We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.

In this paper we consider a natural generalization of the Principle of Instantial Relevance and give a complete characterization of the probabilistic belief functions satisfying this principle as a family of discrete probability functions parameterized by a single real δ ∊ [0, 1).

As we owe the division of ecology into autecology and synecology to botanists, the arguments for this subdivision and also the definitions and contents of both subsciences as given bySchröter, Flahault &Schröter, Gams andDu Rietz are communicated in full. The same is the case with the division of ecology given by the zoologistsAdams andChapman. Moreover the opinions of these authors in this respect are critisized in detail as well as in their general aspects. This critique is connected with the author's (...) own positive opinion, which is given at the end of the paper, where also the remarks covered by the first two papers of this series are summarised.In ecology as a biological science either the individual or the complex of individuals has to occupy a central position. Therefore science about the environment, especially the abiotic one, as well as science about a definite region or spot of the earth ought not to be incorporated in biology.In autecology the individual occupies a central position, it is one of the subsciences of idiobiology, it is a science about the relations to environment, taken in the broadest sense. Dependent upon the contents of this we have many definitions of ecology, the most important ones being: 1) ecology is a biogeographical subscience; 2) ecology is taken in the sense of ethology; 3) ecology is taken as a science of the teleological relations of the individual to its environment and the objects in it, thus of the non-causal relations, the causal ones being assigned to physiology. These non-causal relations appear under four aspects, all called teleological, i.e. the true purpose-notion, relation in the sense of requirement, that in the sense of wholeness, and of adaptation and the degree of adaptation. Adaptation is taken in a broad sense, covering as well the degree of adaptation , as the latitude of the possibility of adaptation and the degree of variability of the individual to adapt itself. The proposal is made to confine the term autecology to this teleological aspect of the relations of the individual, i.e. of all its characters, not of the epharmonic ones only, to environment.In synecology the complex of individuals, showing direct real connections during individual life, occupies a central position, with equal scientific interest for all members of the complex. Synecology contains all biological scientific contents about this matter. The application ofTschulok's system of subsciences to synecology is critisized and the development of the system of these subsciences is left to its developmental fate in time. Considering the importance of the knowledge of the tendencies of thought for the development of synecology an attempt is made to state those already applied in synecology; author distinguishes the systematical, the mathematical, the causal, the historical, the teleological and the essential tendency of thought. Also the difference in the tendencies of thought shows that autecology and synecology are to be separated in a logical system of biological subsciences.Puisque c'est aux botanistes que nous devons la division de l'écologie en autécologie et synécologie, l'auteur passe en revue tous les arguments qui ont amené les biologistes à faire cette subdivision, ainsi que les définitions de ces deux subsciences et les matières qu'elles comprennent, comme elles sont données parSchröter, Flahault &Schröter, Gams etdu Rietz. Il en fait de même pour la division de l'écologie faite par les zoologistesAdams etChapman. En outre il discute les opinions de ces auteurs sous ce rapport, dans leurs détails aussi bien que dans leurs aspects généraux. Cette discussion est en rapport avec l'opinion positive de l'auteur, qu'il expose à la fin de l'article, où se trouvent résumées également les remarques qui se trouvaient déjà dans les deux premiers articles de cette série.Dans l'écologie, en tant que science biologique, l'individu — ou bien l'ensemble des individus — doit occuper une position centrale. C'est pourquoi ni la science qui concerne le milieu, en particulier le milieu abiotique, ni la science qui se rapporte à une région ou un endroit défini de la terre, ne devrait être incorporée dans la biologie.Dans l'autécologie l'individu occupe une position centrale. Cette science est une des subsciences de l'idiobiologie; elle se rapporte aux relations entre le sujet et son milieu — „milieu” pris dans le sens le plus large du mot. Selon les significations diverses qu'on peut attacher aux termes „relations” et „milieu”, nous avons plusieurs définitions de l'écologie, parmi lesquelles les plus importantes suivent ci-dessous:1)L'écologie est une subscience biogéographique; 2) le terme „écologie” est pris dans le sens d'éthologie; 3) l'écologie est considérée comme la science des relations téléologiques entre l'individu et son milieu et les objets se trouvant dans ce milieu; elle est donc considérée comme la science des relations non-causales, les relations causales étant conférées à la physiologie. Ces relations non-causales se présentent sous quatre aspects, tous appelés téléologiques, c. à. d. la vraie notion de but, les relations dans le sens de besoins, les relations dans le sens de „tout” et les relations dans le sens d'adaptation et de degré d'adaptation.Le mot „adaptation” est pris dans un sens étendu, comprenant aussi bien le degré d'adaptation que l'amplitude de la possibilité d'adaptation et le degré de variabilité dans l'adaptation de l'individu à son milieu. L'auteur propose de restreindre le terme „autécologie” à cet aspect téléologique des relations entre l'individu et son milieu; il s'agit ici, bien entendu, de toutes les qualités de l'individu et non seulement des qualités epharmoniques.Dans la synécologie l'ensemble des individus montrant des rapports directs et réels durant la vie individuelle occupe une position centrale et offre un intérêt scientifique pareil pour tous les membres de l'ensemble. La synécologie comprend tout ce qu'il y a à dire sur cette matière par rapport à la science biologique. L'application du système des subsciences deTschulok à la synécologie est critiquée par l'auteur, qui juge prématuré de s'occuper déjà d'un tel système de subsciences: l'avenir seul nous apprendra quel système se développera ici. Vu l'importance d'une connaissance exacte des différentes tendances de penser pour le développement de la synécologie, l'auteur s'efforce de rassembler celles qui ont déjà été appliquées dans la synécologie; il distingue les tendances de penser systématique, mathématique, causale, historique, téléologique et essentielle . En outre les différences entre ces tendances de penser démontrent, que l'autécologie et la synécologie doivent être séparées dans un système logique de subsciences biologiques. (shrink)

One of the most extensive yet least conclusive methodological debates within religious studies revolves around the question of what, precisely, the phenomenology of religion is and what contribution it can make to the study of religion. I do not intend to answer this important question here. To do so satisfactorily would require a range of historical, philosophical and methodological inquiry which would go quite beyond the bounds of a single article. My intention in this paper is, by comparison, unambitious. It (...) is to take one view of what phenomenology of religion is and to consider an area outside that usually explored by students of religion which can, nonetheless, shed some light on how religions might be studied in a way which is in accordance with the phenomenology of religion so understood. What follows will offer an answer to the question of what contribution one particular understanding of phenomenology might make to the study of religion, but no attempt will be made to establish whether or not this particular understanding ought to be regarded as normative. (shrink)

This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, (...) the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties). (shrink)

C. J. F. Williams; VI*—Is Identity a Relation?, Proceedings of the Aristotelian Society, Volume 80, Issue 1, 1 June 1980, Pages 81–100, https://doi.org/10.1093/.

In a discussion-note in Mind, Father P. M. Farrell, O.P., gave an account, in what he admitted to be an embarrassingly brief compass, of the Thomist doctrine concerning evil. There is one sentence in this discussion which at first glance appears paradoxical. Father Farrell has been arguing that a universe containing ‘corruptible good’ as well as incorruptible is better than one containing ‘incorruptible good’ only. He continues: ‘If, however, they are to manifest this corruptible good, they must be corruptible and (...) they must sometimes corrupt.’ The final words, despite Father Farrell's italics, strike one as expressing, not a self-evident truth, but a non sequitur. The fact that I am capable of committing murder does not entail that I will at some time commit it. It is not immediately obvious that a similar entailment holds in the case of corruption and corruptibility. (shrink)