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)

Phylogenies are increasingly prominent across all of biology, especially as DNA sequencing makes more and more trees available. However, their utility is compromised by widespread misconceptions about what phylogenies can tell us, and improved tree thinking is crucial. The most-serious problem comes from reading trees as ladders from left to right - many biologists assume that species-poor lineages that appear early branching or basal are ancestral - we call this the primitive lineage fallacy. This mistake causes misleading inferences about changes (...) in individual characteristics and leads to misrepresentation of the evolutionary process. The problem can be rectified by considering that modern phylogenies of present-day species and genes show relationships among evolutionary cousins. Emphasizing that these are extant entities in the 21st century will help correct inferences about ancestral characteristics, and will enable us to leave behind 19th century notions about the ladder of progress driving evolution. (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

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)

A model for the ideal state includes discussions of the nature and application of justice, the role of the philosopher in society, the goals of education, and the effects of art upon character.

In recent years the writings of Ludwig Wittgenstein have received much attention from philosophers in general and especially from philosophers interested in religion; and there is no doubt that Wittgenstein's legacy of thought is both highly suggestive and highly problematical. It seems likely, however, that the vogue which Wittgenstein now enjoys owes not a little to his peculiar place in the development of modern philosophy and, in particular, of that empiricist tradition in philosophy which stems from what has been called (...) the revolution in philosophy in the early decades of the present century. (shrink)

This paper argues against the thesis of Professor Savan, that Spinoza's views about words and about the imagination are such that he could not consistently say, and indeed did not think, that philosophical truths can be expressed adequately in language. The evidence for this thesis is examined in detail, and it is argued that Spinoza should have distinguished between two types of imagination, corresponding roughly to Kant's transcendental and empirical imagination. Finally, it is suggested that the bulk of the argument (...) of the Ethics is conducted on the level of the ?second kind of knowledge?, reason, but that it also contains examples of the use of the first and third kinds of knowledge. (shrink)