Let H be a proof system for quantified propositional calculus (QPC). We define the Σqj-witnessing problem for H to be: given a prenex Σqj-formula A, an H-proof of A, and a truth assignment to the free variables in A, find a witness for the outermost existential quantifiers in A. We point out that the Σq1-witnessing problems for the systems G*1and G1 are complete for polynomial time and PLS (polynomial local search), respectively. We introduce and study the systems G*0 and G0, (...) in which cuts are restricted to quantifier-free formulas, and prove that the Σqj-witnessing problem for each is complete for NC1. Our proof involves proving a polynomial time version of Gentzen’s midsequent theorem for G*0 and proving that G0-proofs are TC0-recognizable. We also introduce QPC systems for TC0 and prove witnessing theorems for them. We introduce a finitely axiomatizable second-order system VNC1 of bounded arithmetic which we prove isomorphic to Arai’s first order theory AID + Σb0-CA for uniform NC1. We describe simple translations of VNC1 proofs of all bounded theorems to polynomial size families of G*0 proofs. From this and the above theorem we get alternative proofs of the NC1 witnessing theorems for VNC1 and AID. (shrink)

The 14th International Congress of Philosophy, held late last summer in Vienna, had an entire subsection devoted to Hegel. Several papers were presented by philosophers from America, including: "Hegel In Light of His First American Followers", by Professor Loyd D. Easton of Ohio Wesleyan University; "Hegel and Husserl", by Professor W.H. Werkmeister of The Florida State University; "Hegel's Theory of Signification & The Origin of Dialectic", by Professor Daniel Cook of Herbert H. Lehman College ; "Beginning the System: Kierkegaard (...) and Hegel", by Professor Robert Perkins, University of South Alabama. These papers and others will be published in the Congress Proceedings. Inquiries should be directed to the University of Vienna Department of Philosophy. * * * Professor H.S. Harris of Glendon College, York University, Toronto, will shortly have published in a volume titled Essays in Honour of Max Fisch "The Fragment on Faith and Being in Hegel's Early Theological Writings". The essay contains the text translation and a full commentary on the fragment Glauben und Sein in Nohl. * * * The Fall issue of Philosophy Today contain an article by Professor Howard P. Kainz of Marquette University titled "Hegel's Characterization of Truth in the Phenomenology". * * * James F. Donaldson of Texas Technological College has an article titled "The Origin of Hegel's Dialectic" in the current issue of Lavel Theologique et Philosophique. A brief abstract of the paper may be found in the Fall, 1969 Philosopher's Index. (shrink)

In "Realism and Reason" Hilary Putnam has offered an apparently strong argument that the position of metaphysical realism provides an incoherent model of the relation of a correct scientific theory to the world. However, although Putnam's attack upon the notion of the "intended" interpretation of a scientific theory is sound, it is shown here that realism may be formulated in such a way that the realist need make no appeal to any "intended" interpretation of such a theory. Consequently, it can (...) be shown that realism is immune to Putnam's criticism and that attempts at reformulating this criticism are not likely to meet with success. (shrink)

This paper and its predecessor () are about the question: 'Are the events in the entire universe encoded in and predictable from any of its parts?' To approach a positive answer in classical physics, the following result is proved and commented on: in Newton's theory of gravitation, the entire trajectory of a particle can be predicted given any segment of it, regardless of how the other particles are moving-provided that there is only a finite number of particles and that their (...) speeds remain bounded. (It is this condition, together with a set of parameters characterising the motion of the other particles, which enables us to estimate the effect of the other particles on the trajectory of the given particle.) The extension of this result to other theories, in particular to special relativity, is discussed. (shrink)

H G WellsHerbert George Wells, an English writer, was born on 21st 1866 and died on 13 Aug 1946. He was renowned for his works of science fiction especially 'The Time Machine'. He is also referred as 'The Father of Science Fiction'.

'Uncertainty and chance' is a subject with a broad span, in that there is no academic discipline or walk of life that is not beset by uncertainty and chance. In this book a range of approaches is represented by authors from varied disciplines: natural sciences, mathematics, social sciences and medical sciences. At one extreme, this volume is concerned with the foundations of probability. At the other extreme, we have scholars who acknowledge the concept of chance and uncertainty but do not (...) cope with it by means of systematic measurement or quantative analysis. (shrink)