Given an admissible indexing φ of the countable atomless Boolean algebra B, an automorphism F of B is said to be recursively presented (relative to φ) if there exists a recursive function $p \in \operatorname{Sym}(\omega)$ such that F ⚬ φ = φ ⚬ p. Our key result on recursiveness: Both the subset of $\operatorname{Aut}(\mathscr{B})$ consisting of all those automorphisms which are recursively presented relative to some indexing, and its complement, the set of all "totally nonrecursive" automorphisms, are uncountable. This arises (...) as a consequence of the following combinatorial investigations: (1) A comparison of the cycle structures of f and f̄, where f is a permutation of some free basis of B and f̄ is the automorphism of B induced by f. (2) An explicit description of the permutations of ω whose conjugacy classes in $\operatorname{Sym}(\omega)$ are (a) uncountable, (b) countably infinite, and (c) finite. (shrink)

Schelling's first systematic attempt to articulate a complete philosophy of nature.

The author is a student of the renowned German medievalist, Josef Koch. Having himself worked for more than ten years on medieval commentaries on Aristotle's Physics and Metaphysics, Zimmermann wishes to make the result of his researches available to others. To reduce his mass of material to tractable dimensions, he follows the pattern of F. Stegmüller's Repertorium of commentaries on Lombard's Sentences, giving first a description of the manuscripts examined, then a transliteration of the titles of all questions treated (...) in the respective commentaries, together with the folio at which each question begins, and grouping the works of identified authors before the anonymous works in each category. The first volume is limited to manuscripts contained in collections at Munich, Innsbruck, Cambridge, Oxford, London, Paris, and Cambrai; a second volume, with wider coverage, is promised shortly. The majority of the authors reported on in the first volume are anonymous, but those identified include Adam of Bocfeld, Augustine Triumphus of Ancona, Boethius of Dacia, Geoffrey of Aspall, John of Wacfeld, Peter of Alvernia, Radulfus Brito, Siger of Brabant, Simon of Faversham, William Bonkys, William of Chelvestun, and William of Clifford. This, like Stegmüller's, is clearly a reference work for scholars, and its principal merit lies in that it provides an accurate list of physical and metaphysical topics being discussed at centers of learning in England and on the Continent from the mid-thirteenth to the mid-fourteenth centuries. It was during this period, of course, that Aristotle was having his greatest impact on Latin Christendom. The questions listed by Zimmermann have their intrinsic interest, but even more they provide historians of science and of philosophy with considerable material for investigation, for analysis, and, hopefully, for the dating and identification of the works listed as anonymous. Zimmermann makes no attempt at completeness of reference, supplying only a few citations in his notes; on Geoffrey of Aspall, for instance, he refers only to Emden's Biographical Register, missing Enya MacRae's Geoffrey of Aspall's Commentaries on Aristotle, Medieval and Renaissance Studies 6. Regrettably the volume has neither a subject index nor a register of names, deficiencies that seriously impair its usefulness--W. A. W. (shrink)

This is an English translation of Schelling's Ideas for a Philosophy of Nature (first published in 1797 and revised in 1803), one of the most significant works in the German tradition of philosophy of nature and early nineteenth-century philosophy of science. It stands in opposition to the Newtonian picture of matter as constituted by inert, impenetrable particles, and argues instead for matter as an equilibrium of active forces that engage in dynamic polar opposition to one another. In the revisions of (...) 1803 Schelling incorporated this dialectical view into a neo-Platonic conception of an original unity divided upon itself. The text is of more than simply historical interest: its daring and original vision of nature, philosophy, and empirical science will prove absorbing reading for all philosophers concerned with post-Kantian German idealism, for scholars of German Romanticism, and for historians of science. (shrink)

Few editors of Virgil have given these last three words a satisfactory sense: none, to my knowledge, has fully recognized their difficulty. The root of the trouble lies in the Roman repugnance for limiting words to a single, specialized, technical sense: licium and tela are, consequently, found with a variety of different meanings. Notwithstanding this difficulty, however, I hope to show that this passage has a meaning that is both simple and unambiguous.

Sir D'Arcy Thompson's emendation of νθρωπоς to νоς in several passages of the Historia Animalium , and his explanation of the corruption as due to confusion between νος and an abbreviation both receive strong confirmation from a passage of Polybius, describing an allenged procession held by Demetrius of Phalerum, in which a similar emendation has already been made and widely accepted.

For 20th century mathematicians, the role of Cantor's sets has been that of the ideally featureless canvases on which all needed algebraic and geometrical structures can be painted. (Certain passages in Cantor's writings refer to this role.) Clearly, the resulting contradication, 'the points of such sets are distinc yet indistinguishable', should not lead to inconsistency. Indeed, the productive nature of this dialectic is made explicit by a method fruitful in other parts of mathematics (see 'Adjointness in Foundations', Dialectia 1969). This (...) role of Cantor's theory is compared with the role of Galois theory in algebraic geometry. (shrink)

Schelling’s masterpiece investigating evil and freedom.

On the History of Modern Philosophy is a key transitional text in the history of European philosophy. In it, F. W. J. Schelling surveys philosophy from Descartes to German Idealism and shows why the Idealist project is ultimately doomed to failure. The lectures trace the path of philosophy from Descartes through Spinoza, Leibniz, Kant, Fichte, Jacobi, to Hegel and Schelling's own work. The extensive critiques of Hegel prefigure many of the arguments to be found in Feuerbach, Kierkegaard, Marx, Nietzsche, Heidegger, (...) and Derrida. This is the first English translation of On the History of Modern Philosophy. In his introduction Andrew Bowie sets the work in the context of Schelling's career and clarifies its philosophical issues. The translation will be of special interest to philosophers, intellectual historians, literary theorists, and theologians. (shrink)

Part novella, part philosophy, Clara was Schelling's most popular work during his lifetime, and appears here in English for the first time.

A new English translation of Schelling’s unfinished magnum opus, complete with a contextualizing introduction by the translator.

Makes Schelling’s dialogue Bruno readily accessible to the English-language reader, with valuable commentary on the work itself, which details Schelling’s account of his differences from Fichte.