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)

Two welcome extensions of evolutionary thinking have come to prominence over the last thirty years: the so-called ’extended evolutionary synthesis’ (EES) and debate about biological kinds and individuals. These two agendas have, however, remained orthogonal to one another. The EES has mostly restricted itself to widening the explanations of adaptation offered by the preceding ’modern evolutionary synthesis’ by including additional mechanisms of inheritance and variation; while discussion of biological kinds has turned toward philosophical questions of essential vs. contingent properties of (...) life forms and realist vs. epistemological approaches to categorization and classification. Here we attempt to broaden the explanatory scope of evolutionary theory by linking these two agendas. We expand on the mechanistic orientation of the EES, using new understandings of networked systems of components in order to engage the distinct intellectual challenge of the origination of “historical kinds”. With this phrase we designate a subset of natural kinds that acquires, through evolutionary processes, a quasi-independent lineage-history. Such kinds emerge in both biology and culture, and we enlarge the limited number of historical kinds that have thus far been recognized in evolutionary biology in a series of paradigmatic exemplars, from genes and cell types to rituals and music. For each exemplar we discern specific mechanisms by which it arose and persists; comparing these, we suggest a general unity in the ways in which diverse historical kinds originate. (shrink)

Our society is in the middle of the AI revolution. We discuss several applications of AI, in particular medical causality, where deep-learning neural networks screen through big data bases, extracting associations between a patient’s condition and possible causes. While beneficial in medicine, several questionable AI trading strategies have emerged in finance. Though advantages in many aspects of our lives, serious threats of AI exist. We suggest several regulatory measures to reduce these threats. We further discuss whether ‘full AI robots’ should (...) be programmed with a virtual consciousness and conscience. While this would reduce AI threats via motivational control, other threats such as the desire for AI—human socioeconomic equality could prove detrimental. (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)

We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary reflection, the strong reflection principle, and the existence of square sequences.

The effects of the forcing axioms \, \ and \ on the failure of weak threaded square principles of the form \\) are analyzed. To this end, a diagonal reflection principle, \, and it implies the failure of \\) if \. It is also shown that this result is sharp. It is noted that \/\ imply the failure of \\), for every regular \, and that this result is sharp as well.

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.

This book is open access under a CC BY 4.0 license. We must find new and innovative ways of conceptualizing transboundary energy issues, of embedding concerns of ethics or justice into energy policy, and of operationalizing response to them. This book stems from the emergent gap; the need for comparative approaches to energy justice, and for those that consider ethical traditions that go beyond the classical Western approach. This edited volume unites the fields of energy justice and comparative philosophy to (...) provide an overarching global perspective and approach to applying energy ethics. We contribute to this purpose in four sections: setting the scene, practice, applying theory to practice, and theoretical approaches. Through the chapters featured in the volume, we position the book as one that contributes to energy justice scholarship across borders of nations, borders of ways of thinking and borders of disciplines. The outcome will be of interest to undergraduate and graduate students studying energy justice, ethics and environment, as well as energy scholars, policy makers, and energy analysts. (shrink)

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)

Ehrenfeucht’s lemma asserts that whenever one element of a model of Peano arithmetic is definable from another, they satisfy different types. We consider here the analogue of Ehrenfeucht’s lemma for models of set theory. The original argument applies directly to the ordinal-definable elements of any model of set theory, and, in particular, Ehrenfeucht’s lemma holds fully for models of set theory satisfying V=HOD. We show that the lemma fails in the forcing extension of the universe by adding a Cohen real. (...) We go on to formulate a scheme of natural parametric generalizations of Ehrenfeucht’s lemma, namely, the principles of the form EL, which asserts that P-definability from A implies Q-discernibility. We also consider various analogues of Ehrenfeucht’s lemma obtained by using algebraicity in place of definability, where a set b is algebraic in a if it is a member of a finite set definable from a. Ehrenfeucht’s lemma holds for the ordinal-algebraic sets, we prove, if and only if the ordinal-algebraic and ordinal-definable sets coincide. Using a similar analysis, we answer two open questions posed earlier by the third author and C. Leahy, showing that algebraicity and definability need not coincide in models of set theory and the internal and external notions of being ordinal algebraic need not coincide. (shrink)

I develop a translation procedure between λ-structures, which correspond to premice in the Friedman–Jensen indexing convention on the one hand and s-structures, which are essentially the same as premice in the Mitchell–Steel indexing scheme.

This paper examines the relation between intuition and concept in Kant in light of John McDowell's neo-Kantian position that intuitions are concept-laden.2 The focus is on Kant's twofold pronouncement that thoughts without content are empty and that intuitions without concepts are blind. I show that intuitions as singular representations are not instances of passive data intake but the result of synthetic unification of the given manifold of the senses by the power of the imagination under the guidance of the understanding. (...) Against McDowell I argue that the amenability of intuitions to conceptual determination is not due some pre-existing, absolute conceptuality of the real but to the "work of the subject."3 On a more programmatic level, this paper seeks to demonstrate the limitations of a selective appropriation of Kant and the philosophical potential of a more comprehensive and thorough consideration of his work. Section 1 addresses the unique balance in Kant's philosophy between the work on particular problems and the orientation toward a systematic whole. Section 2 outlines McDowell's take on the Kantian distinction between intuition and concept in the context of the Kant readings by Sellars and Strawson. Section 3 exposes McDowell's relapse into the Myth of the Given. Section 4 proposes a reading of Kant's theoretical philosophy as an epistemology of metaphysical cognition. Section 5 details Kant's original account of sensible intuition in the Inaugural-Dissertation of 1770. Section 6 presents the transition from the manifold of the senses to the synthesis in the imagination and the unification through the categories in the Critique of pure reason . Section 7 addresses Kant's formalism in epistemology and metaphysics.Esse artigo examina a relação entre intuição e conceito em Kant à luz da posição neokantiana de John McDowell de que intuições estão conceitualmente "carregadas". 1 O foco é sobre o duplo pronunciamento de Kant, segundo o qual pensamentos sem conteúdo são vazios e intuições sem conceitos são cegas. Mostro que intuições como representações singuares não são casos de introdução passiva de dados, mas o resultado da unificação sintética do múltiplo dado dos sentidos pelo poder da imaginação sob a orientação do entendimento. Contra McDowell, defendo que a amabilidade das intuições para com a determinação conceitual não é devida a alguma conceitualidade pré-existente, absoluta do real, mas ao "trabalho do sujeito".2 Num nível mais programático, o presente artigo visa demonstrar as limitações de uma apropriação seletiva de Kant e o potencial filosófico de uma análise mais abrangente e aprofundada de sua obra. A seção 1 aborda o equilíbrio único na filosofia de Kant entre o trabalho com problemas particulares e a orientação em direção a um todo sistemático. A seção 2 descreve a posição de McDowell acerca da distinção kantiana entre intuição e conceito no contexto das leituras de Kant por Sellars e Strawson. A seção 3 expõe a reincidência de McDowell no "mito do dado". A seção 4 propõe uma leitura da filosofia teórica de Kant como uma epistemologia do conhecimento metafísico. A seção 5 detalha a explicação original de Kant sobre a intuição sensível na "Dissertação de 1770". A seção 6 apresenta a transição do múltiplo dos sentidos para a síntese na imaginação e para a unificação por meio das categorias na Crítica da razão pura . A seção 7 aborda o formalismo de Kant na epistemologia e na metafísica. (shrink)

We investigate various strong notions of rigidity for Souslin trees, separating them under ♢ into a hierarchy. Applying our methods to the automorphism tower problem in group theory, we show under ♢ that there is a group whose automorphism tower is highly malleable by forcing.

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)

Realism is a term that can be understood only by contrasting it with an opposite term, such as idealism or representationalism. But representationalism has indeed to presuppose something that is represented,in order for the representation to be possible at all. This does not mean,however, to fall prey to a naïve realism: our grasp on reality is always determined by our own way of accessing it. A realism which can take hold of this presupposition is to be called phenomenological realism. In (...) this sense, reality is always given only in representation, that is, mediated by our access to it, but is not itself representation. It is an objectivity opposed to ourself, it has a particular place and it appears, but its appearance does not belong to the subject, it is simply there. Therefore, appearances are spatial and have to be described as such. (shrink)

I investigate the relationships between three hierarchies of reflection principles for a forcing class $\Gamma $ : the hierarchy of bounded forcing axioms, of $\Sigma ^1_1$ -absoluteness, and of Aronszajn tree preservation principles. The latter principle at level $\kappa $ says that whenever T is a tree of height $\omega _1$ and width $\kappa $ that does not have a branch of order type $\omega _1$, and whenever ${\mathord {\mathbb P}}$ is a forcing notion in $\Gamma $, then it is (...) not the case that ${\mathord {\mathbb P}}$ forces that T has such a branch. $\Sigma ^1_1$ -absoluteness serves as an intermediary between these principles and the bounded forcing axioms. A special case of the main result is that for forcing classes that don’t add reals, the three principles at level $2^\omega $ are equivalent. Special attention is paid to certain subclasses of subcomplete forcing, since these are natural forcing classes that don’t add reals. (shrink)

Continuing the work of Fuchs [1], I show that the translation functions developed previously map iterable λ-structures to iterable s-structures and vice versa. To this end, I analyse how the translation functions interact with the formation of extender ultrapowers and normal iterations. This analysis makes it possible to translate iterations, and, in a last step, iteration strategies, thus arriving at the result.

It is shown that the boldface maximality principle for subcomplete forcing,, together with the assumption that the universe has only set many grounds, implies the existence of a well‐ordering of definable without parameters. The same conclusion follows from, assuming there is no inner model with an inaccessible limit of measurable cardinals. Similarly, the bounded subcomplete forcing axiom, together with the assumption that does not exist, for some, implies the existence of a well‐ordering of which is Δ1‐definable without parameters, and ‐definable (...) using a subset of ω1 as a parameter. This well‐order is in. Enhanced versions of bounded forcing axioms are introduced that are strong enough to have the implications of mentioned above, and along the way, a bounded forcing axiom for countably closed forcing is proposed. (shrink)

The contribution examines the aesthetic aspect of cognition in Kant by exploring the central function of the power of the imagination (Einbildungskraft) in Kant’s critical epistemology, first featured in the Critique of Pure Reason (1781; 1787) and revisited in the Critique of the Power of Judgment (1790). First, the focus will be on the relationship between the power of the imagination and the two main sources of (theoretical) cognition in Kant, viz., sensibility and the understanding. Second, special attention will be (...) devoted to the distinction between schema and symbol, as alternative products of the power of the imagination in the service of rendering discursive concepts intuitive – with schemata serving to make sensible the concepts of the understanding (Verstand) and symbols suited to provide intuitional counterparts to the concepts of reason (Vernunft). (shrink)

I prove that there is a recursive function T that does the following: Let X be transitive and rudimentarily closed, and let X ′ be the closure of X ∪ {X } under rudimentary functions. Given a Σ0-formula φ and a code c for a rudimentary function f, T is a Σω-formula such that for any equation image ∈ X, X ′ ⊧ φ [f ] iff X ⊧ T [equation image]. I make this precise and show relativized versions of (...) this. As an application, I prove that under certain conditions, if Y is the Σω extender ultrapower of X with respect to some extender F that also is an extender on X ′, then the closure of Y ∪ {Y } under rudimentary functions is the Σ0 extender ultrapower of X′ with respect to F, and the ultrapower embeddings agree on X. (shrink)

Gadamer’s hermeneutics is no discipline or simply a foundation of the Humanities, but addresses the fundamental problem of phenomenology: how things show themselves and can be attained. It does so, however, not in Husserl’s terminology but in its “ontological turn”. In elaborating on the ontology of language, Gadamer equates the accessibility of things and their Being, a move eminent in the “speculative character of language” discussed in the third part of Truth and Method. For Gadamer as well as for Heidegger, (...) ontology is possible only as phenomenology. How things show themselves, however, cannot be understood in relation to an absolute consciousness or understanding Dasein, but, following Plato, from the “evidence of the beautiful” in an hermeneutics of the artwork. Gadamer’s phenomenology thus describes the accessibility of things as the coming to pass of their truth and presence, much as the later Heidegger does in relation to physis and openness. Hermeneutical reflection of the fundamental problem of phenomenology also reveals the displacement in the continuity of coming to pass as the “space between words” opened in the manifold of interpretations. (shrink)

In seinem 1960 erschienenen Hauptwerk "Wahrheit und Methode" nimmt Gadamer die bis in die Antike zuruckreichende hermeneutische Tradition auf, um vor allem im Anschluss an Hegel und Heidegger eine philosophische Hermeneutik zu begrunden.

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.

Der vorliegende Aufsatz diagnosiziert im Sinne Nietzsche eine Krise des traditionellen Wahrheitsbegriffs, in dem Wahrheit als metaphysische Wahrheit verstanden wurde, die den Wahrheitsbegriffs, in dem Wahrheit als metaphysische Warheit verstanden wurde, die den Wahrheitsträgern zeitlos, zeichenunvermittelt und interperationsunabhängig zukommt. Die Kritik an diesem Verständnis bedient sich sowohl der Unterscheidung zwischen einem engen und einem weiten Sinn als auch der Gegenüberstellung einer alten und einer neuen Rede von Wahrheit. Letztere wird mit Hilfe eines drei-stufigen Modells der Zeichen- und Interpretationsverhältnisse entfaltet. Dadurch (...) gelingt es, Wahrheit als Funktion von Zeichen- und Interpretationsprozessen zu konzipieren und in ihrer Rolle zur Geltung zu bringen. Dieses neue Modell der Wahrheit erlaubt darüber hinaus einerseits eine Reformulierung älterer Aspekte der Wahrheitsfrage, andererseits aber auch die Neubestimmung der Wahrheit als zeichen- und interpretationsprozessual, historische, genealogisch und gradierbar.The article startes from a Nietzschean inspired diagnosis of the crisis of the traditional concept of truth, understood as timeless metaphysical truth, unmediated by signs and independent of interpretations. The critique of this notion makes use of a distinction between a narrow and a wide concept of truth as well as contrasting two construals of truth: an old and a new one. the latter is elaborated by means of a three-leveled model of signo-interpretational relations. This enables us to bring to the fore a notion of truth as a function of signo-interpretational processes. In addition, this new model of truth makes it possible to reformulate some of the old aspects of truth, while at the same time allowing for a new conception of truth as signo-interpretational, historical, genealogical, and gradable in character. (shrink)

This article gives an account of the material on the art of Paul Klee found in the Nachlass of Martin Heidegger and indicates ideas central to Heidegger’s encounter with Klee.