Aristotle's philosophically most explicit and sophisticated account of the concept of a (primary-)universal proof is found, not in "Analytica Posteriora" 1.4, where he introduces the notion, but in 1.5. In 1.4 Aristotle merely says that a universal proof must be of something arbitrary as well as of something primary and seems to explain primacy in extensional terms, as concerning the largest possible domain. In 1.5 Aristotle improves upon this account after considering three ways in which we may delude ourselves into (...) thinking we have a primary-universal proof. These three sources of delusion are shown to concern situations in which our arguments do establish the desired conclusion for the largest possible domain, but still fail to be real primary-universal proofs. Presupposing the concept of what may be called an immediate proof, in which something is proved of an arbitrary individual, Aristotle in response now demands that a proof be immediate of the primary thing itself and goes on to sketch a framework in which an intensional criterion for primacy can be formulated. For the most part this article is a comprehensive and detailed commentary on Aristotle's very concise exposition in 1.5. One important result is that the famous passage 74a17-25 referring to two ways of proving the alternation of proportions cannot be used as evidence for the development of pre-Euclidean mathematics. (shrink)

In Metaphysics M.2, 1077a9-14, Aristotle appears to argue against the existence of Platonic Forms on the basis of there being certain universal mathematical proofs which are about things that are ‘beyond’ the ordinary objects of mathematics and that cannot be identified with any of these. It is a very effective argument against Platonism, because it provides a counter-example to the core Platonic idea that there are Forms in order to serve as the object of scientific knowledge: the universal of which (...) theorems of universal mathematics are proven in Greek mathematics is neither Quantity in general nor any of the specific quantities, but Quantity-of-type-x. This universal cannot be a Platonic Form, for it is dependent on the types of quantity over which the variable ranges. Since for both Plato and Aristotle the object of scientific knowledge is that F which explains why G holds, as shown in a ‘direct’ proof about an arbitrary F (they merely disagree about the ontological status of this arbitrary F, whether a Form or a particular used in so far as it is F), Plato cannot maintain that Forms must be there as objects of scientific knowledge - unless the mathematics is changed. (shrink)

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

In chapter 8 of the Sophistical Refutations, Aristotle claims that his theory of fallacy is complete in the sense that there cannot be more fallacies than the ones he lists. In this article I try to explain how Aristotle could have justified this completeness claim by analysing how he conceptualizes fallacies (dialectical mistakes which do not appear so) and what conceptual ingredients play a role in his discussion of fallacies. If we take the format of dialectical discussions into account, we (...) will see that there are only so many mistakes one can make which still do not appear to be mistakes. Aristotle’s actual list is almost identical to these apparent mistakes. (shrink)

How do, according to Aristotle, peirastic arguments, which are employed by nonscientists to put professed scientists to the test, work, and how do they differ from genuine scientific arguments? A peirastic argument succeeds in unmasking a would-be scientist if it establishes an inconsistency among the answers given. These answers may only comprise: propositions which are proper to the field and which everybody can know; propositions which only scientists may know; “common” propositions that everybody, including various sciences, uses in all kind (...) of arguments. On the other hand, a peirastic argument fails to do its job if it either features or presupposes in addition propositions which would justify a fallacy, or if it purports to be scientific. The latter type of bad peirastic argument crucially depend on common propositions where scientific arguments explain by reference to combinations of the primitive items of the science in question. (shrink)

Aristoteles war zwar kein Mathematiker, aber er kannte sich mit der zeitgenössischen Mathematik gut aus. Er ist direkt oder indirekt unsere wichtigste Quelle für unsere Kenntnis der voreuklidischen Mathematik. Die Sammlungen von Heiberg und Heath geben Zeugnis von der Breite und Vielseitigkeit seines Interesses an den mathematischen Wissenschaften.

Ausgangspunkt der Betrachtung von Aristoteles’ Ansichten zur Ontologie mathematischer Gegenstände ist die Sichtweise seines Lehrers Platon auf die Gegenstände der Mathematik. Dieser war der Ansicht, dass die eigentlichen Gegenstände der mathematischen Wissenschaften Geometrie und Arithmetik sowohl unveränderlich als nicht wahrnehmbar sind, und daher als getrennt von den physikalischen Gegenständen existierend angenommen werden müssen. Die Gründe, die Platon dafür hatte, sind von zweierlei Art.

Inleidend overzicht van de wijsgerige ethiek.

Scientific realists have suggested that changes in our scientific communities over the course of their history have rendered those communities progressively less vulnerable to the problem of unconcieved alternatives over time. I argue in response not only that the most fundamental historical transformations of the scientific enterprise have generated steadily mounting obstacles to revolutionary, transformative, or unorthodox scientific theorizing, but also that we have substantial independent evidence that the institutional apparatus of contemporary scientific inquiry fosters an exceedingly and increasingly theoretically (...) conservative form of that inquiry. I conclude that contemporary scientific communities are actually more vulnerable to the problem of unconceived alternatives than their historical predecessors, and I briefly suggest how we might seek to pursue scientific inquiry in a less theoretically conservative way. (shrink)

인간의 이성적 의식과 법의 관계를 밝히고 법의 해석 과 판단에 인간의 의식이 어떻게 작용하는가를 고찰 한 저술. 제1부에서는 법의 형이상학적인 측면에서 법의 실체, 그리스의 법, 데카르트의 법, 로크와 법, 칸트와 법, 헤겔과 법, 아담스미스의 법의 경제, 중국의 도덕과 법사상을 다루었다. 제2부에서는 심리학적 분석으로 헌법의 심리학적 해석, 법의 판결절차, 증거법, 형법과 죄, 청소년과 가족법, 조세법, 플라톤의 법, 칸트의 도덕론의 경험적 확인, 헤겔의 자아와 노동법, 법의 4차원에 대해 다뤘다.

George Berkeley is one of the greatest and most influential modern philosophers. In defending the immaterialism for which he is most famous, he redirected modern thinking about the nature of objectivity and the mind's capacity to come to terms with it. Along the way, he made striking and influential proposals concerning the psychology of the senses, the workings of language, the aims of science, and the scope of mathematics. In this Companion volume a team of distinguished authors not only examines (...) Berkeley's achievements but also his neglected contributions to moral and political philosophy, his writings on economics and development, and his defense of religious commitment and religious life. The volume places Berkeley's achievements in the context of the many social and intellectual traditions - philosophical, scientific, ethical, and religious - to which he fashioned a distinctive response. (shrink)

One diagnosis of what is wrong with the Knowledge Argument rests on the Ability Hypothesis. This couples an ability analysis of knowing what an experience is like together with a denial that phenomenal propositions exist. I argue against both components. I consider three arguments against the existence of phenomenal propositions and find them wanting. Nevertheless I deny that knowing phenomenal propositions is part of knowing what an experience is like. I provide a hybrid account of knowing what an experience is (...) like which is the coherent expression of a single idea: knowing what an experience is like is knowing what it would be like to have the phenomenal content of the experience as the content of an experience one is currently having. I explain how my conclusions indicate that the focus of discussion should be on the alleged explanatory gap between phenomenal facts and physical facts and not on the Knowledge Argument. The latter is a poor expression of the difficulty Physicalists face. (shrink)

Typical discussions of virtual reality (VR) fixate on technology for providing sensory stimulation of a certain kind. They thus fail to understand reality as the place wherein we live and work, misunderstanding it instead as merely a sort of presentation. The first half of the paper examines popular conceptions of VR. The most common conception is a shallow one according to which VR is a matter of simulating appearances. Yet there is, even in popular depictions, a second, more subtle conception (...) according to which VR is a matter of facilitating new kinds of interaction. The latter half of the paper turns to questions about the contemporary technology of Internet chatrooms. The fact that chatrooms can be used in certain ways suggests something about the prospects for VR. The penultimate section asks whether chatrooms may legitimately be thought of as places. (In a sense, they may.) The final section asks whether cybersex may legitimately be thought of as sex. (Again, yes.) Chatroom technology thus provides an argument for the second conception of VR over its much ballyhooed rival. (shrink)

There has been an increase in recent years in the use of empirical methods in healthcare ethics. Appeals to empirical data cannot answer moral questions, but insights into the knowledge, attitudes, experience, preferences and practice of interested parties can play an important part in the development of healthcare ethics. In particular, while we may establish a general ethical principle to provide explanatory and normative guidance for healthcare professionals, the interpretation and application of such general principles to actual practice still requires (...) interpretation and judgement. And many situations in healthcare practice are complex and may involve a variety of principles, each of which may conflict with the others. Simple surveys or interview studies may not be sufficient if we wish to develop a nuanced approach to ethical practice that can be set out in guidelines, codes or directives. We do not resolve moral questions by plebiscite. In this paper, the authors argue for the use of consensus methods to develop shared understanding of ethical practice, and they argue further for the combination of the Delphi method with the use of vignettes to illustrate the kind of situations that may occur in practice. They develop their argument in part by reference to their experience of using this approach in their recent research. (shrink)

As family physicians, general practitioners play a key role in safeguarding children. Should they suspect child abuse or neglect they may experience a conflict between responding to the needs and interests of the child and those of an adult patient. English law insists on the paramountcy of the interests of the child, but in family practice many other interests may be at stake. The authors argue that uncritical adoption of the paramountcy principle is too simplistic and can lead, paradoxically, to (...) greater harm. They argue for a more subtle and nuanced view of interests and of conflicts of interest in safeguarding children. (shrink)

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events and when we lack them. The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in (...) the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering. (shrink)

On-line, just as off-line, there are ways of assessing the credibility of information sources. The Internet, although it arguably makes for nothing wholly new in this regard, complicates the ordinary task of assessing credibility. In the first section, I consider a specific example and argue that Internet content providers have no clear interest in resolving these comlications. In the second, I consider four general ways that we might assess credibility and explore how they apply to life online. Finally, I argue (...) that even careful information gathering may pose subtle pitfalls but that some of these may be mitigated on-line. (shrink)