We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a nonperturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the nonrelativistic limit to the nonrelativistic Faddeev equations. The aim of this (...) program is to develop equations which explicitly depend upon physically observable input variables, and do not require “renormalization” or “dressing” of these parameters to connect them to the boundary states. As a unitary, cluster decomposible, multichannel theory, physical systems whose constituents are confined can be readily described. (shrink)

Generic self-gravitating quantum solutions that are not critically dependent on the specifics of microscopic interactions are presented. The solutions incorporate curvature effects, are consistent with the universality of gravity, and have appropriate correspondence with Newtonian gravitation. The results are consistent with known experimental results that indicate the maintenance of the quantum coherence of gravitating systems, as expected through the equivalence principle.

We here use our nonperturbative, cluster decomposable relativistic scattering formalism to calculate photon–spinor scattering, including the related particle–antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it a unitary two-particle amplitude for quantum–particle scattering. We verify that we have done this correctly by showing that our calculated photon–spinor amplitude reduces in the (...) weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models. (shrink)

The canonical proper time formulation of relativistic dynamics provides a framework from which one can describe the dynamics of classical and quantum systems using the clock of those very systems. The framework utilizes a canonical transformation on the time variable that is used to describe the dynamics, and does not transform other dynamical variables such as momenta or positions. This means that the time scales of the dynamics are described in terms of the natural local time coordinates, which is the (...) most meaningful parameterization of phenomena such as the approach to equilibrium, or the back reaction of interacting systems. We summarize the formalism of the canonical proper time framework, and provide example calculations of the eigenvalues of the hydrogen atom and near horizon description of a scalar field near a Schwarzschild black hole. (shrink)

Starting from a unitary, Lorentz invariant two-particle scattering amplitude, we show how to use an identification and replacement process to construct a unique, unitary particle–antiparticle amplitude. This process differs from conventional on-shell Mandelstam s, t, u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel non-perturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations (...) recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle–antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the non-relativistic Coulomb problem, including the forward scattering singularity, the essential singularity in the phase, and the Bohr bound-state spectrum. (shrink)

A naive introduction of a dependency of the mass of a black hole on the Schwarzschild time coordinate results in singular behavior of curvature invariants at the horizon, violating expectations from complementarity. If instead a temporal dependence is introduced in terms of a coordinate akin to the river time representation, the Ricci scalar is nowhere singular away from the origin. It is found that for a shrinking mass scale due to evaporation, the null radial geodesics that generate the horizon are (...) slightly displaced from the coordinate singularity. In addition, a changing horizon scale significantly alters the form of the coordinate singularity in diagonal (orthogonal) metric coordinates representing the space-time. A Penrose diagram describing the growth and evaporation of an example black hole is constructed to examine the evolution of the coordinate singularity. (shrink)

Original and penetrating, this book investigates of the notion of inference from signs, which played a central role in ancient philosophical and scientific method. It examines an important chapter in ancient epistemology: the debates about the nature of evidence and of the inferences based on it--or signs and sign-inferences as they were called in antiquity. As the first comprehensive treatment of this topic, it fills an important gap in the histories of science and philosophy.

In this work a calculation of the cluster decomposable formalism for relativistic scattering as developed by Lindesay, Markevich, Noyes, and Pastrana (LMNP) is made for an ultra-light quantum model. After highlighting areas of the theory vital for calculation, a description is made of the process to go from the general theory to an eigen-integral equation for bound state problems, and calculability is demonstrated. An ultra-light quantum exchange model is then developed to examine calculability.

The rejection of a “characterless” moral self is central to some of Bernard Williams’ most important contributions to philosophy. By the time of Truth and Truthfulness, he works instead with a model of the self constituted and stabilized out of more primitive materials through deliberation and in concert with others that takes inspiration from Diderot. Although this view of the self raises some difficult questions, it serves as a useful starting point for thinking about the process of developing an authentic (...) moral point of view in the context of contemporary living. In what follows, I begin to fill out and extend this picture of the self and its related notion of authenticity by exploring some of the “technologies of the self” at play in Rachel Cusk’s recent work (primarily, the Outline trilogy, Coventry, Second Place, and “The Stuntman”) that ask us to rethink the possibility and importance of stability; seek a way of constituting oneself and one’s values outside the confining structures of traditional narrative (focusing instead on a framework that might be provided by the visual arts); and give a different role to the sort of internalized other Williams sees as being at work in the mechanisms of shame. (shrink)

Additional theorizing about mathematical practice is needed in order to ground appeals to truly useful notions of the virtues in mathematics. This paper aims to contribute to this theorizing, first, by characterizing mathematical practice as being epistemic and “objectual” in the sense of Knorr Cetina The practice turn in contemporary theory, Routledge, London, 2001). Then, it elaborates a MacIntyrean framework for extracting conceptions of the virtues related to mathematical practice so understood. Finally, it makes the case that Wittgenstein’s methodology for (...) examining mathematics and its practice is the most appropriate one to use for the actual investigation of mathematical practice within this MacIntyrean framework. At each stage of thinking through mathematical practice by these means, places where new virtue-theoretic questions are opened up for investigation are noted and briefly explored. (shrink)

No other volume has this scope. Students in bioethics, public and international health, and ethics will find this book particularly useful.

In this book, distinguished theologian and political scientist James V. Schall explores Maritain's political philosophy, demonstrating that Maritain understood society, state, and government in the tradition of Aristotle and Aquinas, of natural law and human rights and duties. Schall pays particular attention to the ways in which evil appears in political forms, and how this evil can be dealt with morally.

In 1973, Rittel and Webber coined the term ‘wicked problems’, which they viewed as pervasive in the context of social and policy planning.1 Wicked problems have 10 defining characteristics: they are not amenable to definitive formulation; it is not obvious when they have been solved; solutions are not true or false, but good or bad; there is no immediate, or ultimate, test of a solution; every implemented solution is consequential, it leaves traces that cannot be undone; there are no criteria (...) to prove that all potential solutions have been identified and considered; every wicked problem is essentially unique; every wicked problem can be considered to be a symptom of another problem; a wicked problem can be explained in numerous ways and the choice of explanation determines what will count as a solution and the actors are liable for the consequences of the actions they generate.1 One needs only a passing familiarity with the history of HIV prevention research, and with the intellectual traditions of research ethics, to appreciate that the perils and opportunities arising from proposals to conduct research with people who inject drugs in some of the most precarious social and political circumstances around the world and the challenges associated with implementing the findings satisfy Rittel's and Webber's criteria for ‘wicked problems’. HIV prevention research has contributed important new knowledge about the feasibility, efficacy or relative efficacy of various prevention strategies in a variety of contexts around the world. But the pathways and timelines for how this knowledge has contributed to improvements in public health practice and/or the establishment of policies that ensure unfettered access to appropriate healthcare services for PWID are less clear and decidedly non-linear. One account of the transition from trial to policy …. (shrink)

In 1973, Rittel and Webber coined the term ‘wicked problems’, which they viewed as pervasive in the context of social and policy planning. 1 Wicked problems have 10 defining characteristics: they are not amenable to definitive formulation; it is not obvious when they have been solved; solutions are not true or false, but good or bad; there is no immediate, or ultimate, test of a solution; every implemented solution is consequential, it leaves traces that cannot be undone; there are no (...) criteria to prove that all potential solutions have been identified and considered; every wicked problem is essentially unique; every wicked problem can be considered to be a symptom of another problem; a wicked problem can be explained in numerous ways and the choice of explanation determines what will count as a solution and the actors are liable... (shrink)

Face perception plays a central role in social communication and is, arguably, one of the most sophisticated visual perceptual skills in humans. The organization of neural systems for face perception has stimulated intense debate. This article presents an updated model of distributed human neural systems for face perception. It opens up with a discussion of the Core System for visual analysis of faces with an emphasis on the distinction between perception of invariant features for identity recognition and changeable features for (...) recognition of facial gestures such as expression and eye gaze. The study analyses the roles of systems for the representation of emotion, for person knowledge, and for action understanding in face recognition and perception of expression and gaze. It presents systems that are of particular relevance for social communication and that are illustrative of how distributed systems are engaged by face perception. It concludes with a discussion of modularity and distributed processing in neural representation. (shrink)

Friendship is prominently mentioned, to be sure, in the great books, including very often the great books in political philosophy. In addition to Aristotle, whose treatise on friendship remains unsurpassed as a philosophic examination of this exalted topic, we recall Cicero's great essay De Amicitia, Plato's Phaedrus, plus numerous references in The Republic, The Laws, The Symposium, and many other central dialogues. The Gospel of John contains the great tractate on friendship at the Last Supper just before the Trial of (...) Christ, an intellectual association between politics and friendship that is itself cause of the deepest human reflection. The topic of friendship is most familiar to Augustine and Aquinas and later to Montaigne and Francis Bacon. In short, if we moderns and post-moderns might perhaps have difficulty in associating the notions of friendship and political philosophy, our intellectual tradition did not. (shrink)

The Latin word "Docilitas" in the title of this book means the willingness and capacity we have of being able to learn something we did not know. It has not the same connotation as "learning," which is what happens to us when we are taught something. Docility also means our recognition that we do not know many things, that we need the help of others, wiser than we are, to learn most of what we know, though we can discover a (...) few things by or own experience. This book contains some sixteen chapters, each of which was given to an audience in some college or university setting. They consider what it is to teach, what to read, reading places, libraries, and class rooms. They look upon the duties of a teacher or professor as mostly a delight, because the truth should delight us. In Another Sort of Learning, the subject of what a student "owes" his teacher came up. Here, we look at the other side of the question, what does a teacher or professor "do"? But a professor cannot teach unless there is someone willing to be taught, someone willing to recognize that he needs guidance and help. Yet, the end of teaching is not just the "transfer" of what is in the mind of the professor to the mind of the student. It is when both, student and teacher, behold, reflect on, and see the same truth of things that are. This common "seeing" is the read adventure in which student and teacher share something neither "owns." Knowledge and truth are free, but each requires our different insights and approaches so that we can finally realize what "teaching" and "being taught" mean to us. (shrink)

Far from being unwelcome or impossible in a mathematical setting, indeterminacy in various forms can be seen as playing an important role in driving mathematical research forward by providing “sources of newness” in the sense of Hutter and Farías :434–449, 2017). I argue here that mathematical coincidences, phenomena recently under discussion in the philosophy of mathematics, are usefully seen as inducers of indeterminacy and as put to work in guiding mathematical research. I suggest that to call a pair of mathematical (...) facts a coincidence is roughly to suggest that the investigation of connections between these facts isn’t worthwhile. To say of this pair, “That’s no coincidence!” is to suggest just the opposite. I further argue that this perspective on mathematical coincidence, which pays special attention to what mathematical coincidences do, may provide us with a better view of what mathematical coincidences are than extant accounts. I close by reflecting on how understanding mathematical coincidences as generating indeterminacy accords with a conception of mathematical research as ultimately aiming to reduce indeterminacy and complexity to triviality as proposed in Rota Indiscrete thoughts, Birkhäuser, 1997). (shrink)

Annalisa Coliva (Int J Study Skept 10(3–4):346–366, 2020) asks, “Are there mathematical hinges?” I argue here, against Coliva’s own conclusion, that there are. I further claim that this affirmative answer allows a case to be made for taking the concept of a hinge to be a useful and general-purpose tool for studying mathematical practice in its real complexity. Seeing how Wittgenstein can, and why he would, countenance mathematical hinges additionally gives us a deeper understanding of some of his latest thoughts (...) on mathematics. For example, a view of how mathematical hinges relate to Wittgenstein’s well-known river-bed analogy enables us to see how his way of thinking about mathematics can account nicely for a “dynamics of change” within mathematical research—something his philosophy of mathematics has been accused of missing (e.g., by Robert Ackermann (Wittgenstein’s city, The University of Massachusetts Press, Amherst, 1988) and Mark Wilson (Wandering significance: an essay on conceptual behavior, Oxford University Press, Oxford, 2006). Finally, the perspective on mathematical hinges ultimately arrived at will be seen to provide us with illuminating examples of how our conceptual choices and theories can be ungrounded but nevertheless the right ones (in a sense to be explained). (shrink)

James V. Schall presents, in a convincing and articulate manner, the revelational contribution to political philosophy, particularly that which comes out of the Roman Catholic tradition.

An episode of social conflict between Russian and Estonian "mnemonic communities" is used as a framework for exploring issues of collective memory. In order to understand the strong Russian reaction to the Estonian decision to move a memorial statue, it is argued that the notion of "deep memory" is needed, a notion that is, in turn, grounded in the construct of a "narrative template." The particular narrative template examined is the Russian "Expulsion of Foreign Enemies" plot line. The call for (...) recognizing a distinction between abstract narrative templates, on the one hand, and "specific narratives," on the other is viewed as applying to a wide range of cases where mnemonic communities seem to exist in implacable opposition. In such cases deep memory and the narrative templates around which it is organized are set forth as strong underlying conservative forces that resist change in collective memory at a deep level. It is suggested that debates grounded in formal history may help overcome this resistance to change but that such efforts will be limited as long as the forces of deep collective memory are not recognized. (shrink)

L-shaped distributions are not rare and are probably far more prevalent than is generally realized. They are highly conducive to nonrobustness of normality-assuming statistical tests, and they strongly resist transformation to normality. The thinner the tail of the distribution, the more unlikely it is that its L-shapedness will be detected by inspecting a sample drawn from it. Yet, as the tail of an L-shaped distribution becomes increasingly shallow, its skewness and kurtosis depart increasingly from their “normal-distribution” values, and the distribution (...) becomes increasingly conducive to drastic nonrobustness. Worse, a fairly common type of experimental situation in psychological research produces shallow-tailed L-shaped distributions. (shrink)

I.One of the most instructive passages I have ever read is found in C. S. Lewis' The Abolition of Man, about the textbook writers and the waterfalls. The story goes that the English poet Coleridge records the reaction of two ordinary tourists on first seeing a particularly lovely waterfall. One of these tourists called it “pretty,” while the other called it “sublime.” Coleridge, of course, thought the tourist calling it “sublime” was correct, while the one calling it merely “pretty” was (...) lacking in some perception or appreciation of the reality before him. There was a note of “culpability” in…. (shrink)

v. 1. Thucydides through Machiavelli.--v. 2. Machiavelli through Marx.--v. 3. Marx through Marcuse.

A Georgetown professor’s look at the subjects one needs to study for a truly well-rounded education. A Student’s Guide to Liberal Learning is an inviting conversation with a learned scholar about the content of an authentic liberal arts education. It surveys ideas and books central to the tradition of humanistic education that has fundamentally shaped our country and our civilization. This accessible volume argues for an order and integration of knowledge so that meaning might be restored to the haphazard approach (...) to study currently dominating higher education. Freshly conveying the excitement of learning from the acknowledged masters of intellectual life, this guide is also an excellent blueprint for building one’s own library of books that matter. (shrink)

Noting the widespread concern about the quality of education in our schools, Schall examines what is taught and read (and not read) in these schools. He questions the fundamental premises in our culture which do not allow truth to be considered. Schall lists various important books to read, and why.