The core Oxford Calculators developed a science of kinematics in which the key concept was the "latitude of velocity." Based upon the concept of "latitude," the Calculators developed parts of a mathematical physics in deductive format that could be applied to quite various situations.

The ArgumentOur understanding of the predisposing factors, the nature, and the fate of the Oxford Calculatory tradition can be significantly increased by seeing it in its social and institutional context. For instance, the use of intricate imaginary cases in Calculatory works becomes more understandable if we see the connection of these works to undergraduate logical disputations. Likewise, the demise of the Calculatory tradition is better understood in the light of subsequent efforts at educational reform.Unfortunately, too little evidence remains about (...) the Calculators and their context to enable anything like a full reconstruction of the relation of the Oxford Calculators' work to its context. Nevertheless, seeking out and fitting together the bits of information that do remain can add to our insight. Among the topics worth further research are the relation of training incalculationesto later careers in church or government, and the special features of the Calculatory tradition as a tradition consisting of multiple parallel manifestations closely interconnected with other disciplines, ranging from logic and natural philosophy to theology and medicine. (shrink)

In his commentary on Lombardʼs Sentences, question 1, Robert Halifax OFM presents a remarkably original and inventive optical argument. It compares two pairs of luminous and opaque bodies with two shadow cones until the luminous bodies reach the zenith. In placing two moving human beings into the shadow cones whose moral evolution parallels the size of the shadows, Halifax creates an unprecedented shadow theater equipped with mathematics and theorems of motion from Thomas Bradwardineʼs Treatise on Proportions. This paper is a (...) first attempt at analyzing this imaginary experiment and the mathematics of the infinite it implies. It also shows that optics had new aims through its connexion with the theorems of motion of the Oxford Calculators. (shrink)

Blasius of Parma deals with intensification and remission of accidental forms, and the related concept of « latitude » in at least three texts : the Questiones de latitudinibus formarum, the Questio disputata de intensione et remissione formarum and Question 10 on Book V of the Physics. The paper is focussed on the two last. Blasius discusses theses about the ontological status of qualities and their relation to their subject of inherence through the issue of their intensification or weakening, at (...) the borderline of physics and metaphysics. In the same time, he takes sides for the calculating procedures that were on debate since the beginning of the 14th century. In binding the quality and its subject closely together, Blasius does not go as far as the Oxford Calculators in the mathematisation of intensive magnitudes. Nonetheless, he does attempt to integrate the new tools into his physics and his ontology. (shrink)

Chishtī Sufis in the Sultanate of Delhi 1190–1400: From Restrained Indifference to Calculated Defiance. By Tanvir Anjum. Karachi: Oxford Univ. Press, 2011. Pp. xviii + 433. $31.95.

The final chapter of the book is devoted to the question of the epistemological status of holistic pragmatism itself. White thinks of it as a thesis, a statement that may have been originally a very generalized description of the methods of science but has become normative. Yet, in its own spirit, that does not make i t immune to correction. Still, as already noted, one is disinclined to modify or reject this sort of statement. White points out, correctly, that our (...) resistance t o reject or modify it is analogous to the reluctance of 19 th century physicists t o reject or modify the law of the conservation of energy. That law was “pinned down” but became later “unpinned”; the same may happen to holistic pragmatism. Here again, as so many times in this little book, one wants to thank its author for raising questions. Indeed the book as a whole is a challenge, a challenge to do philosophy (of culture), to fulfill its ambition. (shrink)

We agree with Archer that human sex differences in aggression are well explained by sexual selection, but note that explanations of human behaviors are not logically mutually exclusive from explanations and therefore should not be framed as such. We discuss why this type of framing hinders the development of both social learning and evolutionary theories of human behavior.

A volume in Transforming Education for the Future Spirituality and spiritual experiences have been the bedrock of every civilization and together form one of the highest mechanisms for making sense of the world for billions of people. Current research paradigms, due to their limitation to empirical, sensory, psychologically, or culturally constructed realities, fail to provide a framework for exploring this essential area of human experience. The development of a spiritual research paradigm will provide researchers from the social sciences and education (...) the tools and abilities to systematically explore fundamental questions regarding human spiritual experiences and spiritual growth. A spiritual research paradigm requires an ontology that considers all reality to be multidimensional, interconnected, and interdependent. It requires an epistemology that integrates knowing from outer sources as well as inner contemplation, acknowledging our integration of soul and spirit with the body and mind. Three additional aspects are useful to a spiritual research paradigm: axiology, methodology, and teleology. An axiology concerns what is valued, good, and ethical. A methodology is the appropriate approach to systematic inquiry. A fifth and less frequently mentioned aspect is teleology, an explanation of the goal or end (telos) to which new knowledge is applied, such as gaining wisdom and truth, touching the divine, increasing inner peace, exploring hidden dimensions, or improving society. This book takes the first step to develop such a research paradigm. We draw from world spiritual traditions as well as scholarship that has arisen from contemplative practices. We also attempt to build a bridge between science and spirituality. Spiritual research is not necessarily opposed to scientific research; in fact, each can shed light on the other. (shrink)

The Oxford Calculator Roger Swyneshed put forward three provocative claims in his treatise on insolubles, written in the early 1330s, of which the second states that there is a formally valid inference with true premises and false conclusion. His example deployed the Liar paradox as the conclusion of the inference: ‘The conclusion of this inference is false, so this conclusion is false’. His account of insolubles supported his claim that the conclusion is false, and so the premise, referring to (...) the conclusion, would seem to be true. But what is his account of validity that can allow true premises to lead to a false conclusion? This article considers Roger’s own account, as well as that of Paul of Venice, writing some sixty years later, whose account of the truth and falsehood of insolubles followed Roger’s closely. Paul endorsed Roger’s three claims. But their accounts of validity were different. The question is whether these accounts are coherent and support Paul’s claim in his Logica Magna that he endorsed all the normal rules of inference. (shrink)

This article responds to a critical research challenge in Medieval philosophy scholarship regarding the internal periodisation of the register. By arguing the case for ‘post-scholasticism’ as an internal period indicator (1349–1464, the era between the deaths of William of Ockham and Nicholas of Cusa), defined as ‘the transformation of high scholasticism on the basis of a selective departure thereof’, the article specifies a predisposition in the majority of introductions to and commentaries in Medieval philosophy to proceed straight from 1349 to (...) 1464, understating 115 years of pertinent Medieval philosophical discourse. It is argued that in the modern account of Medieval philosophy, this understatement is manifested in either a predating of Renaissance philosophy to close the gap between 1349 and 1464 as far as possible or in proceeding straight from 1349 to Renaissance philosophy. The article presents five unique philosophical themes from this delicate period, indicating that ‘post-scholasticism’ was indeed a productive period in late Medieval philosophy, which should not be bypassed as an inconsequential entrance to Renaissance philosophy. The period 1349–1464 should accordingly be appreciated for its idiosyncratic contributions to the history of ideas in the late-14th and early-15th centuries, with reference to the political intensification of the via moderna, the pivotal separation of philosophy and theology and the resulting independence of the natural sciences, in res critique of institutions, transforming pragmatics and the rise of philosophical materialism. Contribution: This article contributes to methodological development in Medieval philosophy by responding to a critical research challenge regarding the internal periodisation of the later Middle Ages. Arguing the case for ‘post-scholasticism’ as an internal period indicator (1349 to 1464 in Medieval philosophy, the article presents unique philosophical themes from the period, indicating that it was a productive stage in late Medieval philosophy which should not be bypassed as an inconsequential entrance to Renaissance philosophy. (shrink)

In the history of medieval semantics, supposition theory is important especially in the twelfth and thirteenth centuries. In this theory the emphasis is on the term, whose properties one tries to determine. In the fourteenth century the focus is on the proposition, of which a term having supposition is a part. The idea is to analyse propositions in order to determine their truth (probare). The Speculum puerorum written by Richard Billingham was the standard textbook for this approach. It was very (...) influential in Europe. The theory of the probatio propositionis was meant to solve problems both in (empirically oriented) scientific propositions such as used by the Oxford Calculators, and theological propositions, especially those about the Trinity. The book is original, concise, but not clear in every respect. Studying medieval commentaries may help us to understand Richard's book. In the present paper three commentaries are presented. The commentators discussed problems about the status of Richard's book, and about its doctrine: what is the relation between probatio and truth, what is the relation between probatio and supposition, what exactly are mediate and immediate terms (e.g.is the pronoun 'this' mediate or immediate?). The commentators sometimes criticize Richard. For example, one of them argues, against Billingham, that the verb 'can' ampliates its subject term and is therefore mediate. (shrink)