© 2016 Regents of the University of California.The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,062 new measurements from 721 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. All the particle properties and search limits are listed in Summary Tables. We also give numerous (...) tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 117 reviews are many that are new or heavily revised, including those on Pentaquarks and Inflation. The complete Review is published online in a journal and on the website of the Particle Data Group. The printed PDG Book contains the Summary Tables and all review articles but no longer includes the detailed tables from the Particle Listings. A Booklet with the Summary Tables and abbreviated versions of some of the review articles is also available. (shrink)

Philosophers of science don't very often discuss the place of mathematics between other sciences or the meaning of mathematics for other sciences. They consider mathematics as a formal language with mainly analytical statements about the use of symbols (Carnap, Russell, Ayer ). Originally Wittgenstein defended this formalistic interpretation of mathematics in his TLP. Gradually, however, he develops himself towards an intuitionistic and ontological position, in which mathematics is conceived as the central and therefore normative part of our thought (of course (...) : on what there is and how it is). Mathematical science plays the role of logic in relation to other sciences. Its universal applicability and efficiency are consequences of its creating beings on a necessary level, in virtue of the number of its relations (always still by substitution). This highly important philosophy of mathematics (misinterpreted by Crispin Wright) starts with his lectures in Cambridge (in the thirties ) and reaches its culmination in the Remarks on the Foundations of Mathematics and in On Certainty. In a second part this philosophical determination of mathematical reasoning is traced backwards through history. David Hume's contribution is reinterpreted from a new point of view. Inside the total field of our beliefs he distinguishes between different sciences with the critérium of the intricacy of relations between items of our knowledge field. The more and stronger these relations, the more forceful and necessary their influence on the remaining parts of the system of our belief. So mathematics is in the centre, the loose reveries of our fancy on the periphery. Quine's representation of ‘the tribunal of sense experience’, by which the total field should be judged and corrected, must be disqualified. Hume's dictum ‘Whatever we conceive, we conceive it to be existent’ reveals sharply that this evaluative and corrective role is performed by the necessary thoughts (or, if one likes it so, ‘realities’) of mathematical science. That reason and especially mathematical reason is the highest judge on the population and structure of our world and a very precious heritage of Pythagorism and Platonism. From the sources of Sextus Empiricus and Aristotle the author tries to reconstruct exactly the original assertion of Pythagoristic mathematical philosophy, which has nothing to do with a naive hypostazation of numbers or a kabbalistic number mysticism. Philolaos' saying, that some propositions are stronger than we, is demonstrated to refer to mathematical laws. The pythagorical position is fully integrated in Plato's dialectical philosophy. Mathematics is the great mediator towards the intuition of true being, the ‘metaxu’ between sensible phenomena and ideas. This tradition of philosophical taxation of mathematics as the ‘logic of science’ is broken by Aristotle, who didn't use mathematics in his qualitative natural science and considered mathematics as an abstract science (about the quantitative aspect of being). Moreover, he disowned its logical role and created a special science for this task. Human reason is mathematical in so far it is sure of its language and thought, which is excellently expressed by the Greek μαθηματιxα (= what can be understood, learned and taught) and by the Dutch word ‘wiskunde’ (= science of what is certain). The remarks and reflections of Wittgenstein have produced a new perspective on the placevalue (‘Stellenwert’) of mathematics among all possible sciences and beliefs and have proven that its onto-logical purport is an unavoidable implication. (shrink)

Overzicht van de invloed van klassieke auteurs op het werk van de Nederlandse wijsgeer.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Vertaling (verkorte versie) van en commentaar op de wijsgerige verhandeling van de Nederlandse filosoof (1632-1677) over de betekenis van het christendom.

In an almost forgotten passage of the Postenor Analytics (Bk I, ch. III) Aristotle argues against 'another school', according to which it is possible to proof things 'by each other and in a circle'. His logical refutation of this opinion became so dominant in the Western philosophical tradition, that the 'vicious circle' has always deemed a crime since. A scientific demonstration has to be built on firm premisses in order to deduce conclusions from them in a straight, ongoing proces, in (...) which one does not have to return to the premisses for a reconsideration of them on the basis of their implications. Although Aristotle does not mention names, he in fact reacts against Plato and the mainstream of Greek thought, which stresses the essential circularity of human argumentation. In the first, the historical part of the treatise the roots of this circular logic are unearthed in the work of Heraclitus and Parmenides, who both defended a ring structure of their metaphysical explication of nature. Truth is described as well-rounded, because you can follow it in a circle, passing through each of its links in turn, back to your startingpoint. The association of circular motion with thought is fully present in the work of Plato, who speeks many times about the 'periforas tès dianoias' and the essential interdependance of our ideas. Not the theory of an anonymous alternative school but Aristotle's own rectilinear formal logic was the exceptional, untraditional standpoint, which, moreover, was in conflict with his explication of divine thinking as 'noèsis noèseôs'. In modern times Hegel, Nietzsche and Heidegger were the main representatives of an anti-Aristotelian attitude. All three reject the logical prohibition of the circular argument, because it is inadequate to the life of concrete scientific thinking. The path of science always turns around towards its origins and results in a correction of its fundamental hypotheses on a higher level. Circularity is considered as a hallmark of sound logical procedure, as a characteristic of excellence in human understanding. The famous 'hermeneutic circle' is interpreted as the modern equivalent of the Hegelian 'Kreislauf and the Greek ' to par'allèlôn'. In the second, the more systematic part of the text the circular nature of our cognitive and scientific behaviour is demonstrated along three different lines. Reflection on the natural language with its finite stock of words, whose meanings are structurally connected, leads us to the so called semiotical circularity. Natural language is a complex network in which circular argumentation is not only unavoidable, but even the only means of explication. We have to work with the material contained in our dictionary, in which the items are defined by each other. The second reason is constituted by the system-orientation of science. In science we try to systematize our knowledge by means of formalisations and abstractions. The development of science can be characterised as a succession of systems, in which every element gets its meaning from the whole organisation. If we accept systematicity as the arbiter of truth, our logic is anti-fundamentalistic and the path of our thought is in fact circular (or better : spiralistic). The third adstruction of our theory is afforded by the coupling, that is realised in a rational proof. We draw conclusions from the coherence of our perceptions, from the reciprocal implications of our ideas. Never any of our ideas is without the repercussions of the movements elsewhere in the field. When we proof something, we also disproof and correct our startingpoints at the same time. The tradition of the circular nature of human thinking is very old, but not antiquated. The accusation of committing a fallacy in the case of circularity in normal and in scientific thinking is unfouded. It is now the formal logicians turn to defend his claim. (shrink)

Outside France the epistemology of G. Bachelard is unknown ; in France his influence is considerable, especially on philosophers like L. Althusser, M. Foucault, G. Canguilhem, J. Hyppolite, M. Serres, G. G. Granger, D. Lecourt and many others. Bachelard occupies a strategic point on the crossroads of all theoretical debates concerning science. The fact that he seems to give satisfactory answers on the problems which have risen after the breakdown of the logical-positivistic philosophy of science, justifies an exposition and evaluation (...) of his original contribution to philosophy. The author distinguishes the following items. 1. The determination of Bachelards philosophy as a scientific philosophy which is wedded to a history of the sciences, especially the natural sciences. 2. The 'systematicity' as the criterium of science against other, traditional, criteria like empiricalness, logical deducibility, correspondence with reality and so on. 3. The rectification-principle : the formation of a scientific system cannot be conceived otherwise than as the restructuring or reorganisation of the ruling system or system-sets. 4. The transformation of scientific knowledge shows many discontinuities in all its phases and branches. Bachelard calls them ruptures. 5. The translation of a theory into another, more coherent and comprehensive one, is baptised as a 'dialectisation' of the concept. By a dialectisation a system is both generalised and specified. Formal logic, which is based on identity and the principle of the excluded middle, is not able to interprete this dynamic aspect of scientific thinking. 6. Central in Bachelards philosophy is also the concept of recurrence. Each new organisation of the scientific system (global or partial) sheds new light on their history and their logical foundations. History has to be rewritten after each progress. Recurrence, however, also has systematic implications. Science always desimplifies its own evidences. 7. The scientist has to demolish the obstacles which he made himself by surcharging the content of the concepts not in use and by not assimilating them in the system. 8. Bachelards philosophy of science is both idealistic and realistic ; the phenomenology becomes phenomenotechnique under the hands and in the brains of the scientist. 9. He always denies (negativity) the earlier theories and objects by incorporating them in new relationships. 10. This constructive aspect of theory formation is the same in natural science and mathematics. Bachelard opposes the logical-positivistic idea that these are methodically dissimilar. In a critical commentary the author discusses the question of 'dialectical logic' in the sciences, in relation to some recent research in this field by I. Lakatos en Errol E. Harris. In his opinion the epistemology of Bachelard affords a creative renewal of the understanding of science, although further research is needed in many aspects. (shrink)

The traditional philosophical treatises on culture, who mostly started from neohumanistic inheritance, recently got a serious, though revolutionary partner for discussion in the person of Herbert Marcuse. The ideas, which this thinker launches on culture and society, are not loose propositions or emotionally determined interpretations, but form a structural theory, that earns further consideration. This article tries to give a survey of his opinions on this theme as well as a critical look at their suppositions and coherence. Eventually are discussed (...) Marcuse's concept of the prevailing culture as an affirmative culture, i.e. an attitude in which one accepts the existing social conditions and resigns to them. After that it discusses Marcuse's deepened interpretation of culture as a civilisation, in which the repression of the truely human needs and impulses is so to say institutionalised, and finally his matured judgement on the recovery of culture by means of the play-impulse and sufficient space for speculative and practical negation in a non-operational dimension. Retrospecting we stated that Marcuse is taking back now something of his original, marxistic aversion of the theoretical attitude, that is inaugured by the Greeks. One must also criticise his unilateral reviewing of the technical and social acquisitions of mankind. But his realising and objectifying of the old spiritual ideal of culture is no doubt a profit in relation to the neo-humanistic philosophy of culture. (shrink)