INTRODUCTION In ita original form the present paper was presented to the American Mathematical Society, April 2k,, as a companion piece to the writer's ...

We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV)), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP, APP, MA, AM) in PV₁ + dWPHP(PV).

We investigate the substitution Frege () proof system and its relationship to extended Frege () in the context of modal and superintuitionistic propositional logics. We show that is p-equivalent to tree-like , and we develop a “normal form” for -proofs. We establish connections between for a logic L, and for certain bimodal expansions of L.We then turn attention to specific families of modal and si logics. We prove p-equivalence of and for all extensions of , all tabular logics, all logics (...) of finite depth and width, and typical examples of logics of finite width and infinite depth. In most cases, we actually show an equivalence with the usual system for classical logic with respect to a naturally defined translation.On the other hand, we establish exponential speed-up of over for all modal and si logics of infinite branching, extending recent lower bounds by P. Hrubeš. We develop a model-theoretical characterization of maximal logics of infinite branching to prove this result. (shrink)

Das Buch erkundet Wege und Umwege des Gedachtnisses in Philosophie und erzahlender Literatur. Es fragt nach der existentiellen Bedeutung der Erinnerung: Wieso verlangt der Mensch nach Erinnerung? Wonach strebt die Suche nach der verlorenen Zeit? Lebenserinnerung verfolgt ein zweifaches Ziel: die zerrinnende Zeit anzuhalten und sich in seinem Leben gegenwartig zu werden. Sie wehrt sich gegen das Vergehen und Vergessen, in ihr sucht der Mensch sich zu finden und sich uber sein Leben zu verstandigen. Erinnerung vollzieht sich in mannigfachen Formen. (...) Das Vergangene kann in spontanen Bildern wiederkehren oder verschlossen sein und sich nur der beharrlichen Arbeit des Gedachtnisses offnen; Erinnerungen konnen in Leidenserfahrungen und in Glucksversprechen wurzeln. Sich erinnern entspricht einem ursprunglichen Bedurfnis der Menschen und geht ein in den Vollzug eines gelingenden Lebens. (shrink)

We show how to formalize approximate counting via hash functions in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several applications, including a proof of the tournament principle, and an improvement on the known relationship of the collapse of the bounded arithmetic hierarchy to the collapse of the polynomial-time hierarchy.

1. Fichtes idealismus und die geschichte. Rechtsphilosophie. Hegel in seinem verhältnis zur weltanschaung der aufklärung. Gibt es einen "Primat der praktischen vernunft" in der logik?--2. Die logik der philosophie und die kategorienlehre. Die lehre vom urteil.--3. Platon. Zum system der logik. Zum system der wissenschaften.

Excerpt from Rechtsphilosophie Fast samtliche Anhanger absoluter rechtsphilosophischer Wertprinzipien im neunzehnten Jahrhundert so z. B. Stahl, Trendelenburg, Lasson haben den Empirismus auf sich wirken lassen und eine Versohnung der Spekulation mit der positiven Rechtswissenschaft zum mindesten angestrebt. In neuester Zeit hat vor allem Stammler die Einordnung des Rechts in absolute Zweckzusammenhange mit der Ansicht zu vereinigen gewusst, dass die formale Gesetzmassigkeit oder gegenstandliche Richtig keit lediglich einen Massstab fur oder eine unbedingte Anforde rung an das Recht, ein Ziel fur den (...) Gesetzgeber, nicht aber eine ausserlich verbindliche Norm fur das Zusammenleben der Menschen bedeuten kann. So erfullt die kritische Wertspekulation die Forderung Bergbohms, Philosophie des positiven Rechts zu sein. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.". (shrink)

We develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of the Blok–Esakia (...) theorem and the theory of modal companions to systems of multiple-conclusion rules or (finitary structural global) consequence relations, and a characterization of splittings in the lattices of consequence relations over monomodal or superintuitionistic logics with the finite model property. (shrink)

It has been argued that there is a genuine conflict between the views of geometry defended by Hume in the Treatise and in the Enquiry: while the former work attributes to geometry a different status from that of arithmetic and algebra, the latter attempts to restore its status as an exact and certain science. A closer reading of Hume shows that, in fact, there is no conflict between the two works with respect to geometry. The key to understanding Hume's view (...) of geometry is the distinction he draws between two standards of equality in extension. (shrink)

Until the issue of Altheim's book Roemische Religionsgeschichte there was little doubt about the correctness of Wissowa's view that the two groups of the diindigetes and the di novensides combined with each other represent the whole of theRoman pantheon, the di indigetes being the old, indigenous deities of the Roman people, inherited so to speak from the days of Romulus, the di novensides the new deities, imported in historical times from foreign peoples. This view has now been abandoned, owing to (...) Altheim's arguments. Besides this, Altheim and later C. Koch have proved that the proximity of the expressions divi novensiles and di indigetes in Livy's report about the devotio of P. Decius Mus does not in itself justify the conclusion that the di indigetes and the di novensides are linked together in such a manner that the solution of the problem of one group involves that of the other. Hence the questions arise, first, what is the nature of the di novensides or of the di indigetes, and whether either of these questions has been satisfactorily answered; secondly, is it possible to establish any relationship between these two groups of deities, and can such a relation be usedas a starting-point from which to investigate the nature of the other group? In choosing this line of research it seems to me that an attempt to solve the problem of the novensides rather than that of the indigetes promises greater success. I shall, therefore, treat the di novensides in the first part of this paper. (shrink)