Bisimulations, behavioral equivalence and logical equivalence are investigated for stochastic image-coalgebras that interpret coalgebraic logic which is defined in terms of predicate liftings. We investigate the conditions for the functor under which these notions of equivalence are related by discussing congruences for the underlying stochastic relation. It is demonstrated that logics as diverse as continuous time stochastic logic and general modal logics can be usefully approached through coalgebraic methods.

We propose a probabilistic interpretation of Propositional Dynamic Logic (PDL). We show that logical and behavioral equivalence are equivalent over general measurable spaces. This is done first for the fragment of straight line programs and then extended to cater for the nondeterministic nature of choice and iteration, expanded to PDL as a whole. Bisimilarity is also discussed and shown to be equivalent to logical and behavioral equivalence, provided the base spaces are Polish spaces. We adapt techniques from coalgebraic stochastic logic (...) and point out some connections to Souslin's operation A from descriptive set theory. This leads to a discussion of complete stochastic Kripke models and model completion, which permits an adequate treatment of the test operator. (shrink)

We generalize stochastic Kripke models and Markov transition systems to stochastic right coalgebras. These are coalgebras for a functor with as an endofunctor on the category of analytic spaces, and is the subprobability functor. The modal operators are generalized through predicate liftings which are set-valued natural transformations involving the functor. Two states are equivalent iff they cannot be separated by a formula. This equivalence relation is used to construct a cospan for logical equivalent coalgebras under a separation condition for the (...) set of predicate liftings. Consequently, behavioral and logical equivalence are really the same. From the cospan we construct a span. The central argument is a selection argument giving us the dynamics of a mediating coalgebra from the domains of the cospan. This construction is used to establish that behavioral equivalent coalgebras are bisimilar, yielding the equivalence of all three characterizations of a coalgebra’s behavior as in the case of Kripke models or Markov transition systems. (shrink)

Excerpt from Kant Contra Haeckel: Fur den Entwicklungsgedanken, Gegen Naturwissenschaftlichen Dogmatismus Meine Schrift wendet sich an die, welche, geblendet von Haeckels beruhmtem Namen und wohlverdientem wissenschaftlichen Ruf, auch in philosophischen Fragen von ihm Auskunft erwarten. Sie mochte den philosophischen Nimbus, der ihn umgibt, zerstoren und so an ihrem Teil der Vernunft zum Durchbruch verhelfen. 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)

© The Author [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] Dedekind was a contemporary of Bernhard Riemann, Georg Cantor, and Gottlob Frege, among others. Together, they revolutionized mathematics and logic in the second half of the nineteenth century. Dedekind had an especially strong influence on David Hilbert, Ernst Zermelo, Emmy Noether, and Nicolas Bourbaki, who completed that revolution in the twentieth century. With respect to mainstream mathematics, he is best known for his (...) contributions to algebra and number theory. With respect to logic and the foundations of mathematics, many of his technical results — his conceptualization of the natural and real numbers, his analysis of proofs by mathematical induction and definitions by recursion (extended to the transfinite by Zermelo, John von... (shrink)

This article compares representations of war in Walter Flex’ The Wanderer between Two Worlds, Ernst Jünger’s Storm of Steel, and Erich Maria Remarque’s All Quiet on the Western Front. It shows the extent to which these representations are shaped by political and ideological convictions. The difference between the romantic idealism of Flex and Jünger’s “soldierly nationalism”,which he proposed as a model for the time to come, reflects a major shift during World War I itself. By contrast, neither past (...) nor future seem to be of any use in Remarque’s famous antiwar novel, in which the war generation surprisingly is described as having nothing else to live for beyond the present, i.e. beyond war. Finally, the article suggests how these different representations of war each, in their own way, contributed to the aesthetics and ideology of fascism. (shrink)

Der Biologe Erich Wasmann SJ ging in seinem Buch “Die moderne Biologie und die Entwicklungstheorie” und in seinen Berliner Vorträgen 1907, in denen er sich mit dem Monisten Ernst Haeckel auseinandersetzte, das Problem der Evolution an. In Bezug auf die Entwicklung des Menschen vertrat er in beiden eine offene Position: Er hielt die Entwicklung des Menschen aus dem Tierreich für nicht erwiesen, rechnete jedoch damit, dass sie eines Tages bewiesen werden könnte, und betonte, dass sie nicht prinzipiell der (...) Offenbarung widerspreche. Dies führte zu Klagen in Rom. Der Jesuitengeneral Wernz erklärte, es sei “theologice certum”, dass der Mensch auch dem Leibe nach nicht aus dem Tierreich abstammen könne. Wasmann solle daher in künftigen Neuauflagen seines Buches nur die biologische Seite behandeln und Spekulationen über die prinzipielle Vereinbarkeit einer Humanevolution mit der Offenbarung unterlassen. Dies hatte zur Folge, dass es keine Neuauflage mehr gab.The Jesuit and biologue Erich Wasmann dealt in his book “Die moderne Biologie und die Entwicklunstheorie” and in his Berlin conferences in 1907, dealing with the monist Ernst Haeckel, the problem of evolution. Regarding the evolution of mankind, he defended an open position: he judged that it had not been proved, but reckoned with the possibility that it could be proved one day, and insisted that there would be no contradiction with Christian revelation. That provoked, in the time of the Modernist crisis, complaints to Rome. The Jesuit General Wernz declared that it would be “theologice certum” that mankind could not descend, not even regarding the body, from animal ancestors. Therefore Wasmann should deal, in future editions, only with the biological questions and omit speculations about the theoretical compatibility of human evolution with the revelation. That had the consequence, that no new edition of the book was ever published. (shrink)

In this paper, I present an outline of the oppression account of cultural appropriation and argue that it offers the best explanation for the wrongfulness of the varied and complex cases of appropriation to which people often object. I then compare the oppression account with the intimacy account defended by C. Thi Nguyen and Matt Strohl. Though I believe that Nguyen and Strohl’s account offers important insight into an essential dimension of the cultural appropriation debate, I argue that justified objections (...) to cultural appropriation must ultimately be grounded in considerations of oppression as opposed to group intimacy. I present three primary objections to the intimacy account. First, I suggest that in its effort to explain expressive appropriation claims (those that purportedly lack an independent ground), the intimacy account doubles down on the boundary problem. Second, I question whether group intimacy possess the kind of bare normativity that Nguyen and Strohl claim for it. Finally, I argue that these objections give us reason to accept the importance of group intimacy to the cultural appropriation debate, but question the source of its significance as identified by Nguyen and Strohl. (shrink)

Is there something morally wrong with cultural appropriation in the arts? I argue that the little philosophical work on this topic has been overly dismissive of moral objections to cultural appropriation. Nevertheless, I argue that philosophers working on epistemic injustice have developed powerful conceptual tools that can aid in our understanding of objections that have been levied by other scholars and artists. I then consider the relationship between these objections and the harms of cultural essentialism. I argue that focusing on (...) the systematic nature of appropriative harms may allow us to sidestep the problem of essentialism, but not without cost. (shrink)

The book, with its emphasis on the interaction of microstructures with the entire biosphere, ecosystems etc., and on how micro- and macrocosmos mutually create the conditions for their further evolution, provides a comprehensive framework for a deeper understanding of human creativity in a time of transition.

The first of Erich Neumann's works to be translated into English, this eloquent book draws on a full range of world mythology to show that individual consciousness undergoes the same archetypal stages of development as has human consciousness as a whole. Neumann, one of Jung's most creative students and a renowned practitioner of analytical psychology in his own right, shows how the stages begin and end with the symbol of the Uroboros, or tail-eating serpent. The intermediate stages are projected (...) in the universal myths of the World Creation, Great Mother, Separation of the World Parents, Birth of the Hero, Slaying of the Dragon, Rescue of the Captive, and Transformation and Deification of the Hero. Throughout the sequence the Hero is the evolving ego consciousness. (shrink)

We introduce an atomic formula ${\vec{y} \bot_{\vec{x}}\vec{z}}$ intuitively saying that the variables ${\vec{y}}$ are independent from the variables ${\vec{z}}$ if the variables ${\vec{x}}$ are kept constant. We contrast this with dependence logic ${\mathcal{D}}$ based on the atomic formula = ${(\vec{x}, \vec{y})}$ , actually equivalent to ${\vec{y} \bot_{\vec{x}}\vec{y}}$ , saying that the variables ${\vec{y}}$ are totally determined by the variables ${\vec{x}}$ . We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. (...) We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using = ${(\vec{x}, \vec{y})}$ have. (shrink)

This translation of four of Plato's dialogues brings these classic texts alive for modern readers. Allen introduces and comments on the dialogues in an accessible way, inviting the reader to re-examine the issues Plato continually raises.

Those who comment on modern scientific institutions are often quick to praise institutional structures that leave scientists to their own devices. These comments reveal an underlying presumption that scientists do best when left alone—when they operate in what we call the ‘scientific state of nature’. Through computer simulation, we challenge this presumption by illustrating an inefficiency that arises in the scientific state of nature. This inefficiency suggests that one cannot simply presume that science is most efficient when institutional control is (...) absent. In some situations, actively encouraging unpopular, risky science would improve scientific outcomes. 1 Introduction2 Scientists and Bandits3 Choosing an ϵ4 Structure of Communication5 Discussion. (shrink)

Various contributors to recent philosophy of mathematics havetaken Richard Dedekind to be the founder of structuralismin mathematics. In this paper I examine whether Dedekind did, in fact, hold structuralist views and, insofar as that is the case, how they relate to the main contemporary variants. In addition, I argue that his writings contain philosophical insights that are worth reexamining and reviving. The discussion focusses on Dedekind''s classic essay Was sind und was sollen die Zahlen?, supplemented by evidence from Stetigkeit und (...) irrationale Zahlen, his scientific correspondence, and his Nachlaß. (shrink)

This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.