We show that for any real number, the class of real numbers less random than it, in the sense of rK-reducibility, forms a countable real closed subfield of the real ordered field. This generalizes the well-known fact that the computable reals form a real closed field. With the same technique we show that the class of differences of computably enumerable reals (d.c.e. reals) and the class of computably approximable reals (c.a. reals) form real closed fields. The d.c.e. result was also (...) proved nearly simultaneously and independently by Ng (Keng Meng Ng. Master's Thesis. National University of Singapore, in preparation). Lastly, we show that the class of d.c.e. reals is properly contained in the class or reals less random than Ω (the halting probability), which in turn is properly contained in the class of c.a. reals, and that neither the first nor last class is a randomness class (as captured by rK-reducibility). (shrink)

We show that if T is a trivial uncountably categorical theory of Morley Rank 1 then T is model complete after naming constants for a model.

Over the last few years there has been a resurgent interest in various scientific disciplines in Popper’s arguments. To gain a greater appreciation of Popper’s scientific arguments, they need to be viewed in relation to his broader philosophy and where this stands within the history of ideas. This book aims to take seriously those aspects of Popper’s writings that have received less attention and wherein he advanced metaphysical, speculative, mystical-poetic, aesthetic and Platonic arguments. Such arguments are crucial for an appreciation (...) of his scientific and political writings. I argue that Popper, much like Wittgenstein previously has been misconstrued as an Anglo-analytic philosopher. This book provides an interpretation of Popper’s mature philosophy within his Central-European intellectual context. The aim of which is to open up a fruitful line of investigation into Popper’s thought that I hope would continue over the coming years. Alexander Naraniecki has spent time at the Popper Archives at the University of Klagenfurt in Austria whilst researching for this book. He has also been a visiting scholar at Duke University and has completed a postdoctoral research fellowship at Deakin University in Melbourne. Dr Naraniecki also publishes on issues relating to multiculturalism, globalization, cosmopolitanism as well as inter-cultural relations and dialogue. He has published on Popper in various leading journals such as Philosophy, Boston Studies in the Philosophy of Science, and The European Legacy. He is currently building his research on Popper in a broader direction by exploring issues related to creativity and problem solving for critical thinking. (shrink)

This paper focuses on Gundissalinus’s particularly important contribution to metaphysics which it presents in three steps: firstly, a succinct overview of the history of the relevant metaphysical terminology from the Late Ancient period to the Middle Ages shows how, for the first time, Gundissalinus interpreted metaphysics as the name of a discipline ; in a second step, the paper analyzes the specific epistemological foundation of metaphysics as an autonomous science, namely as ontology, in the chapter on metaphysics in Gundissalinus’s De (...) divisione philosophiae, paying particular attention to his criticism of twelfth-century theology as this was developed in the School of Chartres; thirdly, the paper examines a crucial text from the treatise on the division of the sciences: in it, Gundissalinus included an otherwise unknown translation of a passage from Avicenna’s Book of Demonstration which discusses the thorny issue of the subordination of the philosophical disciplines to metaphysics. This subject is one which would continue to receive plenty of attention in later times, as the examples of Robert Kilwardby and John Duns Scotus demonstrate, both of which authors may be considered to have continued Gundissalinus’s metaphysical project. (shrink)

A special issue of_ New German Critique_ The posthumous publication of Theodor W. Adorno’s works on music continues to reveal the special relationship between music and philosophy in his thinking. These important works have not, however, received as much scholarly attention as they deserve. Contributors to this issue seek to provide insight into some of the key themes raised in these works, including the sociology of musical genre, the historical transformation of music from the "heroic" or high-bourgeois era to late (...) modernity, the meaning of both performance and listening in the era of mass communication, and the specific challenges or deformations of the radio on musical form, a theme that implicates many of the digital practices of our own age. There is much left to discover in these new publications, and they pose again, with renewed vigor, the question of Adorno’s _Aktualität_—his polyvalent, untranslatable term for, among other things, the intellectual relationship between the present and the past. Contributors Daniel K. L. Chua, Lydia Goehr, Peter E. Gordon, Martin Jay, Brian Kane, Max Paddison, Alexander Rehding, Fred Rush, Martin Scherzinger. (shrink)

An accessible dictionary of the key terms, ideas, influence and legacy of G.W.F. Hegel, one of the most important German Philosophers of the 19th Century.

Although metaphysics as a discipline can hardly be separated from Aristotle and his works, the questions it raises were certainly known to authors even before the reception of Aristotle in the thirteenth century. Even without the explicit use of this term the twelfth century manifested a strong interest in metaphysical questions under the guise of «natural philosophy» or «divine science», leading M.-D. Chenu to coin the expression of a twelfth century «éveil métaphysique». In their commentaries on Boethius and under the (...) influence of Neoplatonism, twelfth century authors not only anticipate essential elements of thirteenth century metaphysics, they also make an original contribution to the history of metaphysics by attempting to integrate the theory of first principles, philosophical theology and ontology. This volume presents and examines the contributions of the twelfth century to metaphysics made by selected Jewish, Christian and Muslim authors of the Iberian Peninsula and Francia. -/- Contributors include Matthias Lutz-Bachmann (Frankfurt am Main), Andreas Speer (Würzburg), Charles Burnett (London), Alexander Fidora (Frankfurt am Main), Thomas Ricklin (Neuchâtel), Yossef Schwartz (Jerusalem), Josep Udina (Barcelona), Jack C. Marler (St. Louis/USA), Gillian R. Evans (Cambridge), Andreas Niederberger (Frankfurt am Main) and Françoise Hudry (Paris). (shrink)

If the total state of the universe is encodable by a real number, Hardin and Taylor have proved that there is a solution to one version of the problem of induction, or at least a solution to a closely related epistemological problem. Is this philosophical application of the Hardin-Taylor result modest enough? The paper advances grounds for doubt. [A longer and more detailed sequel to this paper, 'Proving Induction', was published in the Australasian Journal of Logic in 2011.].

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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. 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. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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)

This Is A New Release Of The Original 1898 Edition.