Bilder gehören zu den ältesten Zeugnissen der menschlichen Kultur. Sie sind, soweit bekannt, wesentlich älter als jede Form des sprachlich vermittelten diskursiven Denkens. Bereits dieser historische Umstand markiert die Bilder als etwas Vortheoretisches. Philosophische Theorien über Bilder stützen von Beginn an diese geschichtliche Kontingenz. Die Bildtheorie verdankt Platon die bis in unsere Tage überaus wirksame Denkposition, dass sich Bilder primär an die Sinnlichkeit wenden und nicht an den Verstand. Eine alte Feindschaft - die zwischen Sprache und Bild, dem Diskursiven und (...) Nicht-Diskursiven oder dem Propositionalen und Nicht-Propositionalen - wurde im Laufe der Zeit von disparat bestehenden philosophischen Traditionen erhärtet. Die seit Anfang der 90er Jahre des 20. Jh. s immer intensiver betriebene Bildtheorie konzentriert sich ebenfalls auf das, was Bilder von der Sprache trennt. Im folgenden wird dagegen jener Aspekt hervorgehoben, den Bilder mit der Sprache gemeinsam haben. Bilder sind wie sprachliche Äußerungen in erster Linie äußerst flexible und vielseitig einsetzbare Werkzeuge. Die Frage nach ihrer Bedeutung gleicht der Frage nach ihrem Gebrauch durch die Menschen. (shrink)

We prove that a variant of Robinson arithmetic $\mathsf{Q}$ with nontotal operations is interpretable in the theory of concatenation $\mathsf{TC}$ introduced by A. Grzegorczyk. Since $\mathsf{Q}$ is known to be interpretable in that nontotal variant, our result gives a positive answer to the problem whether $\mathsf{Q}$ is interpretable in $\mathsf{TC}$. An immediate consequence is essential undecidability of $\mathsf{TC}$.

A modal theory Z using the Guaspari witness comparison signs $\leq, is developed. The theory Z is similar to, but weaker than, the theory R of Guaspari and Solovay. Nevertheless, Z proves the independence of the Rosser fixed-point. A Kripke semantics for Z is presented and some arithmetical interpretations of Z are investigated. Then Z is enriched to ZI by adding a new modality sign for interpretability and by axioms expressing some facts about interpretability of theories. Two arithmetical interpretations of (...) ZI are presented. The proofs of the validity of the axioms of ZI in arithmetical interpretations use some strengthening of Solovay's result about interpretability in Godel-Bernays set theory. (shrink)

A Kripke-style semantics developed by de Jongh and Veltman is used to investigate relations between several extensions of interpretability logic, IL.

With the passing of disputations between Jewish and Christian thinkers as to whose tradition has a more universal ethics, the task of Jewish and Christian ethicists is to constitute a universal horizon for their respective bodies of ethics, both of which are essentially particularistic being rooted in special revelation. This parallel project must avoid relativism that is essentially anti-ethical, and triumphalism that proposes an imperialist ethos. A retrieval of the idea of natural law in each respective tradition enables the constitution (...) of some intelligent common ground for ethical cooperation in both theory and practice between the traditions. This essay also suggests how the constitution of this common ground could include Muslims as well. The constitution of this common ground enables religious ethicists to present more cogent ethical arguments in secular space, but only of course, when those who now control secular space are open to arguments from members of any religious tradition. (shrink)

The decision problem for provability logic remains PSPACE-complete even if the number of propositional atoms is restricted to one.

: An analysis of traditional Jewish texts yields neither the capitalist notion of medicine nor the socialist one. Neither alternative is sufficient to ground the respect for the sanctity of the human person as a being created in the image of God that is so rationally appealing. That is why the Jewish ethical tradition, which is based on this respect for the sanctity of human personhood, both individual and collective, is so attractive—if only for its insights, rather than its authority; (...) its guidance, rather than its governance. (shrink)

Steve Fuller has argued that a scientific discovery will not be recognized unless it can be justified within the history of the relevant science. He cites Mendel's work on genetics, which was not recognized until thirty-five years after its publication, as an example. This essay argues that Mendel's work comes out of the tradition of work by both agricultural breeders and academics in nineteenth century Austria. Thus, Fuller is mistaken, and one must look elsewhere for the neglect of Mendel's work. (...) This essay also places Mendel's work within the philosophy of Jan Comenius, whose work was very likely known to Mendel.--------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- -----------------------------------------------. (shrink)

We present an alternative, purely semantical and relatively simple, proof of the Statman's result that both intuitionistic propositional logic and its implicational fragment are PSPACE-complete.

Efforts to bring science into early 19th century breeding practices in Central Europe, organised from Brno, the Hapsburg city in which Mendel would later turn breeding experiments into a body of timeless theory, are here considered as a significant prelude to the great discovery. During those years prior to Mendel's arrival in Brno, enlightened breeders were seeking ways to regulate the process of heredity, which they viewed as a force to be controlled. Many were specialising in sheep breeding for the (...) benefit of the local wool industry while others were showing an interest in commercial plants, especially fruit trees and vines, and later cereals. Breeders explained their problems in regulating heredity in terms of climatic influences disruption due to crossing sports or saltations. Practical experience led them to the concepts of 'inheritance capacity' and the 'mutual elective affinity' of parents. The former was seen to differ among individuals and also among traits; the latter was proposed as a means of adding strength to heredity. The breeders came to recognise that traits might be hidden and yet transmitted as a 'potential' to future generations. They also grew to understand that heredity would be strengthened when a quality was 'fixed' within a lineage by 'pure blood relations.' Continued selection of the desired quality might then lead to 'a higher perfection.' But the ultimate 'physiological' question about breeding, 'what is inherited and how?,' found no answer. Major figures in this development included Abbot Napp, the one who asked this question and who was due to receive Mendel into the monastery in 1843, and Professor Diebl whose lectures on agriculture and natural science at the Brno Philosophical Institute Mendel would attend in 1846. Here we analyse their progress in theorizing about breeding up until about 1840. In discussing this development, we refer to certain international contacts, especially with respect to information transfer and scientific education, within the wider context of the late Enlightenment. (shrink)

We study Fermat's last theorem and Catalan's conjecture in the context of weak arithmetics with exponentiation. We deal with expansions of models of arithmetical theories (in the language ) by a binary (partial or total) function e intended as an exponential. We provide a general construction of such expansions and prove that it is universal for the class of all exponentials e which satisfy a certain natural set of axioms. We construct a model and a substructure with e total and (...) (Presburger arithmetic) such that in both and Fermat's last theorem for e is violated by cofinally many exponents n and (in all coordinates) cofinally many pairwise linearly independent triples. On the other hand, under the assumption of ABC conjecture (in the standard model), we show that Catalan's conjecture for e is provable in (even in a weaker theory) and thus holds in and. Finally, we also show that Fermat's last theorem for e is provable (again, under the assumption of ABC in ) in “coprimality for e”. (shrink)

Axiomatization of Gödel-Dummett predicate logics S2G, S3G, and PG, where PG is the weakest logic in which all prenex operations are sound, and the relationships of these logics to logics known from the literature are discussed. Examples of non-prenexable formulas are given for those logics where some prenex operation is not available. Inter-expressibility of quantifiers is explored for each of the considered logics.

Each closed (i.e. variable free) formula of interpretability logic is equivalent in ILF to a closed formula of the provability logic G, thus to a Boolean combination of formulas of the form n.

Die Philosophie wurde von so unterschiedlichen Philosophen wie Wolff und Russell als Moglichkeitswissenschaft bezeichnet. Doch erwiesen sich die modalen Konzepte von Moglichkeit und Notwendigkeit als sperrig und vieldeutig, und ihr Verhaltnis zum Wirklichkeitsbegriff bleibt problematisch. Die vorliegende Sammlung beleuchtet die Metaphysik und Logik von Moglichkeit und Wirklichkeit aufs Neue und betrachtet sie aus unterschiedlichsten Perspektiven jenseits der Dichotomie von analytischer und kontinentaler Philosophie. Die Philosophiegeschichte (von der griechischen Antike bis zu David Lewis) kommt ebenso zu Wort wie die Semantik moglicher (...) Welten; Logik, Mathematik und Computerwissenschaft ebenso wie Literatur und Neue Medien; Formen des wissenschaftlichen ebenso wie des fiktionalen Diskurses. Philosophy has been called the science of the possible by philosophers as diverse as Christian Wolff and Bertrand Russell. The modal concepts of possibility and necessity, however, have proved to be ambiguous and recalcitrant to analysis, and their relation to the concept of reality have remained problematic up to the present day. Transcending the worn-out dichotomy between analytic and continental philosophy, this collection of papers takes a fresh look at the metaphysics and logic of possibility and reality, and illuminates them from a great variety of perspectives. Topics include the history of philosophy (from Greek antiquity to David Lewis) as well as the semantics of possible worlds; logic, mathematics and computer science as well as literature and the new media; forms of scientific as well as fictional discourse.". (shrink)

Fowers et al. recently made a general argument for virtues as the characteristics necessary for individuals to flourish, given inherent human limitations. For example, people can flourish by developing the virtue of friendship as they navigate the inherent human dependency on others. This general argument also illuminates a pathway to flourishing during the COVID-19 pandemic, the risks of which have induced powerful fears, exacerbated injustices, and rendered life and death decisions far more common. Contexts of risk and fear call for (...) the virtue of courage. Courage has emerged more powerfully as a central virtue among medical personnel, first responders, and essential workers. Longstanding inequalities have been highlighted during the pandemic, calling for the virtue of justice. When important personal and public health decisions must be made, the central virtue of practical wisdom comes to the fore. Wise decisions and actions incorporate the recognition of relevant moral concerns and aims, as well as responding in fitting and practical ways to the specifics of the situation. Practicing courage, justice, and practical wisdom illuminates a path to flourishing, even in a pandemic. (shrink)

In this paper, we provide an overview of some of the results obtained in the mathematical theory of intermediate quantifiers that is part of fuzzy natural logic. We briefly introduce the mathematical formal system used, the general definition of intermediate quantifiers and define three specific ones, namely, “Almost all”, “Most” and “Many”. Using tools developed in FNL, we present a list of valid intermediate syllogisms and analyze a generalized 5-square of opposition.

[Scotus` doctrine of the univocity of being. and the controversy concerning its interpretation in Baroque Scotism].

Here we attempt to define a specifically human ecology within which male reproductive strategies are formulated. By treating the domestic and public spheres of social life as "ecological niches" that men have been forced to compete within or to avoid as best they can, we generate a typology of four "social modes" of human male behavior. We then attempt to explain the broad distribution of social modes within and between human groups based on the relative intensity of scramble and contest (...) competition. (shrink)

This paper is a contribution to the development of model theory of fuzzy logic in narrow sense. We consider a formal system EvŁ of fuzzy logic that has evaluated syntax, i. e. axioms need not be fully convincing and so, they form a fuzzy set only. Consequently, formulas are provable in some general degree. A generalization of Gödel's completeness theorem does hold in EvŁ. The truth values form an MV-algebra that is either finite or Łukasiewicz algebra on [0, 1].The classical (...) omitting types theorem states that given a formal theory T and a set Σ of formulas with the same free variables, we can construct a model of T which omits Σ, i. e. there is always a formula from Σ not true in it. In this paper, we generalize this theorem for EvŁ, that is, we prove that if T is a fuzzy theory and Σ forms a fuzzy set , then a model omitting Σ also exists. We will prove this theorem for two essential cases of EvŁ: either EvŁ has logical constants for all truth values, or it has these constants for truth values from [0, 1] ∩ ℚ only. (shrink)

The second volume of The Cambridge History of Jewish Philosophy provides a comprehensive overview of Jewish philosophy from the seventeenth century to the present day. Written by a distinguished group of experts in the field, its essays examine how Jewish thinking was modified in its encounter with modern Europe and America and challenge longstanding assumptions about the nature and purpose of modern Jewish philosophy. The volume also treats modern Jewish philosophy's continuities with premodern texts and thinkers, the relationship between philosophy (...) and theology, the ritual and political life of the people of Israel and the ways in which classic modern philosophical categories help or hinder Jewish self-articulation. These essays offer readers a multi-faceted understanding of the Jewish philosophical enterprise in the modern period. (shrink)

This essay presents and analyzes the recent work of four prominent contemporary Jewish ethicists: Eugene Borowitz, David Novak, Byron Sherwin, and Walter Wurzburger. These authors are united in their affirmation of covenant as the central category of Jewish moral obligation and their concern to construct a Jewish ethic out of the classical sources of Judaism. Yet, as an individual analysis of their books will show, they adopt markedly different views of the authority of traditional Jewish law , the respective roles (...) of individual and community in moral deliberation, and the degree to which changing historical circumstances alter moral truths. (shrink)

Efforts to bring science into early 19th century breeding practices in Central Europe, organised from Brno, the Hapsburg city in which Mendel would later turn breeding experiments into a body of timeless theory, are here considered as a significant prelude to the great discovery. During those years prior to Mendel's arrival in Brno, enlightened breeders were seeking ways to regulate the process of heredity, which they viewed as a force to be controlled. Many were specialising in sheep breeding for the (...) benefit of the local wool industry while others were showing an interest in commercial plants, especially fruit trees and vines, and later cereals. Breeders explained their problems in regulating heredity in terms of (1) climatic influences (2) disruption due to crossing (3) sports or saltations. Practical experience led them to the concepts of 'inheritance capacity' and the 'mutual elective affinity' of parents. The former was seen to differ among individuals and also among traits; the latter was proposed as a means of adding strength to heredity. The breeders came to recognise that traits might be hidden and yet transmitted as a 'potential' to future generations. They also grew to understand that heredity would be strengthened when a quality was 'fixed' within a lineage by 'pure blood relations.' Continued selection of the desired quality might then lead to 'a higher perfection.' But the ultimate 'physiological' question about breeding, 'what is inherited and how?,' found no answer. Major figures in this development included Abbot Napp, the one who asked this question and who was due to receive Mendel into the monastery in 1843, and Professor Diebl whose lectures on agriculture and natural science at the Brno Philosophical Institute Mendel would attend in 1846. Here we analyse their progress in theorizing about breeding up until about 1840. In discussing this development, we refer to certain international contacts, especially with respect to information transfer and scientific education, within the wider context of the late Enlightenment. (shrink)

This book provides an interdisciplinary examination of the relationship between compromise and democracy. Compromises have played a significant role in our representative democracies and yet the nature of the relationship between compromise and democracy has generally raised tricky theoretical questions and generated ambiguous evaluations. This book focuses on the relationship between compromise and liberal democracies from both a cultural and institutional perspective and addresses new and lesser-explored aspects of the relationship. It explores a variety of topics including: compromise and in-commensurable (...) values, antagonist paradigms, compromise and majority decisions, compromise and publicity, compromise and post-conflict societies, compromise and anti-system political parties, and compromise and the understanding of political representation. Compromises in Democracy offers an original perspective on the topic by assembling contributions from the fields of philosophy, sociology, political theory, political science and history of ideas. (shrink)