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Following Jacques Hadamard, applied mathematicians typically investigate their models in the form of well-set problems, which actually consist of a family of applicational circumstances that vary in specific ways with respect to their initial and boundary values. The chief motive for investigating models in this wider manner is to avoid the improper behavioral conclusions one might reach from the consideration of a more restricted range of cases. Suitable specifications of the required initial and boundary variability typically appeal to (...) previously established experimental conclusions as to how the target system will behave under a range of eternally applied manipulations of the form “If the conditions pertaining to S were altered in manner M, internal features X would/would not alter”. In his investigations of causal reasoning within other parts of science, our first author has emphasized the conceptual importance of counterfactuals of this nature, for which he was been often criticized by authors of a self-styled “metaphysical” inclination. The purpose of this note is to argue, pace these objections, that closely analogous considerations have long been part of the practice of investigating differential equation models in a sensible way. (shrink)

Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Le;vi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases (...) for the existence of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in computers and cognitive science, his book, originally titled The Psychology of Invention in the Mathematical Field , remains an important tool for exploring the increasingly complex problem of mental life. The roots of creativity for Hadamard lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness. His discussion of this process comprises a wide range of topics, including the use of mental images or symbols, visualized or auditory words, "meaningless" words, logic, and intuition. Among the important documents collected is a letter from Albert Einstein analyzing his own mechanism of thought. (shrink)

Over the course of an illustrious career, the late Bernard Diamond established himself as the preeminent forensic psychiatrist of the century. _The Psychiatrist in the Courtroom_ brings together in a single volume Diamond's pivotal contributions to a variety of important issues, including the nature of diminished capacity, the fallacy of the impartial expert, the predictability of dangerousness, and the unacceptability of hypnotically facilitated memory in courtroom proceedings. Ably introduced and edited by Jacques M. Quen, M.D., a close colleague of (...) Diamond's and leading historian of forensic psychiatry, these writings enable experts and neophytes alike to track Diamond's evolving positions while clarifying where current legal and psychiatric opinion converge -- and diverge -- on a host of critical topics. For the forensic specialist, _The Psychiatrist in the Courtroom_ is not only an invaluable reference work but a compassionate reminder of the clinician's obligation to protect patients in legal proceedings. And in an age when clinicians are increasingly called into court, the book will be no less valuable to psychoanalysts and other mental health professionals eager for an introduction to the intricacies of judicial reasoning. Then, too, owing to Diamond's clinical acumen, the book is a compelling human document. With great erudition and deep compassion, Diamond tackles these and other knotty questions, always with an eye to clarifying the legal and clinical implications of the answers. By combining superb clinical gifts with an incisive understanding of legal principle, Diamond produced a seminal corpus whose relevance to discussions of therapeutic ethics and to legal debates will continue well into the next century. (shrink)

_Distinguer pour unir, ou Les degrés du savoir_ was first published in 1932 by Jacques Maritain. In this new translation of _The Degrees of Knowledge_, Ralph McInerny attempts a more careful expression of Maritain's original masterpiece than previous translations. Maritain proposes a hierarchy of the forms of knowledge by discussing the degrees of rational and suprarational understanding. Nine appendices, some longer than the chapters of the book, advance Maritain's thought, often by taking on criticism of earlier editions of the (...) work. Rightly called Maritain's cardinal work, _The Degrees of Knowledge_ is a magnificent and sagacious achievement. Jacques Maritain's masterpiece proposes a hierarchy of forms of knowledge that culminate in mystical experience and wisdom, which is a gift of the Holy Ghost. Maritain argues that the intellectual life is meant to be complemented by the spiritual life and should culminate in sanctity. (shrink)

We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)

. Fresh evidence from Free Choice Items (FCIs) in French question the current perception of the class. The role of some standard distinctions found in the literature is weakened or put in a new perspective. The distinction between universal and existential is no longer an intrinsic property of FCIs. Similarly, the opposition between variation-based vs intension-based analyses is relativized. We show that the regime of free choiceness can be characterized by an abstract constraint, that we call Non-Individuation (NI), and which (...) can be satisfied in different ways that match current distinctions. NI says that the information conveyed by a sentence containing a FCI should not be reducible to a referential situation, that is a situation in which particular individuals satisfy the sentence in the current world. The widely used resource of modal variation becomes a particular scenario of free-choiceness, not its essence. In fact, we show that under certain conditions, FCIs can occur in episodic, non-modal sentences, a fact that NI can accommodate. We also discuss more fine-grained aspects of the semantics of FCIs, such as their emotional colour. (. . .) the tripod fell spontaneously, because, though it stood on its feet so as to serve for a seat, it did not fall so as to serve for a seat. Aristotle, Physics II,6. (shrink)

v. 1. Half brain fables and figs in paradise -- v. 2. The corpus and the cortex -- v. 3. Scorpions and the anatomy of time.

This two-volume work examines far-reaching debates on the concept of courage from Greek antiquity to the Christian and mediaeval periods, as well as the modern era. Volume 1 explains how competing accounts of epistêmê, rational wisdom, and truth dominated classical antiquity. Early Christian and mediaeval thinkers, in contrast, favoured fortitude founded on faith and fear of God over philosophical reasoning left to its own devices. Volume 2 turns to theories of courage from the early modern period to the present. It (...) shows how the twin laws of polis and physis are at the heart of post-medieval thought. Courage is found at the crossroads of love and dread, freedom and fate, happiness and suffering, as well as power and submission to the ruling order. The later influence of evolutionism, existentialism, and the social and natural sciences on moral philosophy is also addressed at some length. The protection of people's best interests, the passions and powers of the human will, and the rule of active energy in all aspects of life supplant courage formerly viewed through the lens of reason or faith, or a combination of the two. These new ideas, paradoxically, herald the end of the ethics of courage. They also undermine the courage of ethical thinking. Courage is no longer an end in itself, nor is it a means to happiness "at the end." Regardless of what Gandhi, Tillich, and Foucault have to say about the topic, late modernity and the global age witness a marked loss of interest in courage as an idea worthy of conceptual investigation. Debates about the moral implications of courage give way to the value-free science of resilience, which studies how people can recover from past trauma and find wellness, primarily in the realm of physis. (shrink)

This two-volume work examines far-reaching debates on the concept of courage from Greek antiquity to the Christian and mediaeval periods, as well as the modern era. Volume 1 begins with Homeric poetry and the politics of fearless demi-gods thriving on war. The tales of lion-hearted Heracles, Achilles, and Ulysses, and their tragic fall at the hands of fate, eventually give way to classical views of courage based on competing theories of rational wisdom and truth. Fears of the enemy and anxieties (...) about suffering and death are addressed through the lenses and teachings of medicine, geography, military history, moral philosophy, and metaphysics. For early Christian thinkers, the ethics of fear, fate, and fealty to the Almighty supplant the voice of reason and the wisdom of virtue. Much of Christian doctrine's history is a long journey towards bridging the gap between Greek philosophy and devotion to God and spirits in heaven. Some Church Fathers attempt to dispel the fear of suffering through a joyful craving for martyrdom and the eternal blessings that follow. Others show openness to one or more of the following principles: the abstractions of moral philosophy, the metaphysics of Gnostic enlightenment, the gift of free will and intentionality, the growth of church authority and hegemony, and the intrinsic worth of life on Earth. Augustine, Ambrose, Cassian, and Chrysostom play a central role in revisiting the foundations of Christian fortitude along some or all of these lines. They lay the groundwork for the scholastic adaptations of faith-based rationalism proposed by Peter Lombard, Philip the Chancellor, Albert the Great, and Thomas of Aquinas. The mediaeval period ends with church dissidents and Protestant Reform leaders condemning Rome’s corruption and calling for a return to early Christian faith and the courage of godly fear, submission, suffering, and fate. (shrink)

This paper is an attempt to give a general explanation of pragmatic aspects of linguistic negation. After a brief survey of classical accounts of negation within pragmatic theories (as speech act theory, argumentation theory and polyphonic theory), the main pragmatic uses of negation (illocutionary negation, external negation, lowering and majoring negation) are discussed within relevance theory. The question of the relevance of negative utterance is raised, and a general inferential schema (based on the so-called invited inference) is proposed and tested (...) for the main uses of negation discussed in the paper. (shrink)