This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most (...) striking results are contained in Goedel's work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraissé's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic. (shrink)

Formal principals are isolated to reveal a structure embedded in a wide range of studies, each of which partitions a domain of individuals into types and categories. It is thought that any reasonable theory of types should include these principles.

Descartes's epistemology, morals, and metaphysics – each offer reason to look on real life as a spectator looks on a theater production. The meditator seeking certainty watches his body move as in a dream and employs an entirely passive faculty of knowledge. In order to act firmly and yet not risk disappointment, the moral subject confines action to the soul, refusing to count bodily activities as actions, and cultivates a desire free from passion. After the Meditations, the metaphysician abandons the (...) thesis that soul and body constitute a human being, consequently limiting human goods to goods of the soul alone and devaluing embodied life in the world. (shrink)

CHAPTER Meta-View BRIDGES When I was a child, I lived in an area renowned for its many wooden covered bridges. Sometimes my family would take a Sunday drive ...

This article sketches an idealized strategy for the identification of neural correlates of consciousness. The proposed strategy is based on a state space approach originating from the analysis of dynamical systems. The article then focuses on one constituent of consciousness, phenomenal awareness. Several rudimentary requirements for the identification of neural correlates of phenomenal awareness are suggested. These requirements are related to empirical data on selective attention, on completely intrinsic selection and on globally unconscious states. As an example, neuroscientific findings on (...) synchronized γ activity are categorized according to these requirements. (shrink)

Philosophical discussions on causal inference in medicine are stuck in dyadic camps, each defending one kind of evidence or method rather than another as best support for causal hypotheses. Whereas Evidence Based Medicine advocates the use of Randomised Controlled Trials and systematic reviews of RCTs as gold standard, philosophers of science emphasise the importance of mechanisms and their distinctive informational contribution to causal inference and assessment. Some have suggested the adoption of a pluralistic approach to causal inference, and an inductive (...) rather than hypothetico-deductive inferential paradigm. However, these proposals deliver no clear guidelines about how such plurality of evidence sources should jointly justify hypotheses of causal associations. We here develop such guidelines by first giving a philosophical analysis of the underpinnings of Hill’s viewpoints on causality. We then put forward an evidence-amalgamation framework adopting a Bayesian net approach to model causal inference in pharmacology for the assessment of harms. Our framework accommodates a number of intuitions already expressed in the literature concerning the EBM vs. pluralist debate on causal inference, evidence hierarchies, causal holism, relevance, and reliability. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 63.3 (2002) 371-397 [Access article in PDF] How the "New Science" of Cannons Shook up the Aristotelian Cosmos Mary J. Henninger-Voss [Figures]Approximately halfway through the "Second Day" of Galileo's Dialogue Concerning the Two Chief World Systems Galileo's mouthpiece, the mathematician Salviati, scoffs at his Aristotelian colleague Simplicio: "I see that you have hitherto been of that herd who, in order to learn how (...) matters such as this [motion] take place, and in order to acquire a knowledge of natural effects, do not betake themselves to ships or crossbows or cannons, but retire to their studies... to see whether Aristotle has said anything about them."1 Silly, simple Simplicio! He has been searching for natural philosophical wisdom in the books of natural philosophers rather than in the world of docks and arsenals. Indeed this quotation appears near the outset of Day Two wherein Salviati offers cannonshot as proof for the opposing Aristotelian position that the experience of projectiles proves the motionless state of the earth. Obviously, if the earth rotates toward the east, cannonballs shot point-blank to the west ought to travel much further than to the east. And clearly this is not so. Simplicio agrees that the new arguments offered by the cannon are excellent, "and now I see with how many elegant experiments nature graciously wishes to aid us in coming to the recognition of the truth," Simplicio enthusiastically enjoins. "What a shame there were no cannons in Aristotle's time!" exclaims the third interlocutor, Sagredo. "With them he would indeed have battered down ignorance, and spoken without [End Page 371] [Begin Page 373] the least hesitation concerning the universe."2 The irony here is not only that Aristotle might have used cannons in order to explain the workings of the universe but also that Galileo does so in the following pages. His demonstrations with reference to artillery demolish the Aristotelian position, but he has had Simplicio open the door for him by recognizing this most violent of artifices as an elegant experiment provided by nature.3The cannon provides a primary referent for Galileo's new mathematical physics of motion from his very first dialogue to his very last. The early De Motu culminated in a series of questions about the shot of cannons, while the conversation in his final masterwork, Discourses Concerning Two New Sciences, was set in the Venetian arsenal, and to it Galileo appended a table of the parabolic paths that could be expected from cannons shot at various elevations.4 In some sense Galileo turned inside-out a much older problem, one that had haunted military engineers of sixteenth-century Italy—and Galileo had been trained, and trained others, in military engineering.5 State organizers of war and captain generals were less interested in the implications the arts of fortifications and artillery held for the existing science of natural motion than in the necessity to reduce to a science, that is, a coherent body of knowledge, the rules for manufacturing cannons, planting artillery battery, aiming guns, and fortifying camps, cities, and castles.What Galileo gives us is recognizable as early physics, as a sophisticated mechanical science, a neat triumph of mathematical method in natural philosophy. But the ways and means by which mathematics came together with natural philosophy to address problems of both technology and nature are by no means neat. My claim is that attention to the military sphere will help us sort out some of those ways and means. The curious thing about the historiography on the relationship between early modern science and warfare is that the fact of a connection seems to have been taken for granted, while the implications have seldom been investigated.6 This essay is an attempt to trace those implications by [End Page 373] looking at a mathematician who specifically tried to reduce to a mathematical science the military arts, Niccolò Tartaglia.7 Tartaglia's story shows how the minutia of Aristotelian philosophy was transmuted in early attempts to understand cannonshot... (shrink)

According to the objective Bayesian approach to inductive logic, premisses inductively entail a conclusion just when every probability function with maximal entropy, from all those that satisfy the premisses, satisfies the conclusion. When premisses and conclusion are constraints on probabilities of sentences of a first-order predicate language, however, it is by no means obvious how to determine these maximal entropy functions. This paper makes progress on the problem in the following ways. Firstly, we introduce the concept of a limit in (...) entropy and show that, if the set of probability functions satisfying the premisses contains a limit in entropy, then this limit point is unique and is the maximal entropy probability function. Next, we turn to the special case in which the premisses are categorical sentences of the logical language. We show that if the uniform probability function gives the premisses positive probability, then the maximal entropy function can be found by simply conditionalising this uniform prior on the premisses. We generalise our results to demonstrate agreement between the maximal entropy approach and Jeffrey conditionalisation in the case in which there is a single premiss that specifies the probability of a sentence of the language. We show that, after learning such a premiss, certain inferences are preserved, namely inferences to inductive tautologies. Finally, we consider potential pathologies of the approach: we explore the extent to which the maximal entropy approach is invariant under permutations of the constants of the language, and we discuss some cases in which there is no maximal entropy probability function. (shrink)

Narrative allegory is distinguished from mythology as reality from symbol; it is, in short, the proper intermedium between person and personification. Where it is too strongly individualized, it ceases to be allegory […]. In the community of scholars of intermedia research, the above quoted citation is commonly regarded as Coleridge’s coining of the term “intermedium” or “intermediality”. However, a short glance at the discursive strategy of his argument emphasizes that his notion of “intermedium” must be closely linked to the poetics (...) and aesthetics of 19th-century romanticism. For the romantic poet, the term of “intermedium” does not point to media relations or intermedia processes but to.. (shrink)

This is one of the most important books on quantum mechanics ever written for lay readers, in which an eminent physicist and successful science writer, Heinz Pagels, discusses and explains the core concepts of physics without resorting to complicated mathematics. "Can be read by anyone. I heartily recommend it!" -- New York Times Book Review. 1982 edition.

Knapp sechs Jahre nach Rudolf Heinz' sechzigstem Geburtstag und dem auf dieses Ereignis ausgerichteten Erscheinen der Festschrift "Kontiguitäten. Texte-Festival für Rudolf Heinz" (Christoph Weismüller [Hg.] unter Mitarbeit von Ralf Bohn, Wien: Passagen 1997) folgt die Nachbearbeitung der "Kontiguitäten" und deren Produktion. Die Post-Skripts zum Texte-Festival für Rudolf Heinz setzen ein mit den Dokumenten der Feierlichkeit der Festschriftüberreichung: Laudatio, Geburtstagskomposition - inklusive Audio-CD -, Photographien der Festschriftübergabe. Unter dem topos Festschrift-Mechané folgt diesen Initialien die Korrespondenz von Heide (...) class='Hi'>Heinz und Christoph Weismüller nebst notwendigen Paraphrasen und Hinweisen. Die Après nehmen einschlägige Kontiguitäts-Effekte auf, die mit der Fertigstellung der Festschrift, der Feierlichkeit der Übergabe, ihrer Distribution und ersten Nachbearbeitungen ihrer Konstitution einhergingen oder diesen folgten. Die Katamnese von Heide Heinz und Rudolf Heinz sowie weitere Korrespondenzen - Heide Heinz mit Ralf Bohn, Doris Dorner, Axel Schünemann; Rudolf Heinz mit Manfred Pohlen - finden sich als Zuträge ein. (shrink)

We study questionnaire responses to situations in which sacrificing one life may save many other lives. We demonstrate gender differences in moral judgments: males are more supportive of the sacrifice than females. We investigate a source of the endorsement of the sacrifice: antisocial preferences. First, we measure individual proneness to spiteful behavior, using an experimental game with monetary stakes. We demonstrate that spitefulness can be sizable—a fifth of our participants behave spitefully—but it is not associated with gender. Second, we find (...) that gender is consistently associated with responses even when we account for individual differences in the propensity to spitefulness. (shrink)

As digital media becomes more central to the lives of adolescents, it also becomes increasingly relevant for their sexual communication. Sexting as an important image-based digital medium provides opportunities for self-determined digital communication, but also carries specific risks for boundary violations. Accordingly, sexting is understood either as an everyday, or as risky and deviant behavior among adolescents. In the affectedness of boundary violations gender plays an important role. However, it is still unclear to what extent digital sexual communication restores stereotypical (...) gender roles and restrictive sexuality norms or, alternatively, enables new spaces of possibility. In this sense, current research points to a desideratum regarding adolescents’ orientations toward sexting as a practice between spaces of possibility and boundary violations. This paper discusses the possibilities, but also the risks, of intimate digital communication among adolescents. The main question is, how adolescents themselves perceive sexting practices and how they position themselves between both spaces for possibility and for the exchange of unwanted sexual content. For this purpose, orientations toward normalities and gender of students are reconstructed. To answer these questions, twelve single-sex, group discussions were carried out with students aged 16 and 17 at five different secondary schools in northern Germany. A total of 20 boys and 22 girls took part. The group discussions were structured by a narrative generating guideline. The analysis draws its methodology from the Documentary Method, regarding implicit and explicit forms of knowledge and discourse. It results in a typology of three types with different orientations. The study shows, that most of the students consider sexting to be a risky practice; only one type shows normality in the use of sexting. At the same time, some of the young people are interested in experimenting with image-based intimate digital communication. Further, gender differences in use and affectedness are also documented. In this way, orientations toward gender stereotypes “favor” both the attribution of responsibility to girls, and overlook the responsibility of students who perpetrated the boundary violation. The orientations of adolescents should be taken more into account in research as well as in educational programs for the prevention of sexual violence. (shrink)

Augmented Reality (AR) is commonly defined as a digital layer of information viewed on top of the physical world through a smartphone, tablet or eyewear. Increasingly, this understanding of AR is shifting to a dynamic framework of ‘smart things’, including wearable technology, sensors and artificial intelligence (AI), with the ability to intercede in key moments and to deliver contextual and meaningful experiences. The things that come into context are the logical next steps in an evolutionary development towards computers that are (...) better able to show empathy in relation to people: even more human-oriented, anticipative and ubiquitous. Thus, this outsourcing of meaning to empathic technologies points to one of the fundamental questions concerning the relation of human and technology – the nature of the trust that users place in technology. (shrink)

Der auf Kants kritischer Philosophie fußenden Philosophengeneration galt Herder als hoffnungslos anachronistischer, vorkritischer Philosoph, dessen Denken für das eigene philosophische Programm keine Relevanz zukomme. Das im folgenden dokumentierte Projekt geht demgegenüber von der Hypothese aus, daß Herder in die Vorgeschichte der Philosophie des deutschen Idealismus gehört, daß er Vorläufer und Weggenosse der nachkantischen Philosophengeneration war. Der vorliegende Band versammelt Arbeiten, die zur Begründung und Diskussion dieser Auffassung in unterschiedlicher Weise beitragen: es geht um die Konturierung der für diese Thematik relevanten (...) Aspekte von Herders eigenem Denken, um die Erschließung der gemeinsamen philosophischen und wissenschaftshistorischen Grundlagen des Herderschen Denkens und der Philosophie des deutschen Idealismus, nicht zuletzt geht es um die Erarbeitung der Rezeption von Herders Philosophie in der nachkantischen Philosophengeneration. (shrink)

This paper presents the contributions of Alcindo Flores Cabral, professor of Chemistry at the Faculdade de Agronomia Eliseu Maciel, nowadays part of the Universidade Federal de Pelotas, to chemistry teaching. It is a contribution almost unknown to the Brazilian chemical community, although recognized as valuable by several renowned chemists abroad, like W. Hückel, G. Charlot, F. Strong, E. Fessenden and others. Cabral’s innovative helical representation is presented in connection not only with contemporary representations, but also an incursion is made into (...) the first helical systems proposed, those of Hinrichs and of Baumhauer. Some comments are made not only on Cabral’s Classificação Natural dos Elementos, published in 1946, but also about other texts he wrote for an efficient chemistry teaching. (shrink)

Epistemic scoring rules are the en vogue tool for justifications of the probability norm and further norms of rational belief formation. They are different in kind and application from statistical scoring rules from which they arose. In the first part of the paper I argue that statistical scoring rules, properly understood, are in principle better suited to justify the probability norm than their epistemic brethren. Furthermore, I give a justification of the probability norm applying statistical scoring rules. In the second (...) part of the paper I give a variety of justifications of norms for rational belief formation employing statistical scoring rules. Furthermore, general properties of statistical scoring rules are investigated. Epistemic scoring rules feature as a useful technical tool for constructing statistical scoring rules. (shrink)