawyer Ernst Fraenkel was one of twentieth-century Germany's great intellectuals. During the Weimar Republic he was a shrewd constitutional theorist for the Social Democrats and in post-World War II Germany a respected political scientist who worked to secure West Germany's new democracy. This book homes in on the most dramatic years of Fraenkel's life, when he worked within Nazi Germany actively resisting the regime, both publicly and secretly. As a lawyer, he represented political defendants in court. As (...) a dissident, he worked in the underground. As an intellectual, he wrote his most famous work, The Dual State – a classic account of Nazi law and politics. This first detailed account of Fraenkel's career in Nazi Germany opens up a new view on anti-Nazi resistance – its nature, possibilities, and limits. With grit, daring and imagination, Fraenkel fought for freedom against an increasingly repressive regime. (shrink)

This paper examines two attempts to justify the way in which intuitions about specific cases are used as evidence for and against philosophical theories. According to the concept model, intuitions about cases are trustworthy applications of one’s typically tacit grasp of certain concepts. We argue that regardless of whether externalist or internalist accounts of conceptual content are correct, the concept model flounders. The second justification rests on the less familiar belief model, which has it that intuitions in philosophy derive from (...) one’s beliefs. Although more promising than the concept model, the belief model fails to justify traditional philosophical use of intuitions because it is not clear a priori that the beliefs at issue are true. The latter model may, however, legitimize a less a prioristic approach to intuitions. (shrink)

This paper examines two attempts to justify the way in which intuitions about specific cases are used as evidence for and against philosophical theories. According to the concept model, intuitions about cases are trustworthy applications of one’s typically tacit grasp of certain concepts. We argue that regardless of whether externalist or internalist accounts of conceptual content are correct, the concept model flounders. The second justification rests on the less familiar belief model, which has it that intuitions in philosophy derive from (...) one’s (often tacit) beliefs. Although more promising than the concept model, the belief model fails to justify traditional philosophical use of intuitions because it is not clear a priori that the beliefs at issue are true. The latter model may, however, legitimize a less a prioristic approach to intuitions. (shrink)

In this paper, we consider the bearing intuitions have on semantic theory, and suggest that when the phenomenon is properly understood, they are less important than philosophers tend to think. We also argue that our conclusions go beyond intuitions about semantics, and impugn the idea of intuition more generally.

For Wittgenstein, as Cora Diamond interprets him in the essays collected in her recent The Realistic Spirit , there are no logical truths, and a host of other linguistic constructions, such as ‘A is an object’ are, contrary to appearances, nonsensical. In what follows, after outlining Diamond's account I argue that the position she ascribes to Wittgenstein is incoherent. I also reject some possible responses to this charge, among them an appeal to the distinction between what can be said and (...) what can only be shown. (shrink)

This paper uses a reconstruction of the life and career of Heinrich Poll as a window into developments and professional relationships in the biological sciences in Germany in the period from the beginning of the twentieth century to the Nazi seizure of power in 1933. Poll's intellectual work involved an early transition from morphometric physical anthropology to comparative evolutionary studies, and also found expression in twin research - a field in which he was an acknowledged early pioneer. His advocacy of (...) eugenics led to participation in state-sponsored committees convened to advise on social policy, one of which debated sterilisation and made recommendations that led eventually to the establishment of the notorious Kaiser Wilhelm Institute for Anthropology, Human Heredity and Eugenics. However, his status as a prominent geneticist and, in particular, as a eugenicist had an ironic and ultimately tragic dimension. Heinrich Poll was of Jewish birth, and this resulted in his career being destroyed by an application of the population policies he had helped put in place. (shrink)

We show that in 1929 Cartan and Einstein almost produced a theory in which the electromagnetic (EM) field constitutes the time-like 2-form part of the torsion of Finslerian teleparallel connections on pseudo-Riemannian metrics. The primitive state of the theory of these connections would not, and did not, permit Cartan and Einstein to realize how their torsion field equations contained the Maxwell system and how the Finslerian torsion contains the EM field. Cartan and Einstein discussed curvature field equations, though failing to (...) focus on the fact that teleparallelism automatically implies gravitational field equations with torsion terms as source, both in first and second order. We further show that the first-order contribution of the EM field to the source of the gravitational field may play havoc with the remeasurement of Newton's gravitational constant, even if the experiment is electrically grounded. These results are also used as support for the thesis that there is an alternative to the present way of dealing with the great theoretical questions of physics. On the practical side, the inconveniences faced in measuring G may be greatly compensated by the possibility of manipulating spacetime with electric fields at the first-order level. (shrink)

In a recent paper [J. G. Vargas and D. G. Torr, Found. Phys. 27, 599 (1997)], we have shown that a subset of the differential invariants that define teleparallel connections in spacetime generates a teleparallel Kaluza-Klein space (KKS) endowed with a very rich Clifford structure. A canonical Dirac equation hidden in this structure might be uncovered with the help of a teleparallel Kähler calculus in KKS. To bridge the gap to such a calculus from the existing Riemannian Kähler calculus in (...) spacetime, we commence the construction of a teleparallel Kähler calculus in spacetime. In the process, we notice: (a) Unknown to him, one of Einstein's equations in his attempt at unification with teleparallelism states that the interior covariant derivative of the torsion is zero. (b) A mechanism exists in the tangent bundle of teleparallel spaces for producing confinement (in the applicable cases, one would have to show why nonconfinement also occurs, rather than the other way around). (c) When the torsion is not zero, the interior covariant derivative in the sense of Kähler, δF, does not coincide with *d*F. The system (dF = 0, δF = j) rather than (dF = 0, *d*F = j) should then be used for generalizations of Maxwell's electrodynamics. (shrink)

In an accompanying paper (I), it is shown that the basic equations of the theory of Lorentzian connections with teleparallelism (TP) acquire standard forms of physical field equations upon removal of the constraints represented by the Bianchi identities. A classical physical theory results that supersedes general relativity and Maxwell-Lorentz electrodynamics if the connection is viewed as Finslerian. The theory also encompasses a short-range, strong, classical interaction. It has, however, an open end, since the source side of the torsion field equation (...) is not geometric.In this paper, Kaehler's partial geometrization of the Dirac equation is taken as a starting point for the development of fully geometric Dirac equations via the correspondence principle given in I. For this purpose, Kaehler's calculus (where the spinors are differential forms) is generalized so that it also applies when the torsion is not zero. The point is then made that the forms can take values in tangent Clifford algebras rather than in tensor algebras. The basic “Eigenschaft” of the Kaehler calculus also is examined from the physical perspective of dimensional analysis.Geometric Dirac equations of great structural simplicity are finally inferred from the standard Dirac equation by using the aforementioned correspondence principle. The realm of application of the Dirac theory is thus enriched in principle, though only at an abstract level at this point: the standard spinors, which are scalar-valued forms in the Kaehler version of that theory, become Clifford-valued. In addition, the geometrization of the Dirac equation implies a geometrization of the Dirac current. When this current is replaced in the field equations for the torsion, the theory of Paper I becomes fully geometric. (shrink)

The issue of whether teleparallel nonlinear connections exist is resolved by their explicit construction on Finslerian metrics that arise in the Robertson test theory of special relativity (RTTSR), and on the Minkowski metric in particular. The method is an adaptation to the Finsler bundle of a similar construction for teleparallel linear connections. It suggests the existence of a concept of metric compatibility alternative toω μλ +ω λμ = 0 for teleparallel nonlinear connections. A sophisticated system of partial differential equations whose (...) solutions have been discussed in the computing literature is interpreted in geometric terms. The characteristics of the solutions are checked against compliance with the conditionω μλ +ω λμ = 0, an issue whose relevance for this theory derives from the fact that nonantisymmetric connections repeatedly appear in teleparallel geometry. (shrink)

It is shown that relativistic spacetimes can be viewed as Finslerian spaces endowed with a positive definite distance (ω0, mod ωi) rather than as pariah, pseudo-Riemannian spaces. Since the pursuit of better implementations of “Euclidicity in the small” advocates absolute parallelism, teleparallel nonlinear Euclidean (i.e., Finslerian) connections are scrutinized. The fact that (ωμ, ω0 i) is the set of horizontal fundamental 1-forms in the Finslerian fibration implies that it can be used in principle for obtainingcompatible new structures. If the connection (...) is teleparallel, a Kaluza-Klein space (KKS) indeed emerges from (ωμ, ω0 i), endowed ab initio with intertwined tangent and cotangent Clifford algebras. A deeper level of Kähler calculus, i.e., the language of Dirac equations, thus emerges. This makes the existance of an intimate relationship between classical differential geometry and quantum theory become ever more plausible. The issue of a geometric canonical Dirac equation is also raised. (shrink)

This experiment examined the effects of three elements comprising Jones' (1991) moral intensity construct, (social consensus, personal proximity, and magnitude of consequences) in a cross-cultural comparison of ethical decision making within a human resource management (HRM) context. Results indicated social consensus had the most potent effect on judgments of moral concern and judgments of immorality. An analysis of American, Eastern European, and Indonesian responses also indicted socio-cultural differences were moderated by the type of HRM ethical issue. In addition, individual differences (...) in personal ethical ideology (relativism and idealism) varied reliably with moral judgments after controlling for issue characteristics and socio-cultural background. (shrink)

This paper uses a reconstruction of the life and career of Heinrich Poll as a window into developments and professional relationships in the biological sciences in Germany in the period from the beginning of the twentieth century to the Nazi seizure of power in 1933. Poll's intellectual work involved an early transition from morphometric physical anthropology to comparative evolutionary studies, and also found expression in twin research - a field in which he was an acknowledged early pioneer. His advocacy of (...) eugenics led to participation in state-sponsored committees convened to advise on social policy, one of which debated sterilisation and made recommendations that led eventually to the establishment of the notorious Kaiser Wilhelm Institute for Anthropology, Human Heredity and Eugenics. However, his status as a prominent geneticist and, in particular, as a eugenicist had an ironic and ultimately tragic dimension. Heinrich Poll was of Jewish birth, and this resulted in his career being destroyed by an application of the population policies he had helped put in place. (shrink)

BackgroundAlthough the number of reporting guidelines has grown rapidly, few have gone through an updating process. The STARD statement (Standards for Reporting Diagnostic Accuracy), published in 2003 to help improve the transparency and completeness of reporting of diagnostic accuracy studies, was recently updated in a systematic way. Here, we describe the steps taken and a justification for the changes made.ResultsA 4-member Project Team coordinated the updating process; a 14-member Steering Committee was regularly solicited by the Project Team when making critical (...) decisions. First, a review of the literature was performed to identify topics and items potentially relevant to the STARD updating process. After this, the 85 members of the STARD Group were invited to participate in two online surveys to identify items that needed to be modified, removed from, or added to the STARD checklist. Based on the results of the literature review process, 33 items were presented to the STARD Group in the online survey: 25 original items and 8 new items; 73 STARD Group members (86 %) completed the first survey, and 79 STARD Group members (93 %) completed the second survey.Then, an in-person consensus meeting was organized among the members of the Project Team and Steering Committee to develop a consensual draft version of STARD 2015. This version was piloted in three rounds among a total of 32 expert and non-expert users. Piloting mostly led to rewording of items. After this, the update was finalized. The updated STARD 2015 list now consists of 30 items. Compared to the previous version of STARD, three original items were each converted into two new items, four original items were incorporated into other items, and seven new items were added.ConclusionsAfter a systematic updating process, STARD 2015 provides an updated list of 30 essential items for reporting diagnostic accuracy studies. (shrink)

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one (...) free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant “Robertson's subfamilies.” It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory. (shrink)

Studies have shown that in the mammalian neuromuscular system stretch reflexes are localized within individual muscles. Neuromuscular compartmentalization, the partitioning of sensory output from muscles, and the partitioning of segmental pathways to motor nuclei have also been demonstrated. This evidence indicates that individual motor nuclei and the muscles they innervate are not homogeneous functional units. An analysis of the functional significance of reflex localization and partitioning suggests that segmental control mechanisms are based on subdivisions of motor nuclei–muscle complexes. A partitioned (...) organization of segmental control mechanisms could utilize (1) the potential functional diversity of muscle fiber types, (2) the variety of mechanical actions of individual muscles arising from their distributed origins and insertions, and (3) diverse architectural features such as intramuscular variations in pinnation and complex in-series and in-parallel arrangements of muscle fibers. The differentiated activity observed in some muscles during natural movements also calls for localized segmental control mechanisms. Partitioning may also play a role in mechanical interactions between contracting motor units and in increasing the stability of neuromuscular systems. The functional advantages of reflex localization and partitioning suggest they are probably common features of segmental systems, whose organization reflects the structure and function of their associated neuromuscular systems. (shrink)

BackgroundMany journals prohibit the use of declarative titles that state study findings, yet a few journals encourage or even require them. We compared the effects of a declarative versus a descriptive title on readers’ perceptions about the strength of evidence in a research abstract describing a randomized trial.MethodsStudy participants (medical or dental students or doctors attending lectures) read two abstracts describing studies of a fictitious treatment (Anticox) for a fictitious condition (Green’s syndrome). The first abstract (A1) described an uncontrolled, 10-patient, (...) case series, and the second (A2) described a randomized, placebo-controlled trial involving 48 patients. All participants rated identical A1 abstracts (with a descriptive title) to provide baseline ratings and thus reduce the effects of inter-individual variability. Participants were randomized so that half rated a version of A2 with a descriptive title and half with a declarative title. For each abstract, participants indicated their agreement with the statement “Anticox is an effective treatment for pain in Green’s syndrome” using 100 mm visual analogue scales (VAS) ranging from “disagree completely” to “agree completely.” VAS scores were measured by an investigator who was unaware of group allocation.ResultsOne hundred forty-four participants from four centres completed the study. There was no significant difference between the declarative and the descriptive title groups’ confidence in the study conclusions as expressed on VAS scales—in fact, the mean difference between A1 and A2 was smaller for the declarative title group than that for the descriptive title group (32.6 mm, SD 27.4 vs. 39.8 mm, SD 22.6, respectively, p = 0.09).ConclusionsWe found no evidence that the use of a declarative title affected readers’ perceptions about study conclusions. This suggests that editors’ fears that declarative titles might unduly influence readers’ judgements about study conclusions may be unfounded, at least in relation to reports of randomized trials. However, our study design had several limitations, and our findings may not be generalizable to other situations. (shrink)

It has recently been shown by Vargas, (4) that the passive coordinate transformations that enter the Robertson test theory of special relativity have to be considered as coordinate transformations in a seven-dimensional space with degenerate metric. It has also been shown by Vargas that the corresponding active coordinate transformations are not equal in general to the passive ones and that the composite active-passive transformations act on a space whose number of dimensions is ten (one-particle case) or larger (more than one (...) particle).In this paper, two different (families of) electrodynamics are constructed in ten-dimensional space upon the coordinate free form of the Maxwell and Lorentz equations. The two possibilities arise from the two different assumptions that one can naturally make with respect to the acceleration fields of charges, when these fields are related to their relativistic counterparts. Both theories present unattractive features, which indicates that the Maxwell-Lorentz framework is unsuitable for the construction of an electrodynamics for the Robertson test theory of the Lorentz transformations. It is argued that this construction would first require the formulation of Maxwell-Lorentz electrodynamics in the form of a connection in Finsler space. If such formulation is possible, the sought generalization would consist in simply changing bases in the tangent spaces of the manifold that supports the connection. In addition, the number of dimensions of the space of the Robertson transformations would be ten, but not greater than ten. (shrink)