Following Dirac's generalized canonical formalism, we develop a quantization scheme for theN-dimensional system described by the Lagrangian $L_0 (\dot y,y) = \frac{1}{2}h_{ij} (y)\dot y^i \dot y^j + b_i (y)\dot y^i - w(y)$ which is supposed to be invariant under the gauge transformation $y^i \to y\prime ^i = y^i + (\rho ^i _\alpha + \sigma ^i _{\alpha j} \dot y^j )\delta \Lambda ^\alpha + \tau ^i _\alpha \delta \dot \Lambda ^\alpha$ . The gauge invariance necessarily implies that the Lagrangian is singular. (...) The identities imposed by the gauge invariance are enumerated and reduced to simpler forms. There are primary and secondary constraints, both of which are of first class. The reduced identities are solved explicitly for the case where the secondary constraints constitute the generators of the groupSO(M), and thus an explicit expression for the manifestly gauge-invariant Lagrangian is obtained. By fixing the gauge appropriately, the unphysical variables are eliminated and a quantization is achieved using only physical variables. Our formulation is covariant under an arbitrary point transformation of physical variables. The problem of formulating a quantum action principle is also commented on briefly. (shrink)

Schwinger's action principle is formulated for the quantum system which corresponds to the classical system described by the LagrangianL c( $\dot x$ , x)=(M/2)gij(x) $\dot x$ i $\dot x$ j−v(x). It is sufficient for the purpose of deriving the laws of quantum mechanics to consider onlyc-number variations of coordinates and time. The Euler-Lagrange equation, the canonical commutation relations, and the canonical equations of motion are derived from this principle in a consistent manner. Further, it is shown that an arbitrary point (...) transformation leaves the forms of the fundamental equations invariant. The judicious choice of the quantal Lagrangian is essential in our formulation. A quantum mechanical analog of Noether's theorem, which relates the invariance of the quantal action with a conservation law, is established. The ambiguities in the quantal Lagrangian are also discussed and it is pointed out that the requirement of invariance is not sufficient to determine uniquely the quantal Lagrangian and the Hamiltonian. (shrink)

The Manifestation Requirement, advanced by Dummett in his critique of semantic realism, has been criticized for being behavioristic, and the responses have been made that the critics are mistaken. However, the dispute has failed to exhibit the point of the Requirement. In this paper, I shall argue (1) that, in the light of Anscombe's theory of practical knowledge, knowledge of linguistic meaning is to be seen as the knowledge-how that forms the basis of the practical knowledge that an agent has (...) of his own intentional actions, (2) that such knowledge of linguistic meaning is to be based on mutual agreements in a community, and (3) that the Manifestation Requirement is a condition for the possibility of such mutual agreements. As a result, the Manifestation Requirement finds its basis on the idea that language and linguistic acts are tools that we use while continually improving them. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 20 (2000) 321-323 [Access article in PDF] Frederick J. Streng Book Award David Loy Interview The 1999 winner of the Frederick J. Streng Book Award is David R. Loy, professor on the Faculty of International Studies at Bunkyo University in Chigasaki, Japan. Professor Loy received the award for his book, Lack and Transcendence: The Problem of Death and Life in Psychotherapy, Existentialism, and Buddhism, published by Humanities (...) Press (New Jersey) in 1996. The book places Western patterns of thought developed in tandem with Christian ideas into dialogic contact with Buddhism. It is thus a very Buddhist book, but a signal contribution to the practice of Buddhist-Christian dialogue. Buddhist-Christian Studies asked David about his writing of the volume.Buddhist-Christian Studies: Why did you write this book?David Loy: It was the product of an existential crisis, both intellectual and personal. My father, who had always been healthy and full of life, suddenly became ill with pancreatic cancer. Then my Zen teacher Yamada Koun had a bad fall that led to his death a year later. Not long before that my relationship with him and the Sanbo Kyodan had become somewhat problematic. This threatened my 'spiritual ground'. Finally, I was without a job. All this gave me plenty of time not only to sit intensively but also to read widely everything I could find on death and related issues.Did you think that sitting and studying would lead to a book?I didn't know. I could feel something gestating. I realized something was needed in this area. I was (and still am) very impressed by the last two books of Ernest Becker, but despite their brilliance his notion of death-denial is a little off-center from a Buddhist perspective. Fear of death projects our problem into the future, while the groundlessness of our sense-of-self accounts better for our sense-of-lack right here and now.What was the final trigger for doing the book?Another Zen teacher suggested that I try to write a Zen teisho [sermon or talk]. I sat down but after a few lines so many other thoughts began to bubble up that I couldn't write them down fast enough. There was no obvious or immediate logical connection among them, but they kept coming. This went on for about two, almost non-stop, days. After that the thoughts slowed down. I read over the notes I'd written, which led to more ideas, and then I began to perceive their relationship. After five days or so I had a detailed outline for the book, and the real work began. [End Page 321]What kind of response to the book, both positive and negative, have you received?There have not been many reviews, but they have generally been positive. It's not an easy book to evaluate: it brings together many different thinkers and traditions in order to address many different issues. In the process it attempts what is almost a grand synthesis of Buddhism, existentialism, and psychotherapy around the notion of our 'sense of lack', which I argue motivates us all. This involves close readings of Freud, Heidegger, Nietzsche, Nagarjuna, and many others. Unfortunately, the print is small and not easy to read, the cover is ugly, and the price is too high. For all these reasons readers have my sympathies! But there are some readers for whom the book really 'clicks'. I'm pleased that it seems to work on the existential as well as the intellectual level, for such people.After several years of reflection, would you write it any differently today?Yes, probably. The first thing I would do is take out the last chapter "Transcendence East and West," which was an afterthought and doesn't really fit in very well. As published, the chapter takes the concept of 'lack' into a new dimension which needs to be worked out much more carefully than I did in the book. It argues that, in place of the usual East-West dichotomy, it is more insightful to view South Asian Indian- influenced cultures as in some ways... (shrink)

Marjorie Grene has argued in a number of contexts that any attempt to reduce the explanation of human actions to “mechanistic” explanations is doomed to failure in advance because it is absurd. “This argument examines the status of the reductivist thesis in its own terms and reduces it to absurdity …” ; “the attempt to reduce human purposive, or ‘intentional,‘ action to physiology and ultimately to physics and chemistry is an absurdity rather than simply a confusion”. I wish to show (...) that this argument is fallacious because it involves a petitio principii; and if Plato can be credited with introducing the same argument in the Theaetetus, as she suggests, so much the worse for Plato. (shrink)

In this paper I both summarise the recent volume "Taking Conspiracy Theories Seriously" (Rowman and Littlefield, 2018) and argue as to why we should investigate conspiracy theories rather than assume they are false or irrational by definition.

The difficulty of τєἠν at 8 is notorious, and it has never been answered. The word refers back to Apollo, who has been invoked in the first line, but ‘it is not in accord with epic convention that, after the invocation, reference should be made to it’. I suggest that we simply should not expect Apollonius to conform to the conventions of older epic: he does not do so in a number of other important respects. One is reminded here of (...) the nervous restlessness of Callimachean poetry, particularly Cer. 25. There the goddess is addressed out of the blue with τìν δ’ αύτᾳ, and emendation is unconvincing. Perhaps τєἠν in Apollonius is even more abrupt than the example in Callimachus. Yet Apollonius seems on many occasions to carry further the devices of his master. The astonishing parenthesis at 1. 623 f. is a good example, 52 f, F. Bornmann, Call. Hymnus in Dianam, 1–li). (shrink)

Vedic Voices: Intimate Narratives of a Living Andhra Tradition. By David M. Knipe. New York: Oxford University Press, 2015. Pp. xxii + 340, illus. $35.

Neither can stand. ‘Argos of the land’ is nonsense, and even if it were not, is absurd as an apostrophe of the River Inachus. ‘a plain’, indistinguishable from is similarly impossible: the audience would be baffled; in 6 has to be the first occurrence of the vox; ‘streams’ cannot be apposed to a ‘plain’, even if could have been understood as meaning this.

Adolescence is an important yet vulnerable period of transition from childhood to adulthood. An increasing number of studies support the traditional Catholic view, which sees teens as prone to making poor decisions when influ­enced by emotions or peer pressure but capable of thriving when guided by parents and religion. However, newer policies of medical societies undermine the traditional supports of family and faith with a permissive approach toward sexual exploration. To counter this unhealthy trend, which seems to be based more (...) on postmodern ideology than robust science, Catholic physicians should become experts in adolescent behavior and sexual health. Physicians should be sensitive to opposing viewpoints but participate only in treatments which are ethical and beneficial for their patients. Specifically, Catholic physicians must avoid contraceptives, abortion, and “gender-affirming” therapies. By using good science and emulating the models of service, Socratic dialogue, and accompaniment, physicians can guide adolescents toward a virtuous, healthy adulthood. (shrink)

The analysis of the situation in the Muslim environment shows that at present the process of forming a religious network in Ukraine has largely taken place. The vast majority of communities are under the jurisdiction of three spiritual centers - the Spiritual Administration of the Muslims of Crimea, the Spiritual Administration of the Muslims of Ukraine, the Spiritual Center of the Muslims of Ukraine. In addition, there are communities that do not belong to any of these three centers. From time (...) to time they try to unite. So, today, no spiritual center represents all Muslims of Ukraine and cannot formally and officially speak on their behalf. (shrink)

Formulation of the problem. The clock of antiquity "to our era" is full of values in the occurrence of the pre-Ukrainian religious culture. Therefore, there is a need to manifest the foundations of the Divine. Analysis of recent research and publications. Ukrainian religious scholars, while actualizing the national scientific heritage, see the continuation of their culture in the cultures of other peoples.The purpose of this publication is seen in the search for possible guidelines for determining the essence of the Divine (...) as a certain experiencing equilibrium in human condition. (shrink)

Let κ be a regular cardinal, and let B be a subalgebra of an interval algebra of size κ. The existence of a chain or an antichain of size κ in B is due to M. Rubin (see [7]). We show that if the density of B is countable, then the same conclusion holds without this assumption on κ. Next we also show that this is the best possible result by showing that it is consistent with 2 ℵ 0 = (...) ℵ ω 1 that there is a boolean algebra B of size ℵ ω 1 such that length(B) = ℵ ω 1 is not attained and the incomparability of B is less than ℵ ω 1 . Notice that B is a subalgebra of an interval algebra. For more on chains and antichains in boolean algebras see, e.g. [1] and [2]. (shrink)

Of articles which are submitted for publication in Philosophy, a surprisingly large proportion are about the views of Richard Rorty. Some, indeed, we have published. They, along with pretty well all the articles we receive on Professor Rorty, are highly critical. On the perverse assumption that there must be something to be said for anyone who attracts widespread hostility, it is only right to see what can be said in favour of Rorty's latest collection of papers, entitled, Truth and Progress,.

Name der Zeitschrift: Nietzsche-Studien Jahrgang: 42 Heft: 1 Seiten: 298-298.

Three classes of decidable discrete linear orders with varying degrees of effectiveness are investigated. We consider how a classical order type may lie in relation to these three classes, and we characterize by their order types elements of these classes that have effective nontrivial self-embeddings.