In 1952, Heinrich Scholz published a question in The Journal of Symbolic Logic asking for a characterization of spectra, i.e., sets of natural numbers that are the cardinalities of finite models of first order sentences. Günter Asser in turn asked whether the complement of a spectrum is always a spectrum. These innocent questions turned out to be seminal for the development of finite model theory and descriptive complexity. In this paper we survey developments over the last 50-odd years pertaining (...) to the spectrum problem. Our presentation follows conceptual developments rather than the chronological order. Originally a number theoretic problem, it has been approached by means of recursion theory, resource bounded complexity theory, classification by complexity of the defining sentences, and finally by means of structural graph theory. Although Scholz' question was answered in various ways, Asser's question remains open. (shrink)

Mimesis, the notion that art imitates reality, has long been recognized as one of the central ideas of Western aesthetics and has been most frequently associated with Aristotle. Less well documented is the great importance of mimetic theories of literature, theater, and the visual arts during the Renaissance and the Enlightenment. In this book, the most comprehensive overview of the theory of mimesis since Auerbach's monumental study, Gunter Gebauer and Christoph Wulf provide a thorough introduction to the complex and (...) shifting meanings of the term. Beginning with the Platonic doctrine of imitation, they chart the concept's appropriation and significance in the aesthetic theories of Aristotle, Molière, Shakespeare, Racine, Diderot, Lessing, and Rousseau. They examine the status of mimesis in the nineteenth-century novel and its reworking by such modern thinkers as Benjamin, Adorno, and Derrida. Widening the traditional understanding of mimesis to encompass the body and cultural practices of everyday life, their work suggests the continuing value of mimetic theory and will prove essential reading for scholars and students of literature, theater, and the visual arts. (shrink)

Mimesis, the notion that art imitates reality, has long been recognized as one of the central ideas of Western aesthetics and has been most frequently associated with Aristotle. Less well documented is the great importance of mimetic theories of literature, theater, and the visual arts during the Renaissance and the Enlightenment. In this book, the most comprehensive overview of the theory of mimesis since Auerbach's monumental study, Gunter Gebauer and Christoph Wulf provide a thorough introduction to the complex and (...) shifting meanings of the term. Beginning with the Platonic doctrine of imitation, they chart the concept's appropriation and significance in the aesthetic theories of Aristotle, Molière, Shakespeare, Racine, Diderot, Lessing, and Rousseau. They examine the status of mimesis in the nineteenth-century novel and its reworking by such modern thinkers as Benjamin, Adorno, and Derrida. Widening the traditional understanding of mimesis to encompass the body and cultural practices of everyday life, their work suggests the continuing value of mimetic theory and will prove essential reading for scholars and students of literature, theater, and the visual arts. (shrink)

Figal has long been recognized as one of the most insightful interpreters working in the tradition of philosophical hermeneutics and its leading themes concerned with ancient Greek thought, art, language, and history. With this book, Figal presses this tradition of philosophical hermeneutics in new directions. In his effort to forge philosophical hermeneutics into a hermeneutical philosophy, Figal develops an original critique of the objectification of the world that emerges in modernity as the first stage in his systematic treatment of the (...) elements of experience hermeneutically understood. Breaking through the prejudices of modernity, but not sacrificing the importance and challenge of the objective world that confronts us and is in need of interpretation, Figal reorients how it is that philosophy should take up some of its most longstanding and stubborn questions. World, object, space, language, freedom, time, and life are refreshed as philosophical notions here since they are each regarded as elements of human life engaged in the task assigned to each of us—the task of understanding ourselves and our world. (shrink)

Karl Popper's work is of great diversity. It touches on virtually every intellectual activity. But he himself considered his philosophy of science one of his most important achievements. And indeed his achievement here is revolutionary. It destroyed the philosophy of inductivism which held sway over science for hundreds of years.

A generalization of Příkrý's forcing is analyzed which adjoins to a model of ZFC a set of order type at most ω below each member of a discrete set of measurable cardinals. A characterization of generalized Příkrý generic sequences reminiscent of Mathias' criterion for Příkrý genericity is provided, together with a maximality theorem which states that a generalized Příkrý sequence almost contains every other one lying in the same extension.This forcing can be used to falsify the covering lemma for a (...) higher core model if there is an inner model with infinitely many measurable cardinals – changing neither cardinalities nor cofinalities. Another application is an alternative proof of a theorem of Mitchell stating that if the core model contains a regular limit θ of measurable cardinals, then there is a model in which every set of measurable cardinals of K bounded in θ has an indiscernible sequence but there is no such sequence for the entire set of measurables of K below θ. (shrink)

It is shown that the Magidor forcing to collapse the cofinality of a measurable cardinal that carries a length \ sequence of normal ultrafilters, increasing in the Mitchell order, to \, is subcomplete.

The main result of this paper is the following theorem: Let M be a premouse with a top extender, F. Suppose that (a) M is linearly coarsely iterable via hitting F and its images, and (b) if M * is a linear iterate of M as in (a), then M * is coarsely iterable with respect to iteration trees which do not use the top extender of M * and its images. Then M is coarsely iterable.

For an ordinal \, I introduce a variant of the notion of subcompleteness of a forcing poset, which I call \-subcompleteness, and show that this class of forcings enjoys some closure properties that the original class of subcomplete forcings does not seem to have: factors of \-subcomplete forcings are \-subcomplete, and if \ and \ are forcing-equivalent notions, then \ is \-subcomplete iff \ is. I formulate a Two Step Theorem for \-subcompleteness and prove an RCS iteration theorem for \-subcompleteness (...) which is slightly less restrictive than the original one, in that its formulation is more careful about the amount of collapsing necessary. Finally, I show that an adequate degree of \-subcompleteness follows from the \-distributivity of a forcing, for \. (shrink)

For an arbitrary forcing class Γ, the Γ-fragment of Todorčević’s strong reflection principle SRPis isolated in such a way that the forcing axiom for Γ implies the Γ-fragment of SRP, the sta...

l investigate versions of the Maximality Principles for the classes of forcings which are <κ-closed. <κ-directed-closed, or of the form Col (κ. <Λ). These principles come in many variants, depending on the parameters which are allowed. I shall write MPΓ(A) for the maximality principle for forcings in Γ, with parameters from A. The main results of this paper are: • The principles have many consequences, such as <κ-closed-generic $\Sigma _{2}^{1}(H_{\kappa})$ absoluteness, and imply. e.g., that ◇κ holds. I give an application (...) to the automorphism tower problem, showing that there are Souslin trees which are able to realize any equivalence relation, and hence that there are groups whose automorphism tower is highly sensitive to forcing. • The principles can be separated into a hierarchy which is strict, for many κ. • Some of the principles can be combined, in the sense that they can hold at many different κ simultaneously. The possibilities of combining the principles are limited, though: While it is consistent that MP<κ-closed(HκT) holds at all regular κ below any fixed α. the "global" maximality principle, stating that MP<κ-closed(Hκ ∪ {κ}) holds at every regular κ. is inconsistent. In contrast to this, it is equiconsistent with ZFC that the maximality principle for directed-closed forcings without any parameters holds at every regular cardinal. It is also consistent that every local statement with parameters from HκT that's provably <κ-closed-forceably necessary is true, for all regular κ. (shrink)

The motivation for this paper is the following: In [4] I showed that it is inconsistent with ZFC that the Maximality Principle for directed closed forcings holds at unboundedly many regular cardinals κ (even only allowing κ itself as a parameter in the Maximality Principle for < κ -closed forcings each time). So the question is whether it is consistent to have this principle at unboundedly many regular cardinals or at every regular cardinal below some large cardinal κ (instead of (...) ∞), and if so. how strong it is. It turns out that it is consistent in many cases, but the consistency strength is quite high. (shrink)

This paper contains a discussion of Quine's thesis of indeterminacy of translation within the more general thesis that using and understanding a language are to be conceived of as a creative and interpretative-constructional activity. Indeterminacy is considered to be ineliminable. Three scenarios are distinguished concerning, first, the reasons for indeterminacy, second, the kinds of indeterminacy and, third, different levels of a general notion of recursive interpretation. Translational hypotheses are seen as interpretational constructs. The indeterminacy thesis turns out to be a (...) consequence of the externalizing of language, meaning, and epistemology. By means of a three-leveled interpretation model one can substantiate the crucial aspects, first, that indeterminacy is not an indeterminacy of facts of the matter and, second, that there is a significant difference between indeterminacy and underdetermination. In addition, the relationship between indeterminacy, interpretation, and charity is elucidated. Indeterminacy is seen not as an obstacle to but as a condition for communication. Charity and empathy in dialogue are conditional upon indeterminacy. All three components reveal the interpretative-constructional character of the inseparable connection of meaning and experience. (shrink)

This volume, Futurism and the Technological Imagination, results from a conference of the International Society for the Study of European Ideas in Helsinki.