Let L be a finite relational language. The age of a structure M over L is the set of isomorphism types of finite substructures of M. We classify those ages U for which there are less than 2ω countably infinite pairwise nonisomorphic L-structures of age U.

0-categorical o-minimal structures were completely described by Pillay and Steinhorn 565–592), and are essentially built up from copies of the rationals as an ordered set by ‘cutting and copying’. Here we investigate the possible structures which an 0-categorical weakly o-minimal set may carry, and find that there are some rather more interesting examples. We show that even here the possibilities are limited. We subdivide our study into the following principal cases: the structure is 1-indiscernible, in which case all possibilities are (...) classified up to binary structure; the structure is 2-indiscernible, classified up to ternary structure; the structure is 3-indiscernible, in which case we show that it is k-indiscernible for every finite k. We also make some remarks about the possible structures of higher arities which an 0-categorical weakly o-minimal structure may carry. (shrink)

A countably infinite relational structure M is called absolutely ubiquitous if the following holds: whenever N is a countably infinite structure, and M and N have the same isomorphism types of finite induced substructures, there is an isomorphism from M to N. Here a characterisation is given of absolutely ubiquitous structures over languages with finitely many relation symbols. A corresponding result is proved for uncountable structures.

Originally published in 1936, this book presents the ancient Greek text of the paraphrases and quotations of Zeno's philosophical arguments, together with a facing-page English translation and editorial commentary. Detailed notes are incorporated throughout and a bibliography is also included. This book will be of value to anyone with an interest in Zeno and ancient philosophy.

It is demonstrated that neither the arguments leading to inconsistencies in the description of quantum-mechanical measurement nor those “explaining” the process of measurement by means of thermodynamical statistics are valid. Instead, it is argued that the probability interpretation is compatible with an objective interpretation of the wave function.

The program of a physical concept of information is outlined in the framework of quantum theory. A proposal is made for how to avoid the intuitive introduction of observables. The conventional and the Everett interpretations in principle may lead to different dynamical consequences. An ensemble description occurs without the introduction of an abstract concept of information.

If I were asked to put forward an ethical principle which I considered to be especially certain, it would be that no one can be responsible, in the properly ethical sense, for the conduct of another. Responsibility belongs essentially to the individual. The implications of this principle are much more far-reaching than is evident at first, and reflection upon them may lead many to withdraw the assent which they might otherwise be very ready to accord to this view of responsibility. (...) But if the difficulties do appear to be insurmountable, and that, very certainly, does not seem to me to be the case, then the proper procedure will be, not to revert to the barbarous notion of collective or group responsibility, but to give up altogether the view that we are accountable in any distinctively moral sense. (shrink)

The development of transplantation technology increasingly places before society a multitude of diverse, complex ethical and legal problems. The subject is the more complex because of the various divergent interests involved. There are the interests of the donor of organs, who has a right to protection of his legal position, and those of the patient in need of an often lifesaving organ. There are also the interests of the donor’s relatives, after his death, and those of the transplantation surgeons. The (...) international dimension of transplantation technology makes the picture even more complicated. Though this article is devoted to the European situation, the problems are similar all over the world. (shrink)

The development of transplantation technology increasingly places before society a multitude of diverse, complex ethical and legal problems. The subject is the more complex because of the various divergent interests involved. There are the interests of the donor of organs, who has a right to protection of his legal position, and those of the patient in need of an often lifesaving organ. There are also the interests of the donor’s relatives, after his death, and those of the transplantation surgeons. The (...) international dimension of transplantation technology makes the picture even more complicated. Though this article is devoted to the European situation, the problems are similar all over the world. (shrink)

The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double interpretation of the state vector as a representation of physical states as well as ofinformation about physical states. The concept of relevance being used in all statistical theories of irreversible thermodynamics is demonstrated to be based on the same observer-relatedness. Quantum theories of irreversible processes implicitly use an objectivized process (...) of state vector reduction. The conditions for the reduction are discussed, and it is concluded that the final (subjective) observer system may be carried by a space point. (shrink)

The object of this paper is to show the predominance of the influence of geometrical ideas in Aristotle's account of first principles in the Posterior Analytics— to show that his analysis of first principles is in its essentials an analysis of the first principles of geometry as he conceived them. My proof of this falls into two parts. I. A consideration of the parallel between Aristotle's and Euclid's account of first principles. II. A comparison between the general movement of thought (...) in the Aristotelian παγωγ and πδειξις and in the δινοια and νησις of the Platonic dialectic. (shrink)

The problem which I propose to consider is not whether the distinctions past, present, future, characterize the form of time in such a way that whatever may be true concerning the reality of one of these characteristics must be equally true of the others, but the more particular question of the kind of existence which belongs to the content of the past, or its constituents as events.

The interpretations of measurements in Bohm's and Everett's quantum theories are compared. Since both theories are based on the assumption of a universally valid Schrödinger equation, they face the common problem of how to explain that arrow of time, which in conventional quantum theory is represented by the collapse of the wave function. Its solution requires, in a statistical sense, a very improbable initial condition for thetotal wave function of the universe. The historical importance of Bohm's quantum theory is pointed (...) out. (shrink)

Dans ce volume considérable, on été réunies les contributions d'un Congrès international tenu à Louvain en 1998 pour marquer l'achèvement de la première édition de la Théologie Platonicienne de Proclus. Ces contributions, toutes rigoureusement centrées sur la Théol. Plat. concernent (1) les principes et les sources de la Théol. plat. (2) Les méthodes théologiques de Proclus (3) La postérité de la Théol. plat. dans le monde grec, païen comme chrétien, et dans le monde islamique. Des indices très détaillés permettent de (...) retrouver tous les passages cités et commentés dans ce volume. (shrink)

The excursus of Thucydides on the last years of Pausanias and Themistocles is remarkable for its simple, rapid-flowing style, its storytelling tone, its wealth of personal ancedote, its marked deviation from his normally strict criteria of relevance. These characteristics, which give the excursus a Herodotean flavour, have often been noted by modern scholars, but until recently acceptance of its general credibility has been widespread, and indeed, with one important exception, which seems to have created very little impression almost unchallenged.

Although the decision of Pericles to abandon Attica to devastation in 431 has often been severely criticized, the conviction of Thucydides that his defensive strategy was sound has been widely accepted during the last half-century. On the other hand, the offensive side of his strategic plan, consisting mainly of using his fleet to raid coastal districts of the Peloponnese, has tended to be dismissed as unimportant by modern writers, while a few have condemned it as pointless and wasteful. Because Thucydides (...) devotes so little space to these raids, it is tempting to regard them as minor operations, but his careful record of the naval and military resources engaged, together with his statement that the force which Pericles commanded in 430 was approximately equal to that sent to Sicily in 415 , shows that they were on a substantial scale. Their influence upon the course of the war was slight, but if Periclean strategy is to be fully appreciated, it is clearly important to inquire why they were undertaken. (shrink)

It was at one time almost universally believed, and is still believed by some scholars, that Thucydides cannot have written his account of the Pentekontaetia before his return from exile because he refers in it to the of Hellanicus, in which an event belonging to the year 407/6 was mentioned. This argument in favour of a late date for the composition of the excursus has been disputed and is now much less widely supported. It has been suggested that the reference (...) to Hellanicus in 97. 2, or the whole of that section, was added by Thucydides to a part of his work written much earlier, or that an edition of the including an account of the Pentekontaetia may have been published long before 406 and the work have been subsequently continued. (shrink)

It is argued by means of analogy with certain irreversible processes that a symmetry-violating vacuum need not necessarily be explained by a special cosmic initial condition.

The object of this paper is to show the predominance of the influence of geometrical ideas in Aristotle's account of first principles in the Posterior Analytics— to show that his analysis of first principles is in its essentials an analysis of the first principles of geometry as he conceived them. My proof of this falls into two parts. I. A consideration of the parallel between Aristotle's and Euclid's account of first principles. II. A comparison between the general movement of thought (...) in the Aristotelian παγωγ and πδειξις and in the δινοια and νησις of the Platonic dialectic. (shrink)

Rosamond Kent Sprague’s translations of the _Laches and Charmides_ are highly regarded, and relied on, for their lucidity and philosophical acuity. This edition includes notes by Sprague and an updated bibliography.

If $G$ is a group with a supersimple theory having a finite $SU$-rank, then the subgroup of $G$ generated by all of its normal nilpotent subgroups is definable and nilpotent. This answers a question asked by Elwes, Jaligot, Macpherson and Ryten. If $H$ is any group with a supersimple theory, then the subgroup of $H$ generated by all of its normal soluble subgroups is definable and soluble.

1. Introduction. Logique.--2. Cosmologie.