Studies on the 1616 and 1633 actions brought against Galilei by the Index and the Inquisition generally presumed that part of the documentation was still to be unveiled. This assumption was frequently accompanied by the hypothesis that some available documents were forgeries, merely composed to justify the 1633 condemnation. New documents from the Archive of the Roman Inquisition, including a censure of Saggiatore, official acts concerning the public dissemination of the verdict, and applications for permission to read Galilei¹s works, show (...) that the 1984 edition of his trial was not exhaustive. It is argued, however, that these documents were not concealed intentionally by the Holy Office and their not being found so far has been mainly due to the poor organisation of the Archive. Gianfranco Catelli, Gouhier e la cosiddetta dottrina della terza nozione primitiva In questo studio non si condivide l’opinione, dominante per molti decenni, che il cosiddetto dualismo cartesiano sia dovuto ad un “malinteso”, che può chiamarsi originario, dato che a rimanerne coinvolti furono alcuni tra i primi seguaci della filosofia di Cartesio. Una presa di posizione, questa, che, già sviluppata in altri precedenti lavori, viene qui riproposta relativamente a H. Gouhier, lo studioso che più di ogni altro, con ricchezza di documenti e sottigliezza di analisi interpretative, ha sostenuto la tesi del “malinteso” e ha individuato nella dottrina della terza nozione primitiva la spiegazione autenticamente cartesiana del rapporto sussistente tra anima e corpo. Una interpretazione di cui nel presentge studio si mostra tutta la debolezza, soprattutto se la si considera alla luce dell’altra dottrina, anch’essa cartesiana, ma di gran lunga più articolata, che fa del rapporto tra anima e corpo un nesso da spiegarsi in analogia al rapporto che nel linguaggio intercorre tra il segno e il suo significato. (shrink)

The Scottish physician James Lind is the most celebrated name in the history of research into the causes and cures of scurvy. This is due to the famous experiment he conducted in 1747 on H.M.S. Salisbury in order to compare the efficiency of six popular treatments for scurvy. This experiment is generally regarded as the first controlled trial in clinical science (see e.g. Carpenter 1986, p. 52).

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov function, which (...) assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)

Sufficient conditions are given for the computation of an arc that accesses a point on the boundary of an open subset of the plane from a point within the set. The existence of a not-computably-accessible but computable point on a computably compact arc is also demonstrated.

We use the compactness theorem of continuous logic to give a new proof that $$L^r([0,1]; {\mathbb {R}})$$ isometrically embeds into $$L^p([0,1]; {\mathbb {R}})$$ whenever $$1 \le p \le r \le 2$$. We will also give a proof for the complex case. This will involve a new characterization of complex $$L^p$$ spaces based on Banach lattices.

Reviewed Works:Andrea Sorbi, Complexity, Logic, and Recursion Theory.Klaus Ambos-Spies, Elvira Mayordomo, Resource-Bounded Measure and Randomness.Marat Arslanov, Degree Structures in Local Degree Theory.Jose L. Balcazar, Ricard Gavalda, Montserrat Hermo, Compressibility of Infinite Binary Sequences.S. Barry Cooper, Beyond Godel's Theorem: The Failure to Capture Information Content.Robert A. Di Paola, Franco Montagna, Progressions of Theories of Bounded Arithmetic.Rodney G. Downey, On Presentations of Algebraic Structures.Sophie Fischer, Lane Hemaspaandra, Leen Torenvliet, Witness-Isomorphic Reductions and Local Search.William Gasarch, Carl H. Smith, A Survey of Inductive Inference (...) with an Emphasis on Queries.Andre Nies, A Uniformity of Degree Structures.Piergiorgio Odifreddi, Short Course on Logic, Algebra, and Topology.Andrea Sorbi, The Enumeration Degrees of the $\sigma^0_2$ Sets.Peter van Emde Boas, The Convenience of Tilings. (shrink)

This volume is not restricted to papers presented at the 1988 Colloquium, but instead aims to provide the reader with a (relatively) coherent reading on Algebraic Logic, with an emphasis on current research. To help the non-specialist reader, the book contains an introduction to cylindric and relation algebras by Roger D. Maddux and an introduction to Boolean Algebras by Bjarni Joacute;nsson.

Arguing that the universe is absolutely directioned and that there exist spatial (directional) relations that Leibniz overlooked, H. Scott Hestevold formulates a new relationalist theory of space, exploring its implications for the Special Composition Question, reductivism regarding boundaries and holes, and the nature of spacetime.

Problems for strict and convex Bayesianism are discussed. A set-based Bayesianism generalizing convex Bayesianism and intervalism is proposed. This approach abandons not only the strict Bayesian requirement of a unique real-valued probability function in any decision-making context but also the requirement of convexity for a set-based representation of uncertainty. Levi's E-admissibility decision criterion is retained and is shown to be applicable in the nonconvex case.

Open peer commentary on the article “Religion: A Radical-Constructivist Perspective” by Andreas Quale. Upshot: Quale offers a way of categorizing religious discourse based on radical constructivism. This commentary raises questions about the inter-relation of cognitive and non-cognitive knowledge, the role of testimony in learning about religion, and whether knowledge and belief have different roles in cognitive and non-cognitive knowledge, and suggests that Quale’s analysis opens a tolerant perspective on religious discourse.

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)

Originally published in 1933, this volume contains the emended text of the Adamson Lecture for 1930, delivered by H. J. C. Grierson under the title 'Carlyle and the Hero'. This book will be of value to anyone with an interest in the modern and possibly controversial applications of Carlyle's philosophy.