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)

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)

The Politics of Heaven and Hell makes an invaluable contribution to the understanding of classical, medieval, and modern political philosophy, while explaining the profound problem with modernity. Christianity 'freed men from the overwhelming burden of ever thinking that their salvation will ultimately come from the political order', writes Fr. James Schall, S.J. Modernity, on the other hand, is a perversion of Christianity, which tries to achieve man's salvation in this world. It does this by politicizing everything, which results in (...) the absolute state: 'The distance from the City of God to the Leviathan is not at all far once the City of God is relocated on earth.' The best defense against this tyranny is 'the adequate description of the highest things, of what is beyond politics'"--Inside jacket. (shrink)

A collection of essays on political philosophy, ancient philosophy, and Catholic theology, including a handful of book reviews and a short "autobiographical memoir," by a Catholic priest who taught politics at Georgetown University for decades. The book was planned and prepared by the author prior to his death but published posthumously.

A collection of Fr. James Schall's recent essays, Political Philosophy and Revelation offers a learned, erudite, and coherent statement on the relationship between reason and revelation in the modern world. It addresses political philosophy in the context of an awareness of other humane and practical sciences, including history, literature, economics, theology, ethics and metaphysics.

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.

What is real and what is noble, as well as what is deranged and wrong, can often be stated briefly. Nietzsche was famous for his succinct aphorisms and epigrams. Aquinas in one of his responses could manage to state clearly what he held to be true. Ultimately, all of our thought needs to be so refined and concentrated that we can see the point. So these are "brief" essays and they are largely of a philosophical "hue." They touch on things (...) worth thinking about. Indeed, often they consider things we really need to think about if our lives are to make sense. The advantage of a collection of essays is that it is free to talk about many things. It can speak of them in a learned way or in an amused and humorous way. As Chesterton said, there is no necessary conflict between what is true and what is funny. Oftentimes, the greatest things we learn are through laughter, even laughter at ourselves and our own foibles and faults. So these essays are "brief." And they are largely of philosophical import. At first sight, taxing beer may seem to have no serious principle, except perhaps for the brewer and the consumer. But wherever there is reality, we can find something to learn. Each of these essays begins with the proposition "on"--this is a classical form of essay in the English language. Belloc, one the essay's greatest masters, wrote a book simply entitled "ON"--and several other books with that introductory "ON" to begin it. The word has the advantage of focusing our attention on some idea, place, book, person, or reality that we happen to come across and notice, then notice again, then wonder about. (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)

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)

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

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)

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)

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)

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.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (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)

When William James spoke about belief to the philosophy clubs of Yale and Brown in 1896, he forewarned his audience of the nature of his comments by describing them as a “sermon on justification by faith” (James 13), titling the talk “The Will to Believe.” Although there is disagreement about the substance of James’s remarks, it is fairly innocuous to assert that James thought they were appropriate because of the prevalence of the “logical spirit” of many (...) of those who practiced academic philosophy that led them to the conclusion that religious faith was untenable. Aware of his audience, James presents his view on the permissibility of religious faith on the terms and grounds familiar to professional philosophers. .. (shrink)