Book reviews

Science as Salvation: a Modern Myth and its Meaning, Mary Midgley, 1994. London, Routledge x +256pp., Hb 04 15062713, £35; Pb 04 15107733, £8.99

Philosophical Naturalism, David Papineau, 1993 Oxford, Basil Blackwell xii +219pp., Hb 0631189025, £40; Pb 0631189033, £14.99

F. H. Bradley, Writings on Logic and Metaphysics, James W. Allard & Guy Stock (Eds), 1994. Oxford, Clarendon Press xv+357pp, Hb 0–198–24445–2, £40.00; Pb 0–198–24438‐X, £14.95

Invariance and Heuristics: Essays in Honour of Heinz Post, Steven French & Harmke Kamminga (Eds), 1993 Boston Studies in the Philosophy of Science, Vol. 148 Kluwer Academic Publishers, Dordrecht

Beyond Reason: Essays on the Philosophy of Paul Feyerabend, GONZALO MUNÉVAR (Ed.), 1991. Dordrecht, Kluwer Academic Publishers xxi + 535pp., hb, ISBN 0–7923–1272–4, £104.20

World Changes: Thomas Kuhn and the Nature of Science, Paul Horwich (Ed.), 1993. Cambridge, MA, Bradford Books/MIT Press vi + 356pp., pb, ISBN 0262581388, £14.95

Realism Rescued: How Scientific Progress is Possible, Jerold L. Aronson, Rom Harré & Eileen Cornell Way, 1994 London, Duckworth vii +213pp., Hb 0715624768, £30.00

Scientific Nihilism: On the Loss and Recovery of Physical Explanation, Daniel Athearn, 1994. State University of New York Press, Albany ix + 387pp., Hb ISBN 0–7914–1807–3, £52

Theism, Atheism, and Big Bang Cosmology, William Lane Craig & Quentin Smith, 1993. Oxford, Clarendon Press x +342pp., Hb 0198263481, £35; Pb 019826383X, £13.95     

Three-element nonfinitely axiomatizable matrices

There are exactly two nonfinitely axiomatizable algebraic matrices with one binary connective o such thatx(yz) is a tautology of . This answers a question asked by W. Rautenberg in [2], P. Wojtylak in [8] and W. Dziobiak in [1]. Since every 2-element matrix can be finitely axiomatized ([3]), the matrices presented here are of the smallest possible size and in some sense are the simplest possible.Presented byWolfgang Rautenberg     

Finite structural axiomatization of every finite-valued propositional calculus

In [2] A. Wroski proved that there is a strongly finite consequence C which is not finitely based i.e. for every consequence C ⁺ determined by a finite set of standard rules C C ⁺. In this paper it will be proved that for every strongly finite consequence C there is a consequence C ⁺ determined by a finite set of structural rules such that C(Ø)=C ⁺(Ø) and = (where , are consequences obtained by adding to the rules of C, C ⁺ respectively the rule of substitution). Moreover it will be shown that under certain assumptions C=C ⁺.     

Strong completeness with respect to finite kripke models

We prove that each intermediate or normal modal logic is strongly complete with respect to a class of finite Kripke frames iff it is tabular, i.e. the respective variety of pseudo-Boolean or modal algebras, corresponding to it, is generated by a finite algebra. The author wishes to thank the Editors for calling his attention to the fact that the result of this paper concerning the intermediate logics was announced earlier by A. Wroński at the conference “Logical calculi”, Wrocław, October 5–7, 1975, though without proof. Wroński's result has not been published.     

On finite approximability of ψ-intermediate logics

The aim of this note is to show (Theorem 1.6) that in each of the cases: = {, }, or {, , }, or {, , } there are uncountably many -intermediate logics which are not finitely approximable. This result together with the results known in literature allow us to conclude (Theorem 2.2) that for each : either all -intermediate logics are finitely approximate or there are uncountably many of them which lack the property.