(1975). The History of Salvation in Dr. A. A. van Ruler's Theology An Introduction to his Theology on the Occasion of the Publication of his “Theological Works”. Bijdragen: Vol. 36, No. 4, pp. 391-419.

(1975). The Structure of Dr. A. A. van Ruler's Theology An Introduction to his Theology on the Occasion of the Publication of his “Theological Works”. Bijdragen: Vol. 36, No. 3, pp. 234-249.

The original, Dutch version of this book served in 1979 as a doctoral disserta tion in philosophy at the Free University in Amsterdam. In this preface to the - slightly revised - English translation, I wish once again to express my gratitude to my supervisors, Prof. J. van der Hoeven of the Free University and Prof. G. Nuchelmans of the University of Leiden, for their excellent and stimulating support. Professor van der Hoeven was associated with this project from the outset. (...) It was a privilege to benefit from his incisive commentaries, especially in those instances where the objective was to break through to more fundamental insights. I shall not lightly forget his friendly and heartening encouragement. I am equally grateful for my discussions with Professor Nuchelmans. I almost always tried to follow his advice, since it was based upon awesome expertness and erudition. I am happy to have found in the person of Herbert Donald Morton, Th.M., M.A., an able and enthusiastic translator. Drs. Gerben Groenewoud made the translations of a number of the Latin citations. I acknowledge permission from Routledge and Kegan Paul and the University of Toronto Press to quote from The Collected Works of John Stuart Mill. And I thank the Netherlands Organization for the Advancement of Pure Research (Z.W.O.) for fmancing this translation. (shrink)

Issues of identity and reduction have monopolized much of the philosopher of mind’s time over the past several decades. Interestingly, while investigations of these topics have proceeded at a steady rate, the motivations for doing so have shifted. When the early identity theorists, e.g. U. T. Place ( 1956 ), Herbert Feigl ( 1958 ), and J. J. C. Smart ( 1959 , 1961 ), fi rst gave voice to the idea that mental events might be identical to brain processes, (...) they had as their intended foil the view that minds are immaterial substances. But very few philosophers of mind today take this proposal seriously. Why, then, the continued interest in identity and reduction? Th e concern, as philosophers like Hilary Putnam and Jerry Fodor have expressed it, is that a victory for identity or reduction is a defeat for psychology. For if minds are physical, or if mental events are physical events, then psychologists might as well disassemble their laboratories, making room for the neuroscientists and molecular biologists who are in a better position to explain those phenomena once misdescribed as “psychological.” Th e worry nowadays is not that locating thought in immaterial souls will make psychology intractable, but that locating thoughts in material brains will make it otiose. (shrink)

A subspace V of an infinite dimensional fully effective vector space V ∞ is called decidable if V is r.e. and there exists an r.e. W such that $V \oplus W = V_\infty$ . These subspaces of V ∞ are natural analogues of recursive subsets of ω. The set of r.e. subspaces forms a lattice L(V ∞ ) and the set of decidable subspaces forms a lower semilattice S(V ∞ ). We analyse S(V ∞ ) and its relationship with L(V (...) ∞ ). We show: Proposition. Let U, V, W ∈ L(V ∞ ) where U is infinite dimensional and $U \oplus V = W$ . Then there exists a decidable subspace D such that U |oplus D = W. Corollary. Any r.e. subspace can be expressed as the direct sum of two decidable subspaces. These results allow us to show: Proposition. The first order theory of the lower semilattice of decidable subspaces, Th(S(V ∞ )), is undecidable. This contrasts sharply with the result for recursive sets. Finally we examine various generalizations of our results. In particular we analyse S * (V ∞ ), that is, S(V ∞ ) modulo finite dimensional subspaces. We show S * (V ∞ ) is not a lattice. (shrink)