This paper addresses the doubts voiced by Wigner about the physical relevance of the concept of geometrical points by exploiting some facts known to all but honored by none: Almost all real numbers are transcendental; the explicit representation of any one will require an infinite amount of physical resources. An instrument devised to measure a continuous real variable will need a continuum of internal states to achieve perfect resolution. Consequently, a laboratory instrument for measuring a continuous variable in a finite (...) time can report only a finite number of values, each of which is constrained to be a rational number. It does not matter whether the variable is classical or quantum-mechanical. Now, in von Neumann’s measurement theory (von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, [1955]), an operator A with a continuous spectrum—which has no eigenvectors—cannot be measured, but it can be approximated by operators with discrete spectra which are measurable. The measurable approximant F(A) is not canonically determined; it has to be chosen by the experimentalist. It is argued that this operator can always be chosen in such a way that Sewell’s results (Sewell in Rep. Math. Phys. 56: 271, [2005]; Sewell, Lecture given at the J.T. Lewis Memorial Conference, Dublin, [2005]) on the measurement of a hermitian operator on a finite-dimensional vector space (described in Sect. 3.2) constitute an adequate resolution of the measurement problem in this theory. From this follows our major conclusion, which is that the notion of a geometrical point is as meaningful in nonrelativistic quantum mechanics as it is in classical physics. It is necessary to be sensitive to the fact that there is a gap between theoretical and experimental physics, which reveals itself tellingly as an error inherent in the measurement of a continuous variable. (shrink)

Contrary to what might be expected given a religious or other motivation, Pierre Duhem's interest in mediaeval science was the result of his surprise encounter with Jordanus de Nemore while working on Les origines de la statique in the late autumn of 1903. Historical assumptions common among physicists at that time may explain this surprise, which occasioned a frantic search for more mediaeval precursors for Renaissance mechanics. It also raised serious historiographical problems that threatened even his methodological views, until they (...) were resolved in his To save the phenomena of 1908. (shrink)

Is an ethical leader an oxymoron? Society demands and expects greater accountability from organizational leaders. The literature on leadership, especially business leadership, has neglected ethical issues by focusing only on those approaches and strategies that emphasize self-centred, individualistic concerns. How ever, true and effective leadership is one in which the leader's behaviour and the exercise of the leadership influence process are consistent with ethical and moral values. The authors argue that our understanding of leadership is incomplete, if not deformed, if (...) it does not include the three critical dimensions of ethical leadership. (shrink)

I would like to develop a few critical observations on some substantive moral ideas propounded in Professor R. M. Hare's Freedom and Reason a work where formal and substantive moral arguments are blended in an attractive and plausible, though at times somewhat exasperating, mixture. Hare's formal doctrines, the celebrated theses of prescriptivity and universalizability, will not as such interest me here, though I shall have to take notice of at least one of them, viz. universalizability, in so far as it (...) has a bearing on what I take to be Hare's substantive position. The arguments in Freedom and Reason are compounded of Kantian and utilitarian elements, and culminate in Hare's conceptualization of two antithetical types of person, whom he calls respectively the ‘liberal’ and the ‘fanatic’. This distinction itself is based on a rigid and uncompromising dichotomy of ‘interest’ and ‘ideal’, and it is on this dichotomy that Hare's substantive moral doctrine hinges. Hare's argument is that the morally good person is one who subordinates his ideal to a moral principle that takes interests into account, in contradistinction to the fanatic who allows interests to be overridden by his ideal. There is much to recommend in this doctrine, and distinctions of this nature can and ought to be drawn. But the way in which it is done in Hare's work opens up fresh doubts and fails to solve some fundamental problems. As I do not think that his distinction between ‘interest’ and ‘ideal’ is tenable, I cannot agree wholly to the predominantly formal manner in which Hare deals with the important question of distinguishing between liberalism and fanaticism. The upshot of my arguments is that this distinction can only be made intelligible in substantive terms. Although I cannot here offer a positive alternative to Hare beyond some oblique hints at the end, my critical remarks on Hare's doctrine ought at least to go some way in establishing the need for such an alternative. (shrink)

Much speculation on the sources of Duhem's historical interests fails to account for the major shifts in these interests: neither his belief in the continuous development of physics nor his Catholicism, when his Church was encouraging the study of generally Aristotelian scholastic thought, led to any interest in mediaeval science before 1904. Equally, his own claim that he was merely testing his views on the nature of physical theory is easily squared only with earlier work with no trace of mediaeval (...) science. Behind this discontinuity lies a major crisis. Though not a positivist, Duhem had based all his work on assumptions acceptable to positivists. One of these, the sterility of the Middle Ages, was refuted by his chance discovery of evidence of genuine mediaeval science in the autumn of 1903, but that left the doctrine of scholastic sterility intact. (shrink)

Writers on jurisprudence often stress that conflict between positive laws and morality does not invalidate the positive laws. A law which requires me to compensate another for an injury caused by a dangerous object kept on my property is not invalidated by the fact that I have not been negligent and have no moral obligation to compensate the injured person. And although I have a moral obligation to keep my promises, positive laws may validly imply that I need not keep (...) promises not made for a consideration or under seal. Thus positive law may permit acts not permitted by morals and may forbid acts permitted by morals. The lesson drawn from these thoughts is that to establish a positive law as valid we need not consider the relationships it bears to the rules of morals. A valid law is simply a law created in accordance with the constitutional conventions or ‘rules of recognition’ of the society in which it is to be applied. It is the manner of its establishment, not its relationship to morals, which makes a law valid. (shrink)

The aim of the essay is to devise a logic of conditionality which escapes the paradoxes which arise when the general conditional is identified with the universalization of the material conditional. The assumption I adopt is that the logic of one contingent form differs from that of another to the extent that the two forms have different confirmations and disconfirmations. The logic of conditionals is not, But that of their confirmations and disconfirmations is, At bottom truth-Functional; and the logical relations (...) between conditionals, And between conditionals and non-Conditionals, May be traced through the truth-Functional connections between their respective confirmations and disconfirmations. The approach necessitates the re-Definition of the notions of confirmation and entailment. A peculiarity of the system which emerges is that from it can be derived, Without existential assumptions, The twenty-Four valid forms of the syllogism, The relationships of the square of opposition and the other commonly accepted inferences of traditional logic. (shrink)

Three lectures on Jaina philosophy and ancient civilization.