This paper gives a formalization of general topology in second-order arithmetic using countably based MF spaces. This formalization is used to study the reverse mathematics of general topology. For each poset P we let MF denote the set of maximal filters on P endowed with the topology generated by {Np | p ∈ P}, where Np = {F ∈ MF | p ∈ F}. We define a countably based MF space to be a space of the form MF for some (...) countable poset P. The class of countably based MF spaces includes all complete separable metric spaces as well as many nonmetrizable spaces. The following reverse mathematics results are obtained. The proposition that every nonempty Gδ subset of a countably based MF space is homeomorphic to a countably based MF space is equivalent to [Formula: see text] over ACA0. The proposition that every uncountable closed subset of a countably based MF space contains a perfect set is equivalent over [Formula: see text] to the proposition that [Formula: see text] is countable for all A ⊆ ℕ. The proposition that every regular countably based MF space is homeomorphic to a complete separable metric space is equivalent to [Formula: see text] over [Formula: see text]. (shrink)

We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π2 1 comprehension. An MF space is defined to be a topological space of the form MF(P) with the topology generated by $\lbrace N_p \mid p \in P \rbrace$ . Here P is a poset, MF(P) is the set of maximal filters on P, and $N_p = \lbrace F \in MF(P) \mid p \in F \rbrace$ . If the poset P is countable, (...) the space MF(P) is said to be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, "every countably based MF space which is regular is homeomorphic to a complete separable metric space," is equivalent to Π2 1-CA0. The equivalence is proved in the weaker system Π1 1-CA0. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π2 1 comprehension. (shrink)

We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π12 comprehension. An MF space is defined to be a topological space of the form MF with the topology generated by {Np ∣ p ϵ P}. Here P is a poset, MF is the set of maximal filters on P, and Np = {F ϵ MF ∣ p ϵ F }. If the poset P is countable, the space MF is said to (...) be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, “every countably based MF space which is regular is homeomorphic to a complete separable metric space,” is equivalent to. The equivalence is proved in the weaker system. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π12 comprehension. (shrink)

Let n be a positive integer. By a $\beta_{n}-model$ we mean an $\omega-model$ which is elementary with respect to $\sigma_{n}^{1}$ formulas. We prove the following $\beta_{n}-model$ version of $G\ddot{o}del's$ Second Incompleteness Theorem. For any recursively axiomatized theory S in the language of second order arithmetic, if there exists a $\beta_{n}-model$ of S, then there exists a $\beta_{n}-model$ of S + "there is no countable $\beta_{n}-model$ of S". We also prove a $\beta_{n}-model$ version of $L\ddot{o}b's$ Theorem. As a corollary, we obtain (...) a $\beta_{n}-model$ which is not a $\beta_{n+1}-model$. (shrink)

We study the Lindenbaum algebra ${\fancyscript{A}}$ (WKL o, RCA o) of sentences in the language of second-order arithmetic that imply RCA o and are provable from WKL o. We explore the relationship between ${\Sigma^1_1}$ sentences in ${\fancyscript{A}}$ (WKL o, RCA o) and ${\Pi^0_1}$ classes of subsets of ω. By applying a result of Binns and Simpson (Arch. Math. Logic 43(3), 399–414, 2004) about ${\Pi^0_1}$ classes, we give a specific embedding of the free distributive lattice with countably many generators into ${\fancyscript{A}}$ (...) (WKL o, RCA o). (shrink)

The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to formalize the logic of Reverse Mathematics into a system that we name s-logic. We argue that s-logic captures precisely the “logical” content of the implication and nonimplication relations between subsystems in Reverse Mathematics. We present a sound, complete, decidable, and compact tableau-style deductive system (...) for s-logic, and explore in detail two fragments that are particularly relevant to Reverse Mathematics practice and automated theorem proving of Reverse Mathematics results. (shrink)

We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does not extend to a larger filter. We show that every computable poset has a \Delta^0_2 maximal filter, and there is a computable poset with no \Pi^0_1 or \Sigma^0_1 maximal filter. There is a computable poset on which every maximal filter is Turing complete. We obtain the reverse mathematics result that the principle (...) "every countable poset has a maximal filter" is equivalent to ACA₀ over RCA₀. An unbounded filter is a filter which achieves each of its lower bounds in the poset. We show that every computable poset has a \Sigma^0_1 unbounded filter, and there is a computable poset with no \Pi^0_1 unbounded filter. We show that there is a computable poset on which every unbounded filter is Turing complete, and the principle "every countable poset has an unbounded filter" is equivalent to ACA₀ over RCA₀. We obtain additional reverse mathematics results related to extending arbitrary filters to unbounded filters and forming the upward closures of subsets of computable posets. (shrink)

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$ sentence of a certain form is provable using E-HA ${}^\omega$ along with the axiom of choice and an independence of premise principle, the sequential form of the statement is provable in the classical system RCA. We obtain this and similar results using applications of modified realizability and the Dialectica interpretation. (...) These results allow us to use techniques of classical reverse mathematics to demonstrate the unprovability of several mathematical principles in subsystems of constructive analysis. (shrink)

We show that \\) cannot be proved with one typical application of \\) in an intuitionistic extension of \ to higher types, but that this does not remain true when the law of the excluded middle is added. The argument uses Kohlenbach’s axiomatization of higher order reverse mathematics, results related to modified reducibility, and a formalization of Weihrauch reducibility.

The book is an examination of the problem of the self and the role of error in its identity.

Carl Schmitt and the Problem of the Realization of Law 1. The famous pithy aphorisms that Carl Schmitt used to open his major works - 'the sovereign is he who decides on the exception', 'the concept of the state presupposes the concept of the political', etc. - have become a part of the common discourse of contemporary scholarship on politics and the law. The theoretical framework that animates these slogans, however, has remained somewhat opaque. It has often been (...) argued that there is no such framework, that Schmitt was a situational thinker whose works are best understood as interventions in concrete political debates that do not add up to a grand theoretical vision. (shrink)

I argue that Quine’s naturalization of Lewis’s Kantian pragmatism should be understood in terms of Lewis’s attempt to de-psychologize pragmatist epistemology. Lewis wants epistemology to be a priori in order to be distinct from psychology. Quine’s criticisms of Lewis result in a picture that weakens the distinction between epistemology and psychology. Nevertheless, Quine’s naturalized Kantian pragmatism remains far more Kantian than is widely recognized, due to what Quine retains from Lewis.

Within the book, he discussed the origin and forms of musical activity as well as various theories on the origin of music. This is the first time that this important work is available in English.

One of the most significant political philosophers of the twentieth century, Carl Schmitt is a deeply controversial figure who has been labeled both Nazi sympathizer and modern-day Thomas Hobbes. First published in 1938, The Leviathan in the State Theory of Thomas Hobbes used the Enlightenment philosopher’s enduring symbol of the protective Leviathan to address the nature of modern statehood. A work that predicted the demise of the Third Reich and that still holds relevance in today’s security-obsessed society, this volume (...) will be essential reading for students and scholars of political science. “Carl Schmitt is surely the most controversial German political and legal philosopher of this century. . . . We deal with Schmitt, against all odds, because history stubbornly persists in proving many of his tenets right.”— Perspectives on Political Science “[A] significant contribution. . . . The relation between Hobbes and Schmitt is one of the most important questions surrounding Schmitt: it includes a distinct, though occasionally vacillating, personal identification as well as an association of ideas.”— Telos. (shrink)

The recent accumulation of environmental crises poses a radical challenge to the conceptual organization of the modern Western political imaginary and the history of political thought by unsettling its ontological understanding of ‘nature’. Specifically, to the extent that they rely on such troublesome understandings, this means the central notions we use to orient ourselves politically, such as labor, can no longer straightforwardly serve this purpose. This paper has argued a paradoxical return to Locke against Locke, and the insight into the (...) entanglements of labor, property, and nature this enables, can provide us with a way of holding together the complexity of this predicament. The first part recovered from the critical scholarship on Locke of the past 50 years the manifold ways in which Lockean ideas about labor are caught up with specific assumptions about colonialism, gendered hierarchies, and nature. The second part argued no singular conceptual reconstruction of labor can do justice to its hybrid character, which the present predicament has revealed. The third part argued, by recovering what the Lockean heritage has obscured, the critical scholarship gives us a way into the knotty problems of the organization of labor and the structure of the political collective. (shrink)

On Becoming an Effective Teacher presents the final unpublished writings of Rogers and as such has a unique historical value. It also documents the research results of four highly relevant, related but independent studies which comprise the biggest collection of data ever accumulated to test a person-centred theory in the field of education. This body of comprehensive research on effective teaching was accomplished over a twenty-year period in 42 States in the U.S. and in six other countries including the UK, (...) Germany, Brazil, Canada, Israel, and Mexico, and is highly relevant to the concerns of teachers, psychologists, students, and parents. The principal findings of the research in this book show that teachers and schools can significantly improve their effectiveness through programs focusing on facilitative interpersonal relationships. Teachers who either naturally have, or are trained to have empathy, genuineness (congruence), and who prize their students (positive regard) create an important level of trust in the classroom and exert significant positive effects on student outcomes including achievement scores, interpersonal functioning, self-concept, and attendance. The dialogues between Rogers and Lyon offer a unique and timeless perspective on teaching, counselling and learning. The work of Reinhard Tausch on person-centered teaching to counselors, parents, athletics, and even textbook materials, as well as research on the interactions of teachers and students, is among the most thorough and rigorous research ever accomplished on the significance and potential of a person-centered approach to teaching and learning. (shrink)

The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical (...) philosophy, and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant. (shrink)

Reinholds Briefe uber die Kantische Philosophie gehoren zu den wirkungsmachtigsten Produkten seines umfangreichen Schaffens. Von den Zeitgenossen teils mit grosser Begeisterung aufgenommen, tragen sie wesentlich zur Etablierung der ersten Kant-Bewegung bei. Durch ihr Bestreben, die Vernunftkritik als Theorie der moralisch-religiosen Erneuerung zu prasentieren, gelten sie als die brisanteste unter den damaligen philosophischen Neuerscheinungen. Sie sind wegweisend fur einen Kantianismus, der sich im Laufe der 1790er Jahre als eine die politischen Umwalzungen in Frankreich flankierende Geistesrevolution begreift. Der neu herausgegebene Band enthalt (...) zwolf Briefe, welche die auffallendsten Resultate von Kants Vernunftkritik ausgehend von den dringendsten wissenschaftlichen und moralischen Bedurfnissen unserer Zeit darstellen. Der Adressat erfahrt, dass mit Kants Erkenntniskritik und moralischer Neubegrundung der speziellen Metaphysik ein taugliches Mittel zur Bewaltigung gegenwartiger Grundlagenkrisen im Gebiete von Moral, Naturrecht, Theologie und Asthetik bereitsteht. Mit Nachdruck wird das problemlosende Potential von Kants moraltheologischen Resultaten hervorgehoben. In Kants Vernunftglauben und Statuierung eines moralischen Erkenntnisgrundes fur das Dasein Gottes und die Unsterblichkeit der Seele sieht Reinhold die besten Voraussetzungen fur die Beendigung einer Reihe aufklarungshemmender Debatten. Im Visier steht allem voran der als Pantheismusstreit beruhmt gewordene Disput zwischen Mendelssohn und Jacobi, in dessen Einflussbereich ein wenig ergiebiger Kampf zwischen Naturalisten und Supernaturalisten dominant werden sollte. Die Darstellung geschichtlicher Kontexte zur Idee der Unsterblichkeit der Seele und die eingehende Auseinandersetzung mit den antiken Seelenlehren kulminieren in der These, durch Kants Kritik und Neufundierung der rationalen Psychologie konne auch der bisherige, Antike und Neuzeit durchziehende Gegensatz zwischen Spiritualisten und Materialisten als aufgelost gelten. Wiederholt wird zu Reflexionen uber die Geschichte der Menschheit angesetzt, die deutlich machen, dass Reinhold das Geschichtsbild der Illuminaten mehr und mehr in Anlehnung an Lessings Idee einer kommenden Menschheitsepoche des dritten Evangeliums sowie an Kants Vision eines weltburgerlichen Endzustandes vortragt. Die Neuedition ist mit einer ausfuhrlichen Einleitung und einem Kommentar versehen. In diesen Teilen wird unter anderem auf die Entstehungsgeschichte der Briefe, auf Reinholds Kant-Rezeption sowie auf sein Kant-Verstandnis, das mit der damals gangigen Ansicht uber den Alleszermalmer kontrastiert, eingegangen. Vermerkt werden zudem inhaltlich relevante Abweichungen von fruheren Fassungen der in den Band von 1790 eingeflossenen Textteile. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

T. 1. Die Theorie Literaturverzuchnis (p. 210-217).

Carl Craver investigates what we are doing when we sue neuroscience to explain what's going on in the brain.

Dieser Titel aus dem De Gruyter-Verlagsarchiv ist digitalisiert worden, um ihn der wissenschaftlichen Forschung zugänglich zu machen. Da der Titel erstmals im Nationalsozialismus publiziert wurde, ist er in besonderem Maße in seinem historischen Kontext zu betrachten. Mehr erfahren Sie.

Schmitt, C. Die Tyrannei der Werte.--Jüngel, E. Wertlose Wahrheit.--Schelz, S. Der Wert als ideologischer Begriff.

Carl F. Craver investigates what we are doing when we use neuroscience to explain what's going on in the brain. When does an explanation succeed and when does it fail? Craver offers explicit standards for successful explanation of the workings of the brain, on the basis of a systematic view about what neuroscientific explanations are.

Einfuhrung Carl Schmitt: Der Schatten Gottes. INtrospektionen, Tagebucher und Briefe 1921 bis 1924 Teil I: Tagebuch August 1921 bis August 1922 Bearbeitet von Gerd Giesler und Ernst Husmert Teil II: Tagebuch 1923 und 1924 Bearbeitet von Wolfgang H. SPindler Teil III: Der Schatten Gottes. AUfzeichnungen aus den Jahren 1922 bis 1924 Bearbeitet von Gerd Giesler, Ernst Husmert und Wolfgang H. SPindler Anhang Briefe, Dokumente und Abbildungen Verzeichnis der mehrfach genannten Literatur Quellen und Nachschlagewerke Abbildungs- und Quellennachweis Personenverzeichnis.