Im Hinblick auf den Herbrand'schen Satz für die Prädikatenlogik der ersten Stufe und auf die Lehre vom Beweisverfahren mit Rechenautomaten, die daraus folgt, wird ein Beweis als komputazional synthetisch bezeichnet, wenn er sich auf Objekte bezieht, die im erwiesenen Satz nicht erwähnt sind. Die mathematischen Beweise sind aber auch synthetisch in einem begrifflichen Sinne: die Kontrolle oder die Begrenzung der angewandten Begriffe — die sogenannte Methodenreinheit — ist im allgemeinen unerreichbar.

Im Hinblick auf den Herbrand'schen Satz für die Prädikatenlogik der ersten Stufe und auf die Lehre vom Beweisverfahren mit Rechenautomaten, die daraus folgt, wird ein Beweis als komputazional synthetisch bezeichnet, wenn er sich auf Objekte bezieht, die im erwiesenen Satz nicht erwähnt sind. Die mathematischen Beweise sind aber auch synthetisch in einem begrifflichen Sinne: die Kontrolle oder die Begrenzung der angewandten Begriffe — die sogenannte Methodenreinheit — ist im allgemeinen unerreichbar.

One of the fundamental properties inclassical equational reasoning isLeibniz's principle of substitution. Unfortunately, this propertydoes not hold instandard epistemic logic. Furthermore,Herbrand's lifting theorem which isessential to thecompleteness ofresolution andParamodulation in theclassical first order logic (FOL), turns out to be invalid in standard epistemic logic. In particular, unlike classical logic, there is no skolemization normal form for standard epistemic logic. To solve these problems, we introduce anintensional epistemic logic, based on avariation of Kripke's possible-worlds semantics that need not have a (...) constant domain. We show how a weaker notion of substitution through indexed terms can retain the Herbrand theorem. We prove how the logic can yield a satisfibility preserving skolemization form. In particular, we present an intensional principle for unifing indexed terms. Finally, we describe asound andcomplete inference system for a Horn subset of the logic withequality, based onepistemic SLD-resolution. (shrink)

Gelfond and Lifschitz proposed the notion of a stable model of a logic program. We establish that the set of all stable models in a Herbrand universe of a recursive logic program is, up to recursive renaming, the set of all infinite paths of a recursive, countably branching tree, and conversely. As a consequence, the problem, given a recursive logic program, of determining whether it has at least one stable model, is Σ11-complete. Due to the equivalences established in the (...) authors' previous nonmonotone rule systems papers ), this applies equally to truth maintenance systems and default logics. (shrink)

Reductive intellectualists hold that knowledge-how is a kind of knowledge-that. For this thesis to hold water, it is obviously important that knowledge-how and knowledge-that have the same epistemic properties. In particular, knowledge-how ought to be compatible with epistemic luck to the same extent as knowledge-that. It is argued, contra reductive intellectualism, that knowledge-how is compatible with a species of epistemic luck which is not compatible with knowledge-that, and thus it is claimed that knowledge-how and knowledge-that come apart.

A translation of the Écrits logiques, edited by Jean Van Heijenoort, published in 1968.

In February 2015 the UK became the first country to legalise high-profile mitochondrial replacement techniques, which involve the creation of offspring using genetic material from three individuals. The aim of these new cell reconstruction techniques is to prevent the transmission of maternally inherited mitochondrial disorders to biological offspring. During the UK debates, MRTs were often positioned as a straightforward and unique solution for the ‘eradication’ of mitochondrial disorders, enabling hundreds of women to have a healthy, biologically-related child. However, many questions (...) regarding future applications and potential users remain. Drawing on a current qualitative study on reproductive choices in the context of mitochondrial disorders, this article illustrates how the potential limitations of MRTs have been obscured in public debates by contrasting the claims made about the future beneficiaries with insights from families affected by mitochondrial disorders and medical experts. The analysis illuminates the complex choices with which families and individuals affected by mitochondrial disorders are faced, which have thus far remained invisible. An argument is presented for improved information for the public as well as an intensification of critical empirical research around the complex and specific needs of future beneficiaries of new reproductive biotechnologies. (shrink)

Aristotle is widely regarded as the greatest of all philosophers; indeed, he is traditionally referred to simply as `the philosopher'. Today, after more than two millennia, his arguments and ideas continue to stimulate philosophers and provoke them to controversy. In this book J.L. Ackrill conveys the force and excitement of Aristotle's philosophical investigations, thereby showing why contemporary philosophers still draw from him and return to him. He quotes extensively from Aristotle's works in his own notably clear English translation, and a (...) picture emerges of a lucid, lively, subtle and tough-minded thinker of astonishing range and penetration. Professor Ackrill identifies many striking connections between Aristotle's ideas and ideas in recent philosophy; he also raises philosophical questions of his own, and exemplifies the way in which Aristotle can still be argued with and learned from. (shrink)

A historical investigation of the exclusion of Africa and Asia from modern histories of philosophy.

This comprehensive and important volume includes contributions by activists, journalists, lawyers and scholars from twenty-one countries. The essays map the directions the movement for women's rights is taking--and will take in the coming decades--and the concomittant transformation of prevailing notions of rights and issues. They address topics such as the rapes in former Yugoslavia and efforts to see that a War Crimes Tribunal responds; domestic violence; trafficking of women into the sex trade; the persecution of lesbians; female genital mutilation; and (...) reproductive rights. (shrink)

Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...

This paper argues that for the purposes of any sort of serious discussion about immoral conduct in sport very little is illuminated by claiming that the conduct in question is cheating. In fact, describing some behavior as cheating is typically little more than expressing strong, but thoroughly vague and imprecise, moral disapproval or condemnation of another person or institution about a wide and ill-defined range of improper advantage-seeking behavior. Such expressions of disapproval fail to distinguish cheating from many other types (...) of immoral conduct. The discussion shows that we should set the concept aside and assess the moral disapproval implied by claims of cheating by reference to the moral and other principles that underlie the practice of sport. This allows us to consider carefully the complexity of the issues that are raised when allegations of cheating are made and not be distracted by the emotionally loaded, conversation-stopping tendency of the concept. This means that some types of disputes in sport will be messy and demand more effort to resolve, but the payoff will be better informed and more thoughtful discussions and greater awareness of the moral complexity of sport and of its principled underpinnings. (shrink)

Isaac Newton wrote the manuscript Questiones quaedam philosophicae at the very beginning of his scientific career. This small notebook thus affords rare insight into the beginnings of Newton's thought and the foundations of his subsequent intellectual development. The Questiones contains a series of entries in Newton's hand that range over many topics in science, philosophy, psychology, theology, and the foundations of mathematics. These notes, written in English, provide a very detailed picture of Newton's early interests, and record his critical appraisal (...) of contemporary issues in natural philosophy. Written predominantly in 1664-5, they give a significant perspective on Newton's thought just prior to his annus mirabilis, 1666. This volume provides a complete transcription of the Questiones, together with an 'expansion' into modern English, and a full editorial commentary on the content and significance of the notebook in the development of Newton's thought. It will be essential reading for all those interested in Newton and the intellectual foundations of science. (shrink)

The first English translation of Fichte’s second set of 1804 lectures on the Wissenschaftslehre.

v. 1. Nicomachean ethics. Politics. The Athenian Constitution. Rhetoric. On Poetics.--v. 2. Logic.--v. 3. Physics. Metaphysics. On the soul. Short physical treaties.--v. 4. On the heavens. On generation and corruption. Meteorology. Biological treatises.

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)