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 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)

Timothy Michael Fowler has argued that, as a consequence of their commitment to neutrality in regard to comprehensive doctrines, political liberals face a dilemma. In essence, the dilemma for political liberals is that either they have to give up their commitment to neutrality (which is an indispensible part of their view), or they have to allow harm to children. Fowler’s case for this dilemma depends on ascribing to political liberals a view which grants parents a great degree of freedom in (...) deciding on the education of their children. I show that ascribing this view to political liberals rests upon a misinterpretation of political liberalism. Since political liberals have access to reasons based upon the interests of children, they need not yield to parent’s wishes about the education of their children. A correct understanding of political liberalism thus shows that political liberals do not face the dilemma envisaged by Fowler. (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)

Mixed strategies have been used to show that Pascal’s Wager fails to offer sufficient pragmatic reasons for believing in God. Their proponents have argued that, in addition to outright belief in God, rational agents can follow alternatives strategies whose expected utility is infinite as well. One objection that has been raised against this way of blocking Pascal’s Wager is that applying a mixed strategy in Pascal’s case is tantamount to applying an iterated mixed strategy which, properly understood, collapses into the (...) pure strategy of becoming a theist. I argue that since the assumptions used to develop the iterated mixed strategies response are even more questionable than those the initial objection relies on, this type of response to the mixed strategy objection fails. (shrink)

We study the extension 123) of the theory S21 by instances of the dual weak pigeonhole principle for p-time functions, dWPHPx2x. We propose a natural framework for formalization of randomized algorithms in bounded arithmetic, and use it to provide a strengthening of Wilkie's witnessing theorem for S21+dWPHP. We construct a propositional proof system WF , which captures the Π1b-consequences of S21+dWPHP. We also show that WF p-simulates the Unstructured Extended Nullstellensatz proof system of Buss et al. 256). We prove that (...) dWPHP is equivalent to a statement asserting the existence of a family of Boolean functions with exponential circuit complexity. Building on this result, we formalize the Nisan–Wigderson construction in a conservative extension of S21+dWPHP. (shrink)

We prove that the sharply bounded arithmetic T02 in a language containing the function symbol ⌊x /2y⌋ is equivalent to PV1.

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)

Name der Zeitschrift: Deutsche Zeitschrift für Philosophie Jahrgang: 64 Heft: 1 Seiten: 132-139.

We prove that all axiomatic extensions of the full Lambek calculus with exchange can be axiomatized by formulas on the level of the substructural hierarchy.

Cognitive Science, Volume 46, Issue 9, September 2022.

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.

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)

Why are children better language learners than adults despite being worse at a range of other cognitive tasks? Here, we explore the role of multiword sequences in explaining L1–L2 differences in learning. In particular, we propose that children and adults differ in their reliance on such multiword units in learning, and that this difference affects learning strategies and outcomes, and leads to difficulty in learning certain grammatical relations. In the first part, we review recent findings that suggest that MWUs play (...) a facilitative role in learning. We then discuss the implications of these findings for L1–L2 differences: We hypothesize that adults are both less likely to extract MWUs and less capable of benefiting from them in the process of learning. In the next section, we draw on psycholinguistic, developmental, and computational findings to support these predictions. We end with a discussion of the relation between this proposal and other accounts of L1–L2 difficulty. (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)

IN THE PREFACE to his Philosophy of Right Hegel writes: "Was vernünftig ist, das ist wirklich; und was wirklich ist, das ist vernünftig"--"What is rational is actual, and what is actual is rational." In paragraph 6 of the third edition of his Encyclopedia of Philosophical Sciences he repeats this statement verbatim, calling it "simple." Few interpreters, however, have ever found it so. Even friendly critics are baffled; hostile ones dismiss it as either scandalous or senseless. Two centuries after Hegel's birth (...) there is thus still room for a modest exposition of the meaning of this famous Hegelian statement, much more so for one of its "simplicity." Both tasks, however--and in particular the second, seemingly hopeless one--should be undertaken in full awareness of two conditions which the Encyclopedia passage considers evident but which can be taken as such no longer. One is possession of "religion." The other is the kind of philosophical "culture" which includes "knowledge" of "God.". (shrink)

Die Frage nach dem Ursprung hat die Menschen in allen Kulturen und Epochen beschäftigt. In besonderer Weise bestimmt sie das Denken der Philosophie, das nach klassischem Verständnis der Erforschung der ersten Ursachen und Prinzipien gilt. Es schließt darin an die Fragerichtung des Mythos an, der seinerseits von ersten Anfängen und Gründen berichtet. Auch außerhalb der Philosophie, in Wissenschaften, Weltbildern und Religionen, in Theorien der Natur und der Geschichte, bilden Vorstellungen vom Ursprung in vielfachen Abwandlungen Leitideen des Fragens und der Orientierung. (...) Die Frage nach dem Ursprung ist nicht auf eine Frage zu reduzieren und nicht durch eine Auskunft zu beantworten. Sie gehört in den Kreis jener offenen Fragen, die das Denken nach Kant nicht beantworten, aber ebenso wenig abweisen kann. Die vorliegenden Aufsätze bieten Diskussionsmaterial zur Heterogenität der Fragestellungen und reflektieren das Spannungsverhältnis, das dem Ursprungsbezug insgesamt innewohnt. (shrink)

"Jewish Philosophy and the Academy reflects in broad terms on the current state of Jewish philosophy in the university. This generation of university teachers lives at a unique historic junction. It is the last to be taught by the giants of European Wissenschaft des Judentums and the first to experience the remarkable expansion of Judaic scholarship in Israel and abroad." "Emil Fackenheim suggests that if we are indebted to Athens for the philosophical method, we are also indebted to Jerusalem (...) for the ethical content of philosophy, which is both an intellectual and a moral challenge. This dual challenge shapes the diverse papers in this volume."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved. (shrink)

In this article, Emil Sætra examines how teachers and students construct and experience aims and goods in classroom discussions of controversial issues. This study is situated within the emerging tradition of empirical ethics, and the research strategy comprised two main steps. First, Sætra used interview data to analyze, via the experiences of teachers and students, the following two empirical questions: (1) What goods normatively constitute educative discussions of controversial issues? (2) How are these goods constructed in time and space? (...) Second, in the concluding discussion, Sætra makes explicit some normative implications of the empirical findings and discusses theses in relation to previous research. In brief, what emerges from the conjoined experiences of teachers and students is the notion that practice comprises multiple aims and drives. Moreover, because aims and drives are multiple, decisions regarding priorities will sometimes have to be made, and teachers may be subject to conflicting expectations. This means that practitioners must be able to make reflective judgments about what comprises acceptable ends, what projects should be undertaken to achieve those ends, and what actions ought to be performed as part of those projects. (shrink)