Context: Consistency of mathematical constructions in numerical analysis and the application of computerized proofs in the light of the occurrence of numerical chaos in simple systems. Purpose: To show that a computer in general and a numerical analysis in particular can add its own peculiarities to the subject under study. Hence the need of thorough theoretical studies on chaos in numerical simulation. Hence, a questioning of what e.g. a numerical disproof of a theorem in physics or a prediction in numerical (...) economics could mean. Method: An algebraic simple model system is subjected to a deeper structure of underlying variables. With an algorithm simulating the steps in taking a limit of second order difference quotients the error terms are studied at the background of their algebraic expression. Results: With the algorithm that was applied to a simple quadratic polynomial system we found unstably amplified round-off errors. The possibility of numerical chaos is already known but not in such a simple system as used in our paper. The amplification of the errors implies that it is not possible with computer means to constructively show that the algebra and numerical analysis will ‘on the long run’ converge to each other and the error term will vanish. The algebraic vanishing of the error term cannot be demonstrated with the use of the computer because the round-off errors are amplified. In philosophical terms, the amplification of the round-off error is equivalent to the continuum hypothesis. This means that the requirement of (numerical) construction of mathematical objects is no safeguard against inference-only conclusions of qualities of (numerical) mathematical objects. Unstably amplified round-off errors are a same type of problem as the ordering in size of transfinite cardinal numbers. The difference is that the former problem is created within the requirements of constructive mathematics. This can be seen as the reward for working numerically constructive. (shrink)

Appearing in English for the first time, Schelling’s 1842 lectures develop the idea that many philosophical concepts are born of religious-mythological notions.

With precision and profundity born of 30 years of devoted study, John Boyle offers an essential introduction to St. Thomas Aquinas on Scripture, shedding helpful light on the goals, methods, and commitments that animate the Angelic Doctor's engagement with the sacred page. Because the genius of St. Thomas's approach to the Bible lies not so much in its novelty but rather in the fidelity and clarity with which he recapitulates the riches of the preceding interpretive Tradition, this initiation into St. (...) Thomas's vision of Scripture is itself an orientation to the Church's vision of Scripture, from the Fathers through and beyond the Middle Ages. St. Thomas's embeddedness within the Church's Tradition and his own historical context is integral to his approach to Scripture, yet it sets him at some distance from modern readers, for whom his interpretive vision may seem perplexing or even impenetrable. In this Primer, Boyle first provides an acclimation to this medieval context through a survey and explanation of pertinent technical terminology used by St. Thomas and characteristic of the scholastic theology of the time. With an eye to the medieval practice of considering Scripture according to the fourfold division of causes, Boyle builds on this initial foundation by exploring in turn St. Thomas's accounts of the end or use of Scripture (final cause), its divine and human authorship (efficient cause), its order and division (material cause), and its literary styles or genres (formal cause). Drawing on writings from across St. Thomas's corpus, but especially his work On the Commendation and Division of Sacred Scripture and the prologues to his biblical commentaries, Boyle masterfully elucidates both the hermeneutical principles and deep wisdom of the Angelic Doctor's approach to Scripture, imparting invaluable guidance not only for reading and understanding St. Thomas and other great masters of the Tradition, but also-and ultimately-for understanding Scripture in light of this Tradition and reading it with greater benefit and joy. (shrink)

This paper starts with one of Chalmers’ basic points: first-hand experience is an irreducible field of phenomena. I claim there is no ‘theoretical fix’ or ‘extra ingredient’ in nature that can possibly bridge this gap. Instead, the field of conscious phenomena requires a rigorous method and an explicit pragmatics for its exploration and analysis. My proposed approach, inspired by the style of inquiry of phenomenology, I have called neurophenomenology. It seeks articulations by mutual constraints between phenomena present in experience and (...) the correlative field of phenomena established by the cognitive sciences. It needs to expand into a widening research community in which the method is cultivated further. (shrink)

I begin by criticizing an elaboration of an argument in this journal due to Hawley , who argued that, where Leibniz’s Principle of the Identity of Indiscernibles faces counterexamples, invoking relations to save PII fails. I argue that insufficient attention has been paid to a particular distinction. I proceed by demonstrating that in most putative counterexamples to PII , the so-called Discerning Defence trumps the Summing Defence of PII. The general kind of objects that do the discerning in all cases (...) form a category that has received little if any attention in metaphysics. This category of objects lies between indiscernibles and individuals and is called relationals: objects that can be discerned by means of relations only and not by properties. Remarkably, relationals turn out to populate the universe. (shrink)

This is an English translation of Schelling's Ideas for a Philosophy of Nature (first published in 1797 and revised in 1803), one of the most significant works in the German tradition of philosophy of nature and early nineteenth-century philosophy of science. It stands in opposition to the Newtonian picture of matter as constituted by inert, impenetrable particles, and argues instead for matter as an equilibrium of active forces that engage in dynamic polar opposition to one another. In the revisions of (...) 1803 Schelling incorporated this dialectical view into a neo-Platonic conception of an original unity divided upon itself. The text is of more than simply historical interest: its daring and original vision of nature, philosophy, and empirical science will prove absorbing reading for all philosophers concerned with post-Kantian German idealism, for scholars of German Romanticism, and for historians of science. (shrink)

With fascinating historical anecdotes and incisive scientific analysis, this important work combines ancient thought with modern theory to reveal a new way of viewing our universe that can expand our awareness, our lives, and may well point the way to a new science for the twenty-first century.

"The chief business of twentieth-century philosophy” is “to reckon with twentieth-century history," claimed R. G. Collingwood. In this remarkable collection of essays, Frank Ankersmit demonstrates the prescience of that remark and goes a long way toward meeting its challenge. Responding to the work of Hayden White, Arthur Danto, and Hans-Georg Gadamer, he examines such issues as the difference between historical representation and artistic expression, the status of metaphor in historical description, and the relation of postmodernism to historicism. Ankersmit's fluent grasp (...) of European thought and his ability to incorporate concepts from literary theory, art history, the philosophy of science, and political thought into his analyses assure that this collection will interest readers throughout the humanities. (shrink)

The Continuous Parameter Estimation Model is applied to develop individual genomic-level heritabilities for the latent hierarchical structure and developmental dynamics of Life History (LH) strategy LH strategies relate to the allocations of bioenergetic resources into different domains of fitness. LH has moderate to high population-level heritability in humans, both at the level of the high-order Super-K Factor and the lower-order factors, the K-Factor, Covitality Factor, and General Factor of Personality (GFP). Several important questions remain unexplored. We developed measures of genome-level (...) heritabilities employing an American sample of 316 monozygotic (MZ) and 274 dizygotic (DZ) twin dyads and a Swedish sample of 863 MZ and 475 DZ twin dyads. This novel heritability index measures individual genetic transmissibility, therefore opening new avenues for analyzing complex interactions among heritable traits inaccessible to standard structural equations methods. For these samples: (1) moderate to high heritability of factor loadings of Super-K on its lower-order factors is demonstrated, evidencing biological preparedness, genetic accommodation, and the gene-culture coevolution of biased epigenetic rules of development; (2) moderate to high heritability of the magnitudes of the effect of the higher-order factors upon their loadings on their constituent factors, evidencing genetic constraints upon phenotypic plasticity; and (3) that heritability of the LH factors, of factor loadings, and of the magnitudes of the correlations among factors are weaker among those with slower LH speeds, demonstrating that inter-individual variation in transmissibility is a function of individual socioecological selection pressures. (shrink)

"Not only one of the best but also the most comprehensive treatment of Stoicism written in this century." --Times Literary Supplement.

This landmark work provides a systematic introduction to systems of modal logic and stands as the first presentation of what have become central ideas in philosophy of language and metaphysics, from the "new theory of reference" and non-linguistic necessity and essentialism to "Kripke semantics.".

Ethics for Enemies comprises three original philosophical essays on torture, terrorism, and war. F. M. Kamm deploys ethical theory in her challenging new treatments of these most controversial practical issues. First she considers the nature of torture and the various occasions on which it could occur, in order to determine why it might be wrong to torture a wrongdoer held captive, even if this were necessary to save his victims. In the second essay she considers what makes terrorism wrong--whether it (...) is the intention to harm civilians, rather than harm to them being 'collateral damage,' or something else--and whether terrorism is always wrong. The third essay discusses whether having a right reason, in the sense of a right intention, is necessary in order for a war to be just. Kamm then examines ways in which the harms of war can be proportional to the achievement of the just cause and other goods that war can bring about, so as to make the declaration of war permissible. (shrink)

Neuroscience has studied deductive reasoning over the last 20 years under the assumption that deductive inferences are not only de jure but also de facto distinct from other forms of inference. The objective of this research is to verify if logically valid deductions leave any cerebral electrical trait that is distinct from the trait left by non-valid deductions. 23 subjects with an average age of 20.35 years were registered with MEG and placed into a two conditions paradigm (100 trials for (...) each condition) which each presented the exact same relational complexity (same variables and content) but had distinct logical complexity. Both conditions show the same electromagnetic components (P3, N4) in the early temporal window (250–525 ms) and P6 in the late temporal window (500–775 ms). The significant activity in both valid and invalid conditions is found in sensors from medial prefrontal regions, probably corresponding to the ACC or to the medial prefrontal cortex. The amplitude and intensity of valid deductions is significantly lower in both temporal windows (p = 0.0003). The reaction time was 54.37% slower in the valid condition. Validity leaves a minimal but measurable hypoactive electrical trait in brain processing. The minor electrical demand is attributable to the recursive and automatable character of valid deductions, suggesting a physical indicator of computational deductive properties. It is hypothesized that all valid deductions are recursive and hypoactive. (shrink)

John F. Post argues that physicalistic materialism is compatible with a number of views often deemed incompatible with it, such as the objectivity of values, the irreducibility of subjective experience, the power of the metaphor, the normativity of meaning, and even theism.

Recent advances in physics render a reconsideration of the Place of Mathematics in the Interpretation of the Universe particularly timely. On the one hand, we have the introduction of non-euclidian geometry, which has given rise to much controversy informed or otherwise; on the other hand, we find mysterious forms of mathematics, invented to cope with the quantum difficulties, which so far have escaped metaphysical investigation or criticism. It would seem most desirable that these modes of interpreting reality should be examined (...) from the broader philosophical point of view. (shrink)

Sixteen essays on epistemology, metaphysics, & history & politics, treating aspects of the writings of Descartes, Locke, Hume, Kant, Leibniz, & Hobbes.

The limited aim here is to explain what John Dewey might say about the formulation of the grue example. Nelson Goodman’s problem of distinguishing good and bad inductive inferences is an important one, but the grue example misconstrues this complex problem for certain technical reasons, due to ambiguities that contemporary logical theory has not yet come to terms with. Goodman’s problem is a problem for the theory of induction and thus for logical theory in general. Behind the whole discussion of (...) these issues over the last several decades is a certain view of logic hammered out by Russell, Carnap, Tarski, Quine, and many others. Goodman’s nominalism hinges in essential ways on a certain view of formal logic with an extensional quantification theory at its core. This raises many issues, but the one issue most germane here is the conception of predicates ensconced in this view of logic. (shrink)

Portraits of Wittgenstein is a major collection of memoirs and reflections on one of the most influential and yet elusive personalities in the history of modern philosophy, Ludwig Wittgenstein. Featuring a wealth of illuminating and profound insights into Wittgenstein's extraordinary life, this unique collection reveals Wittgenstein's character and power of personality more vividly and comprehensively than ever before. With portraits from more than seventy-five figures, Portraits of Wittgenstein brings together the personal recollections of philosophers, students, friends and acquaintances, including Bertrand (...) Russell, G. E. Moore, F. R. Leavis, A. J. Ayer, Karl Popper, Friedrich von Hayek, G. H. von Wright, Rush Rhees, Freeman Dyson, G. E. M. Anscombe, Iris Murdoch, Mary Midgley and Mary Warnock. These authors testify to the life-long influence Wittgenstein had on the lives of those he met. Their fascinating memoirs, reflections and commentaries, often at odds with each other, reveal Wittgenstein's kindness, and how much genuine friendship meant to him, as well as his suffering and despair. They show too how the philosopher's ruthless honesty and uncompromising integrity often resulted in stern advice and harsh rebukes to friends and foes alike. Now available in a single, revised and updated volume, Portraits of Wittgenstein includes new selections, revised contributions, photographs, maps and introductory overviews that provide historical context to Wittgenstein's relationships with his intellectual and social circle. This collection of valuable and hard-to-find material is an indispensable resource for scholars and students of the life and work of Ludwig Wittgenstein. (shrink)

The posterior parietal cortex (PPC) is the most likely site where egocentric spatial relationships are represented in the brain. PPC cells receive visual, auditory, somaesthetic, and vestibular sensory inputs; oculomotor, head, limb, and body motor signals; and strong motivational projections from the limbic system. Their discharge increases not only when an animal moves towards a sensory target, but also when it directs its attention to it. PPC lesions have the opposite effect: sensory inattention and neglect. The PPC does not seem (...) to contain a “map” of the location of objects in space but a distributed neural network for transforming one set of sensory vectors into other sensory reference frames or into various motor coordinate systems. Which set of transformation rules is used probably depends on attention, which selectively enhances the synapses needed for making a particular sensory comparison or aiming a particular movement. (shrink)

Disjunctivism about perceptual appearances, as I conceive of it, is a theory which seeks to preserve a naïve realist conception of veridical perception in the light of the challenge from the argument from hallucination. The naïve realist claims that some sensory experiences are relations to mind-independent objects. That is to say, taking experiences to be episodes or events, the naïve realist supposes that some such episodes have as constituents mind-independent objects. In turn, the disjunctivist claims that in a case of (...) veridical perception like this very kind of experience that you now have, the experiential episode you enjoy is of a kind which could not be occurring were you having an hallucination. The common strategy of arguments from hallucination set out to show that certain things are true of hallucinations, and hence must be true of perceptions. For example, it is argued that hallucinations must have non-physical objects of awareness, or that such states are not relations to anything at all, but are at best seeming relations to objects. In insisting that veridical perceptual experience is of a distinct kind from hallucination, the disjunctivist denies that any of these conceptions of hallucination challenges our conception of veridical perceptions as relations to mind-independent objects. More specifically, I assume that the disjunctivist advocates naïve realism because they think that this position best articulates how sensory experience seems to us to be just through reflection. If the disjunctivist is correct in this contention, then anyone who accepts the conclusion of the argument from hallucination must also accept that the nature of sensory experience is other than it seems to us to be. In turn, one may complain that any such error theory is liable to lead to sceptical consequences. A Humean scepticism about the senses launches a challenge about our knowledge of the world through questioning the conception we have of what sense experience is, and how it can provide knowledge of the world. (shrink)

The essays in this collection address different aspects of Dewey's philosophy of logic, from his work at the beginning of the twentieth century to the culmination of his logical thought in the 1938 volume, Logic: The Theory of Inquiry.

All developed human beings possess a practical mastery of a vast range of concepts, including such basic structural notions as those of identity, truth, existence, material objects, mental states, space, and time; but a practical mastery does not entail theoretical understanding. It is that understanding which philosophy seeks to achieve. In this book, one of the most distinguished of living philosophers, assuming no previous knowledge of the subject on the part of the reader, sets out to explain and illustrate a (...) certain conception of the nature of analytical philosophy. Strawson draws on his many years of teaching at Oxford University, during which he refined and developed what he regards as the most productive route to understanding the fundamental structure of human thinking. Among the distinctive features of his exposition are the displacement of an older, reductive conception of philosophical method in favor of elucidating the interconnections between the complex but irreducible notions which form the basic structure of our thinking; and the demonstration that the three traditionally distinguished departments of metaphysics, epistemology, and logic are but three aspects of one unified enquiry. Strawson has produced an elegant work that will be invaluable to students and stimulating for professional philosophers and general readers alike. (shrink)

F. H. Bradley (1846–1924) was the foremost philosopher of the British Idealist school, which came to prominence in the second half of the nineteenth century and remained influential into the first half of the twentieth. Bradley, who was influenced by Hegel and also reacted against utilitarianism, was recognised during his lifetime as one of the greatest intellectuals of his generation, and was the first philosopher to receive the Order of Merit, in 1924. In this major work, originally published in 1883, (...) Bradley discusses the basic principles of logic: judgment and inference. He rejects the idea of a separation between mind and body, arguing that human thought cannot be separated from its worldly context. In the second edition, published in 1922 and reissued here, Bradley added a commentary and essays, but left the text largely unaltered. Volume 1 contains Book 1 on judgment and Book 2 on inference. (shrink)

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting (...) to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents. (shrink)

The reaction to Darwin's Origin of Species varied in many countries according to the roles played by national scientific institutions and traditions and the attitudes of religious and political groups. The contributors to this volume, including M. J. S. Hodge, David Hull, and Roberto Moreno, gathered in 1972 at an international conference on the comparative reception of Darwinism. Their essays look at early pro- and anti-Darwinism arguments, and three additional comparative essays and appendices add a larger perspective. For this paperback (...) edition, Thomas F. Glick has added a new preface commenting on recent research. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Guibert of Tournai's Letter to Lady Isabelle:An Introduction and English TranslationLarry F. Field, Jacques Dalarun, Sean L. Field, and Guibert of TournaiIntroductionGuibert, from the noble family of As-Piès, was born near Tournai around 1200. From his hometown he traveled to Paris for his art degree, and completed the curriculum in theology there before entering the Franciscan Order around 1240. He may have participated in Louis IX's crusade of 1248, (...) but, if so, was surely back in Paris by 1254 at the latest, since he preached a cycle of sermons de dominicis et de sanctis to the university community before summer 1255.1 His regency as Franciscan master of theology at Paris was probably around 1259–1261,2 about the time he [End Page 31] completed his Eruditio regum et principum for Louis IX,3 and began his most substantial work, the Erudimentum doctrinae.4 Other significant treatises include his De pace et animi tranquillitate (ca. 1275)5 written for Marie de Dampierre, and the Collectio de scandalis ecclesiae, prepared for the Second Council of Lyon.6 Guibert died in Tournai on 7 October 1284.7Sometime around 1254, Guibert wrote a long letter of spiritual advice to Isabelle (1225–70), the sister of King Louis IX.8 Isabelle was herself a remarkable figure. She had rejected several proposals of marriage, including that with Conrad, the heir to Emperor Frederick II, in 1243, in spite of pressure from her family and Pope Innocent IV. But following a bout of serious illness at about that time,9 her family accepted her [End Page 32] decision to remain unwed. There is no evidence, however, that Isabelle ever pronounced a formal vow of virginity. Through the 1250s she simply remained at the Capetian court as a virgin princess with an increasing reputation for piety and indeed holiness, praised in lavish terms by Innocent IV in 1253 and Alexander IV in 1256.10 This piety took a distinctly Franciscan turn by 1254, when Pope Innocent IV granted her request for Franciscan confessors,11 which would ultimately result in her foundation of Longchamp, a house of Sorores minores just west of Paris, by 1260.12 Guibert's letter shows no awareness of such a project, indicating that it must have been written before spring 1255, by which time the land for Longchamp was being purchased on Isabelle's behalf.13 Guibert thus wrote at the moment when Isabelle was forming her first ties to the Franciscans, but well before her move to Longchamp, where she lived out the 1260s as resident lay patron (but never a nun).Guibert's Letter is really a short treatise of spiritual and moral advice, tailored to a celibate princess. It is organized around Psalm 44:14–15, All the glory of the king's daughter is within in golden fringes, clothed around with varieties. In a five-part structure, the king's daughter stands for a heavenly inheritance; glory within represents internal purity; gold indicates virginity; the fringes are a sign of humility; and clothed around with varieties points to honest comportment. The resulting "royal garment," however, is rather unequally woven together, with section one on the "heavenly inheritance" and the intertwined sections three and four on virginity and humility receiving by far the most space. In fact, section one forms a sort of treatise-within-a-treatise, organized as a ten-step ascent to the heavenly inheritance awaiting the daughter of the king. [End Page 33]The Letter to Lady Isabelle was first edited by Alphonse de Poorter in 1931, from a manuscript which contained only part of the text.14 The full text was brought into print by Sean Field in 2003,15 and translated into French by Jacques Dalarun in 2014.16 Yet in spite of these advances, the Letter has remained little noticed by scholars. Anne-Hélène Allirot offered several perceptive pages in 2010, stressing the way Guibert's treatment of hereditas implies that female members of the royal family might be particularly able to embody Capetian claims to holiness.17 That same year, in the only recent article dedicated specifically to this Letter, Rina Lahav... (shrink)