We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause source of the ellipsis, our analysis requires no such hidden ambiguity. Further, the analysis follows relatively directly from an abstract statement of the ellipsis interpretation problem. It predicts correctly a wide range of interactions between ellipsis and other semantic phenomena such as quantifier scope and bound anaphora. Finally, although the (...) analysis itself is stated nonprocedurally, it admits of a direct computational method for generating interpretations. (shrink)
Systematic semantic ambiguities result from the interaction of the two operations that are involved in resolving ellipsis in the presence of scoping elements such as quantifiers and intensional operators: scope determination for the scoping elements and resolution of the elided relation. A variety of problematic examples previously noted - by Sag, Hirschbüihler, Gawron and Peters, Harper, and others - all have to do with such interactions. In previous work, we showed how ellipsis resolution can be stated and solved in equational (...) terms. Furthermore, this equational analysis of ellipsis provides a uniform framework in which interactions between ellipsis resolution and scope determination can be captured. As a consequence, an account of the problematic examples follows directly from the equational method. The goal of this paper is merely to point out this pleasant aspect of the equational analysis, through its application to these cases. No new analytical methods or associated formalism are presented, with the exception of a straightforward extension of the equational method to intensional logic. (shrink)
For each natural number n, let C (n) be the closed and unbounded proper class of ordinals α such that V α is a Σ n elementary substructure of V. We say that κ is a C (n) -cardinal if it is the critical point of an elementary embedding j : V → M, M transitive, with j(κ) in C (n). By analyzing the notion of C (n)-cardinal at various levels of the usual hierarchy of large cardinal principles we show (...) that, starting at the level of superstrong cardinals and up to the level of rank-into-rank embeddings, C (n)-cardinals form a much finer hierarchy. The naturalness of the notion of C (n)-cardinal is exemplified by showing that the existence of C (n)-extendible cardinals is equivalent to simple reflection principles for classes of structures, which generalize the notions of supercompact and extendible cardinals. Moreover, building on results of Bagaria et al. (2010), we give new characterizations of Vopeňka’s Principle in terms of C (n)-extendible cardinals. (shrink)
The C (n)-cardinals were introduced recently by Bagaria and are strong forms of the usual large cardinals. For a wide range of large cardinal notions, Bagaria has shown that the consistency of the corresponding C (n)-versions follows from the existence of rank-into-rank elementary embeddings. In this article, we further study the C (n)-hierarchies of tall, strong, superstrong, supercompact, and extendible cardinals, giving some improved consistency bounds while, at the same time, addressing questions which had been left open. In addition, we (...) consider two cases which were not dealt with by Bagaria; namely, C (n)-Woodin and C (n)-strongly compact cardinals, for which we provide characterizations in terms of their ordinary counterparts. Finally, we give a brief account on the interaction of C (n)-cardinals with the forcing machinery. (shrink)
We review the equivalence of the two-flavor Skyrme-Witten model and the two-flavor large-N c quark model. The claimed equivalence for three flavorsbetween these two models is shown to be incorrectly given in the literature, and the properly equivalent extended three-flavor large-N c quark model is constructed and discussed.
This addendum to  shows that the set of tautological quantum logical propositional formulas for a finite dimensional vector space Cⁿ is different for every n, affirmatively answering a question posed therein.
Spade 1988 sugges t s tha t t he r e are ac tua l l y two theo r i e s t o address t h i s ques t i o n t o , an ear l y one and a l a t e r one . 2 Most o f the presen t pape r i s a deve l o pmen t o f t h i s i dea . I sugges t (...) tha t ear l y work by Sherwood and o the r s was a s tudy o f quan t i f i e r s : the i r semant i c s and t he e f f e c t s o f con t e x t on i n f e r e n ce s t ha t can be made f r om quan t i f i e d te rms . La te r , i n the hands o f Bur l e y and o the r s , i t changed i n t o a s tudy o f someth i n g e l se , a s tudy o f what I ca l l g loba l quan t i f i c a t i o n a l e f f e c t . In sec t i o n 1 , I exp l a i n what these two op t i o n s are. (shrink)
Professor N. G. L. Hammond has of late published some of his thoughts on the activities of Philip II in 347 and 346 B.C. In addition he has treated aspects of Philip's earlier involvement in Thessalian, Thracian, and Phokian affairs. In the process he has in many instances disagreed with a number of current findings. Among those challenged are some of mine. Healthy scholarly debate is always desirable, and in this f spirit I should welcome an opportunity to contest Professor (...) Hammond's views on several points, the most important being the basic factor of methodology and the interpretation of various factual details. (shrink)
Publié en 1962, le livre de Charles N.R. McCoy, intitulé The Structure of Political Thought, demeure un travail important, encore qu’oublié, sur l’histoire de la philosophie politique. Bien que l’ouvrage ait reçu de bonnes appréciations, il n’existe pas encore d’examen critique de son traitement de la théorie politique médiévale. Dans le présent article, j’explore la structure de son argument dans les deux chapitres sur la pensée médiévale, en montrant comment McCoy centre sa discussion sur une investigation des différentes méthodes interprétatives (...) qu’emploient Thomas d’Aquin et Marsile de Padoue en lisant Aristote. Il le fait dans le dessein de déterminer comment l’enseignement aristotélicien - touchant la structure de la pensée politique - est le mieux préservé par la Révélation. (shrink)
Instead of the existential quantifier Bernard Bolzano uses his notion of Gegenständlichkeit einer Vorstellung an sich . This approach makes it possible for him to solve the traditional problem of the predication of existence in accordance with an approach common today, namely to take existence to be primarily a property of a corresponding representation in itself, and not a characteristic of individuals. However, Bolzano considers a property of real existence to be attributable also to particular individuals, which is essentially different (...) from the usual practice. (shrink)