Millionenjahrhaus: Zur Konzeption des Raumes der Ewigkeit im konstellativen Königtum in Sprache, Architektur und Theologie. By Stefanie Schröder. Wiesbaden: Harrassowitz Verlag, 2010. Pp. 396, plates. €84.

This book has grown out of eight years of close collaboration among its authors. From the very beginning we decided that its content should come out as the result of a truly common effort. That is, we did not "distribute" parts of the text planned to each one of us. On the contrary, we made a point that each single paragraph be the product of a common reflection. Genuine team-work is not as usual in philosophy as it is in other (...) academic disciplines. We think, however, that this is more due to the idiosyncrasy of philosophers than to the nature of their subject. Close collaboration with positive results is as rewarding as anything can be, but it may also prove to be quite difficult to implement. In our case, part of the difficulties came from purely geographic separation. This caused unsuspected delays in coordinating the work. But more than this, as time passed, the accumulation of particular results and ideas outran our ability to fit them into an organic unity. Different styles of exposition, different ways of formalization, different levels of complexity were simultaneously present in a voluminous manuscript that had become completely unmanageable. In particular, a portion of the text had been conceived in the language of category theory and employed ideas of a rather abstract nature, while another part was expounded in the more conventional set-theoretic style, stressing intui tivity and concreteness. (shrink)

This is the basis of the first part of the book.

"A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical (...) aspects of the tight relation and the complementarity of ranks and probabilities. It closes with comparative remarks on predecessors and other philosophical proposals as well as formal models developed in AI. (shrink)

The systems Kα of transfinite cumulative types up to α are extended to systems K∞α that include a natural infinitary inference rule, the so-called limit rule. For countable α a semantic completeness theorem for K∞α is proved by the method of reduction trees, and it is shown that every model of K∞α is equivalent to a cumulative hierarchy of sets. This is used to show that several axiomatic first-order set theories can be interpreted in K∞α, for suitable α.

SummaryA simple and precise definition is offered of “term t of theory T being T‐theoretical” which can be applied to any formalized theory. The definition is in line with and emends traditional accounts of theoreticity. Its adequacy is demonstrated by application to three examples: exchange economics, classical mechanics and collision mechanics.

The aim of the paper is to explicate the concept of causal independence between sets of factors and Reichenbach's screening-off-relation in probabilistic terms along the lines of Suppes' probabilistic theory of causality (1970). The probabilistic concept central to this task is that of conditional stochastic independence. The adequacy of the explication is supported by proving some theorems about the explicata which correspond to our intuitions about the explicanda.

A comprehensive model for describing various forms of developments in science is defined in precise, set-theoretic terms, and in the spirit of the structuralist approach in the philosophy of science. The model emends previous accounts in centering on single systems in a homogenous way, eliminating notions which essentially refer to sets of systems. This is achieved by eliminating the distinction between theoretical and non-theoretical terms as a primitive, and by introducing the notion of intended links. The force of the model (...) is demonstrated by formally incorporating many of the important, precise meta-theoretic concepts occurring in the literature. (shrink)

Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through information or experience; induction and belief change are one and same topic, after all. The most basic of these rules is simply to conditionalize with respect to the information received; and there are similar and more general rules. 1 Hence, a fundamental reason for the epistemological success of (...) probability theory is that there at all exists a well-behaved concept of conditional probability. Still, people have, and have reasons for, various concerns over probability theory. One of these is my starting point: Intuitively, we have the notion of plain belief; we believe propositions2 to be true (or to be false or neither). Probability theory, however, offers no formal counterpart to this notion. Believing A is not the same as having probability 1 for A, because probability 1 is incorrigible3; but plain belief is clearly corrigible. And believing A is not the same as giving A a probability larger than some 1 - c, because believing A and believing B is usually taken to be equivalent to believing A & B.4 Thus, it seems that the formal representation of plain belief has to take a non-probabilistic route. Indeed, representing plain belief seems easy enough: simply represent an epistemic state by the set of all propositions believed true in it or, since I make the common assumption that plain belief is deductively closed, by the conjunction of all propositions believed true in it. But this does not yet provide a theory of induction, i.e. an answer to the question how epistemic states so represented are changed tbrough information or experience. There is a convincing partial answer: if the new information is compatible with the old epistemic state, then the new epistemic state is simply represented by the conjunction of the new information and the old beliefs. This answer is partial because it does not cover the quite common case where the new information is incompatible with the old beliefs. It is, however, important to complete the answer and to cover this case, too; otherwise, we would not represent plain belief as conigible. The crucial problem is that there is no good completion. When epistemic states are represented simply by the conjunction of all propositions believed true in it, the answer cannot be completed; and though there is a lot of fruitful work, no other representation of epistemic states has been proposed, as far as I know, which provides a complete solution to this problem. In this paper, I want to suggest such a solution. In [4], I have more fully argued that this is the only solution, if certain plausible desiderata are to be satisfied. Here, in section 2, I will be content with formally defining and intuitively explaining my proposal. I will compare my proposal with probability theory in section 3. It will turn out that the theory I am proposing is structurally homomorphic to probability theory in important respects and that it is thus equally easily implementable, but moreover computationally simpler. Section 4 contains a very brief comparison with various kinds of logics, in particular conditional logic, with Shackle's functions of potential surprise and related theories, and with the Dempster - Shafer theory of belief functions. (shrink)

It is widely held that if an object a is identical (or non-identical) to an object b, then it is necessary that a is identical (non-identical) to b. This view is supported an argument from Leibniz's Law and a popular conception of de re modality. On the other hand, there are good reasons to allow for contingent identity. Various alternative accounts of de re modality have been developed to achieve this kind of generality, and to explain what is wrong with (...) the argument from Leibniz's Law. (shrink)

This article discusses the history of the concepts of potential infinity and actual infinity in the context of Christian theology, mathematical thinking and metaphysical reasoning. It shows that the structure of Ancient Greek rationality could not go beyond the concept of potential infinity, which is highlighted in Aristotle's metaphysics. The limitations of the metaphysical mind of ancient Greece were overcome through Christian theology and its concept of the infinite God, as formulated in Gregory of Nyssa's theology. That is how the (...) concept of actual infinity emerged. However, Gregory of Nyssa's understanding of human rationality went still further. He said that access to the infinity of God was to be found only in an asymptotic ascension, as expressed in apophatic theology, and this view endangered the rationality of theology. Deeply influenced by the apophatic tradition, Nicholas of Cusa avoided this danger by showing that infinity could be accessed by symbolic representation and asymptotic mathematical reasoning. Thus, he made an immense contribution in making infinity rationally accessible. This endeavor was finally realized by Georg Cantor. This rational accessibility revealed discernible structures of infinity, such as the continuum hypothesis, and the cardinal numbers. However, the probable logical inconsistency of Georg Cantor's all-encompassing Absolute Infinity points to an intuitive understanding of infinity that goes beyond its rational structures – as in apophatic theology. (shrink)

Buridan endorses the basic idea that q follows from p iff it is impossible that p is true but q is false. Since he also accepts the law that, if p is impossible, the conjunction (p ∧ q) must be impossible, he comes to regard the principle ‘Ex impossibili quodlibet’ (EIQ) as basically correct. However, his logic is based on a ‘nominalist’ view according to which propositions are tokens of spoken, written or thought language existing in space of time, and (...) the truth of such a proposition presupposes that it exists. This conception prompted Buridan to modify the definition of ‘consequence’, but none of his attempts was fully successful. Yet, a large part of his theory of consequences is based on the usual account of necessary truth-conservation. As regards principle EIQ, Buridan distinguishes two variants of impossibility. Proposition p is possible iff the state of affairs as described by p is possible; this doesn’t guarantee, however, that p is ‘possibly true’. E.g. ‘No proposition is negative’ is considered by Buridan as describing a possible state of affairs, but this proposition is not possibly true, because in order to be true, it would have to exist, and as soon as it comes into existence, it becomes false. Accordingly, EIQ requires that the antecedent p is really impossible and not only impossibly true. (shrink)

The central claim of the paper is, roughly, that the fact that it looks to somebody as if p is a defeasibly a priori reason for assuming that p (and vice versa), for any person, even for the perceiver himself. As a preparation, it outlines a doxastic conception suitable to explicate this claim and explains how to analyse dispositions within this conception. Since an observable p has the disposition to look as if p, this analysis generalizes to the central claim (...) which is then argued to be at the bottom of coherentism. Thus, the defense of the claim supports coherentism as opposed to foundationalism and at the same time provides an answer to skepticism about the external world. (shrink)

This paper compares the epistemological conception of Isaac Levi with mine. We are joined in both giving a constructive answer to the relation of belief and probability, without reducing one to the other. However, our constructions differ in at least nine more or less important ways, all discussed in the paper. In particular, the paper explains the similarities and differences of Shackle's functions of potential surprise, as used by Levi, and my ranking functions in formal as well as in philosophical (...) respects. The appendix explains how ranking and probability theory can be combined in the notion of a ranked probability measure (or probabilified ranking function). (shrink)

Quantum B-algebras, the partially ordered implicational algebras arising as subreducts of quantales, are introduced axiomatically. It is shown that they provide a unified semantic for non-commutative algebraic logic. Specifically, they cover the vast majority of implicational algebras like BCK-algebras, residuated lattices, partially ordered groups, BL- and MV-algebras, effect algebras, and their non-commutative extensions. The opposite of the category of quantum B-algebras is shown to be equivalent to the category of logical quantales, in the way that every quantum B-algebra admits a (...) natural embedding into a logical quantale, the enveloping quantale. Partially defined products of algebras related to effect algebras are handled efficiently in this way. The unit group of the enveloping quantale of a quantum B-algebra X is shown to be always contained in X, which gives a functorial subgroup X× of X. Similar subfunctors are obtained for the non-commutative extensions of BCK-algebras and effect algebras. The results of Galatos, Jónsson, and Tsinakis on the splitting of generalized BL-algebras into a semidirect product of a partially ordered group operating on an integral residuated poset are extended to a characterization of twisted semidirect products of a po-group by a quantum B-algebra. (shrink)

Die "Theoretische Psychologie" Sigmund Freuds -- Affekt und Bild vs. Handlung und Symbolisierung - "Mentalisierung" als Regulation. Anmerkungen über eine neuere Konzeption zu Freuds metapsychologischen Schriften -- Bild vs. Sprache : vom Unbewussten zum Bewusstwerden -- Der Primärprozess und das halluzinatorisch-bildliche Erleben des Klein(st) kindes - nebst einem Anhang über das Verhältnis der Leistungen der modernen Gehirnphysiologie zur Erforschung und Erklärung inhaltlich-seelischer Vorgänge -- Träume sind Bildgeschichten -- Erst Verbildlichung, dann Verbalisierung -- Weitere Konsequenzen für die therapeutische Praxis : Fallgeschichten (...) -- Kausales vs. strukturelles Denken in der Psychotherapie. (shrink)

Wieviel normative Gemeinsamkeit benötigt die Demokratie? Wie groß ist der Konsensbedarf der gesellschaftlichen Diskurse in pluralistischen Gesellschaften? Wie ist die Neutralitätsverpflichtung des Liberalismus zu verstehen? Gibt es Grenzen der Toleranz? Welche Rolle kommt den starken metaphysischen und moralischen Überzeugungen der Bürger in einer Demokratie zu? Müssen sie eingeklammert werden? Muß der Bürger verstummen, wenn es um wichtige weltanschauliche Dinge geht, um den Konsens nicht zu gefährden? Im Rahmen einer kritischen AuseinanderSetzung mit Rawls' Konzeption des politischen Liberalismus werden diese Probleme der (...) Integration pluralistischer Gesellschaften diskutiert. Der dabei entwickelte Lösungsweg vermeidet sowohl die diskurSethische Überforderung der Konsensfähigkeit pluralistischer Gesellschaften als auch die Rawlssche Vorstellung einer gerechtigkeitSethischen Verfassung des öffentlichen Vernunftgebrauchs und plädiert zugleich für eine Entdramatisierung des Pluralismus und für einen selbstbehauptungswilligen Liberalismus, der sich von seiner neutralistischen Selbstlähmung befreit und handelt, wenn die Grenzen der Argumentation erreicht sind. (shrink)

The old division of all sciences into the two equally important classes of theoretical and practical disciplines is hardly ever applied today. However, the proprium of a practical science that is aimed at what should be, can be elucidated using medicine as an example. The efforts of medicine are not limited to a mere `application' of methods and results of theoretical disciplines. Even the concepts of `illness' and `diagnosis', which are central to medicine, are defined in a normative-deontological manner. They (...) are supposed not only to help formulating and justifying assertions on facts, but also to be a means to enable and standardise action. Since every action takes place in a concrete situation, a practical science must always bridge the hiatus between the general and the particular. This requires judgement, a personal, individual capacity that cannot be operationalised without residue. In contrast to the theoretical disciplines, such a science is not the master of its own questions and problems; and is subject to the dictate of time, since all action is final and irrevocable. (shrink)

Der Beitrag versucht zu zeigen, dass Intentionalität nicht deshalb problematisch ist, weil sie unser naturalistisches Weltbild herausfordert, sondern deshalb, weil sie gegen gewisse logische Intuitionen zu verstoßen scheint, und dass die angemessene Reaktion auf dieses Problem nicht darin besteht, über die physikalische Realisierung intentionaler mentaler Zustände, sondern über die logische Form intensionaler Sätze nachzudenken. Als Zeuge führt der Autor Fred Dretske an, dessen Analyse der Intentionalität sich bei näherem Hinsehen als naturalistisch verbrämte Theorie der logischen Form intensionaler Sätze herausstellt.

I argue that the project of naturalizing intentionality is misconceived. Intentionality should not be considered as a challenge to our naturalistic world-view, but rather as something which gives rise to a logical problem: how to save the principle of indiscernibility of identicals from apparent counterexamples arising from intensional discourse.