Jan Wolenski

Al-Farahr’s commentarv and short treatise on Aristotle’s De interpretatione. Introduction and translation from Arabic by F. Zimmerman. Oxford: Published for the British Academy by Oxford University Press, 1987. clii + 287 pp. of English. £22.50 Johann Andreas Segner, Specimen logicae universaliter demonstrate. Appendices: Two dissertations De syllogismo. Edited by Mirella Capozzi. Bologna: Editrice CLUEB, 1990. clxxii + 281 pp. 85 000 Lire M. Borga, P. Fregugua And D. Palladino, I contribua fondazionali della scuola di Peano. Milano: Franco Angeli, 1985, 257 pp. No price stated F. Cavaliere. La logica formale in Unione Sovietica. Gli anni del dibattito 1946-1965. Firenze: La Nuova Italia Editrice, 1990. ix + 140pp. Lire 42000 William S. Hatcher, Logic and logos. Essays on science, religion and philosophy. Oxford: George Ronald, 1990. x + 147 pp. £4.50/$9.50 E. J. Lowe, Kinds of being: a study of individuation, identity and the logic of sortal terms. Oxford and New York: Basil Blackwell, 1989. £25.00/$550.00 Reinhardt Grossmann, The fourth way. A theory of knowledge. Bloomington and Indianapolis: Indiana University Press, 1990. 312 pp.$35.00 J. Etchemendy. The concept of logical consequence. Cambridge, Mass, and London, England: Harvard University Press, 1990. vi 4- 174 pp. £19.95 Bernard Bolzano, Las paradojas del infinito. Translated from the German by L. Felipe Segura. Introduction by J. Sebestik. Mexico City: Faculty of Sciences, University of Mexico, 1991. 163 pp. No price stated W. Stantfy Jfvons, Pure logic and other minor works. Photoreprinted Bristol: Thoemmes, 1991. xxiii + 299 pp. No price stated Felix Kaufmann, L’infinito in matematica. Translated from the German, with an introduction, by L. Albertazzi. Gardolo di Trento: Luigi Reverdito Editore, 1990. 297 pp. L. 32.000 Massimo Libardi, Teorie de lie parti e delVintero. Mereologie estensionali. Trento: Centro Studi per la Filosofia Mitteleuropea, Quaderni 4-6, 302 pp. 22,000 lire M. S. Burcjin and V. I. Kuznetsoff, Aksio-logichcskiye aspekîi nauchnikh teorii. Kiev; Naukova Dymka, 1991. 184 pp. 3 roubles Hans Burkhardt and Barry Smith, Handbook of metaphysics and ontology. 2 vols. Munich: Philosophia, 1991. 1005 pp. 650 DM

The problem of induction belongs to the most controversial issues in philosophy of science. If induction is understood widely, it covers every fallible inference, that is, such that its conclusion is not logically entailed by its premises. This paper analyses so-called reductive induction, that is, reasoning in which premises follow from the conclusion, but the reverse relation does not hold. Two issues are taken into account, namely the definition of reductive inference and its justification. The analysis proposed in the paper employs metalogical tools. The author agrees with the view that a quantitative account of degree of confirmation for universal theories via logical probability is problematic. However, prospect for a qualitative approach look as more promising. Using the construction of maximally consistent sets allows to distinguish good and worthless induction as well as shows how to understand induction in a semantic way. A closer analysis of deductivism in the theory of justification shows that it is a hidden inductivism.

This paper investigates relations between truth and consistency. The basic intuition is that truth implies consistency, but the reverse dependence fails. However, this simple account leads to some troubles, due to some metalogical results, in particular the Gödel-Malcev completeness theorem. Thus, a more advanced analysis is required. This is done by employing the concept of ω-consistency and ω-inconsistency. Both concepts motivate that the concept of the standard truth should be introduced as well. The results are illustrated by an interpretation of the well-known logical square and its generalization.

Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of an effectively computable function defined in natural numbers with the notion of a recursive function. Despite the many efforts of prominent scientists, Church's Thesis has never been disproven. There exists a vast literature concerning the thesis. The aim of this book is to provide a one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics, CT and physics, the epistemic status of CT, CT and philosophy of mind, provability of CT and CT and functional programming. Adam Olszewski, is assistant professor of the philosophy of mathematics and mathematical logic at the Department of Philosophy of Pontifical Academy of Theology, Cracow (Poland). Jan Wolenski is professor of philosophy, Institute of Philosphy, Jagiellonian University, Cracow (Poland). He is one of the most distinguished logicians in Poland. Robert Janusz is assistant professor in the Department of Philosophy of Ignatius College, Cracow (Poland).