In this book, which is both a philosophical and historiographical study, the author investigates the fallibility and the rationality of mathematics by means of rational reconstructions of developments in mathematics. The initial chapters are devoted to a critical discussion of Lakatos' philosophy of mathematics. In the remaining chapters several episodes in the history of mathematics are discussed, such as the appearance of deduction in Greek mathematics and the transition from Eighteenth-Century to Nineteenth-Century analysis. The author aims at developing a notion (...) of mathematical rationality that agrees with the historical facts. A modified version of Lakatos' methodology is proposed. The resulting constructions show that mathematical knowledge is fallible, but that its fallibility is remarkably weak. (shrink)

Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable? The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to (...) be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history. (Elsevier). (shrink)

Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable? The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to (...) be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history. (Elsevier). (shrink)

In the paper below the authors describe three super-tasks. They show that although the abstract notion of a super-task may be, as Benacerraf suggested, a conceptual mismatch, the completion of the three super-tasks involved can be defined rather naturally, without leading to inconsistency, by means of a particular kinematical interpretation combined with a principle of continuity.

In an earlier paper the authors discussed some super-tasks by means of a kinematical interpretation. In the present paper we show a semi-formal way that a more abstract treatment is possible. The core idea of our approach is simple: if a super-task can be considered as a union of (finite) tasks, it is natural to define the effect of the super-task as the union of the effects of the finite tasks it consists of. We show that this approach enables us (...) to handle two of the three super-tasks that we discussed earlier. We also argue that recent objections against our original kinematical interpretation do not hold water. One of our arguments is based on the construction of an elegant correspondence between the first of those three super-tasks and Zeno's Achilles and the Tortois. (shrink)

A confluence of scholarly interest has resulted in a revival of Thomistic scholarship across the world. Several areas in the investigation of St. Thomas Aquinas, however, remain under-explored. This volume contributes to two of these neglected areas. First, the volume evaluates the contemporary relevance of St. Thomas's views for the philosophy and practice of education. The second area explored involves the intersections of the Angelic Doctor’s thought and the numerous cultures and intellectual traditions of the East. Contributors to this section (...) examine the reception, creative appropriation, and various points of convergence between St. Thomas and the East. (shrink)

Ivor Grattan-Guinness, Routes of Learning: Highways, Pathways and Byways in the History of Mathematics. Baltimore: The John Hopkins University Press, 2009. xii + 372 pp. $75.00. ISBN 10:978-0-8018-...

In the present paper the roots of the Art of the Catalan philosopher Ramon Llull are examined. Moreover the impact of the Art on seventeenth mathematics is briefly discussed.

This article contains an outline of the development of the classic wind mill with some additional attention to developments in the Netherlands.

Some philosophers have thought that life could only be meaningful if there is no God. For Sartre and Nagel, for example, a God of the traditional classical theistic sort would constrain our powers of self-creative autonomy in ways that would severely detract from the meaning of our lives, possibly even evacuate our lives of all meaning. Some philosophers, by contrast, have thought that life could only be meaningful if there is a God. God and the Meanings of Life is interested (...) in exploring the truth in both these schools of thought, seeking to discover what God could and couldn't do to make life meaningful (as well as what he would and wouldn't do). Mawson espouses a version of the 'amalgam' or 'pluralism' thesis about the issue of life's meaning – in essence, that there are a number of different legitimate meanings of 'meaning' (and indeed 'life') in the question of life's meaning. According to Mawson, God, were he to exist, would help make life meaningful in some of these senses and hinder in some others. He argues that whilst there could be meaning in a Godless universe, there could be other sorts of meaning in a Godly one and that these would be deeper. (shrink)

T. A. Cavanaugh's Hippocrates' Oath and Asclepius' Snake: The Birth of the Medical Profession articulates the Oath as establishing the medical profession's unique internal medical ethic - in its most basic and least controvertible form, this ethic mandates that physicians help and not harm the sick. Relying on Greek myth, drama, and medical experience (e.g., homeopathy), the book shows how this medical ethic arose from reflection on the most vexing medical-ethical problem -- injury caused by a physician -- and argues (...) that deliberate iatrogenic harm, especially the harm of a doctor choosing to kill (physician assisted suicide, euthanasia, abortion, and involvement in capital punishment), amounts to an abandonment of medicine as an exclusively therapeutic profession. The book argues that medicine as a profession necessarily involves stating before others what one stands for: the good one seeks and the bad one seeks to avoid on behalf of the sick, and rejects the view that medicine is purely a technique lacking its own unique internal ethic. It concludes noting that medical promising (as found in the White Coat Ceremony through which U. S. medical students matriculate) implicates medical autonomy which in turn merits respect, including honoring professional conscientious objections. (shrink)

How do we think about animals? How do we decide what they deserve and how we ought to treat them? Subhuman takes an interdisciplinary approach to these questions, drawing from research in philosophy, neuroscience, psychology, law, history, sociology, economics, and anthropology. Subhuman argues that our attitudes to nonhuman animals, both positive and negative, largely arise from our need to compare ourselves to them.

Kit Fine (2000) breaks with tradition, arguing that, pace Russell (e.g., 1903: 228), relations have neither directions nor converses. He considers two ways to conceive of these new "neutral" relations, positionalism and anti-positionalism, and argues that the latter should be preferred to the former. Cody Gilmore (2013) argues for a generalization of positionalism, slot theory, the view that a property or relation is n-adic if and only if there are exactly n slots in it, and (very roughly) that each slot (...) may be occupied by at most one entity. Slot theory (and with it, positionalism) bears the full brunt of Fine's (2000) symmetric completions and conflicting adicities problems. I fully develop an alternative, plural slot theory (or pocket theory), which avoids these problems, key elements of which are first considered by Yi (1999: 168 ff.). Like the slot theorist, the pocket theorist posits entities (pockets) in properties and relations that can be occupied. But unlike the slot theorist, the pocket theorist denies that at most one entity can occupy any one of them. As a result, she must also deny that the adicity of a property or relation is equal to the number of occupiable entities in it. By abandoning these theses, however, the pocket theorist is able to avoid Fine's problems, resulting in a stronger theory about the internal structure of properties and relations. Pocket theory also avoids a serious drawback of anti-positionalism. (shrink)

Exegesis, with text, on the Nyāyasūtra of Gautama, basic aphoristic text of Nyāya.

_Purpose._ This paper aims to investigate the phenomenon of a human being within the Confucian tradition as well as its interpretations from intercultural perspective. _Theoretical basis._ One of the ways to understand the deepest level of the intercultural dialogue is to reveal the interpretations of a human being in philosophical traditions, since they refer to the formation of personality and identity within a given culture including interpersonal, intergroup, and intercultural relations. Humanism based on the unity of Human and Heaven runs (...) like a red thread through the philosophical teachings of Confucius, Mencius, Xunzi, Zhu Xi, Wang Yangming defining the ideas of human nature, his/her duties, his/her place and roles in society that shaped the Chinese mentality. _Originality._ Quite often, Chinese concepts (for example, human dignity beyond the ideas of democracy and mass political participation, guanxi, mianzi) are incomprehensible to the representatives of the Western civilization, which leads to the challenges in intercultural communication. The interpretation of these ideas in the context of Confucianism allows to understand them from the perspective of Others and expand the set of patterns of cultural perception. This ultimately leads to the awareness that there are many social, political, cultural realities, which we perceive through the lens of our own concepts and attitudes. The participants of an intercultural dialogue realize that each of them has a unique experience, own way of posing a problem and resolving it, and no one is better or worse. _Conclusions._ Confucian philosophy shaped the worldview of Chinese people, defined values, goals, meanings, attitudes, communication models, which affected all spheres of Chinese life and culture. The study of the philosophical heritage of the great Chinese civilization enhances the cultural competence of the intercultural communicators and expands the field of dialogue to the level of global communication. (shrink)

Commentary on Hetvābhāsasāmānyanirukti, portion of Tattvacintāmaṇi of Gaṅgeśa, dealing with the definition of fallacies middle term in Navya Nyāya philosophy.

This robust, clear, and well-researched textbook for classes in logic introduces students to both formal logic and to the virtues of intellectual inquiry. Part 1 challenges students to develop the analytical skills of deductive and inductive reasoning, showing them how to identify and evaluate arguments. Part 2 helps students develop the intellectual virtues of the wise inquirer. The book includes helpful pedagogical features such as practice exercises and a concluding summary with definitions of key concepts for each chapter. Resources for (...) professors and students are available through Baker Academic's Textbook eSources. (shrink)