We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study this relation and its interactions with Turing reducibility, classes, hyperimmunity and other recursion theoretic notions.

The usual way for new cells to come into being is by division of old cells. So the zygote, which is a—new—single cell formed from two, the sperm and ovum, is an exception. Textbooks of human genetics usually say that this new cell is beginning of a new human individual. What this indicates is that they suddenly forget about identical twins.

_Zettel, _ an en face bilingual edition, collects fragments from Wittgenstein's work between 1929 and 1948 on issues of the mind, mathematics, and language.

Written over the last 18 months of his life and inspired by his interest in G. E. Moore's defence of common sense, this much discussed volume collects Wittgenstein's reflections on knowledge and certainty, on what it is to know a proposition for sure.

The usual way for new cells to come into being is by division of old cells. So the zygote, which is a—new—single cell formed from two, the sperm and ovum, is an exception. Textbooks of human genetics usually say that this new cell is beginning of a new human individual. What this indicates is that they suddenly forget about identical twins.

One of the ways of dividing all philosophers into two kinds is by saying of each whether he is an ordinary man's philosopher or a philosophers' philosopher. Thus Plato is a philosophers' philosopher and Aristotle an ordinary man's philosopher. This does not depend on being easy to understand: a lot of Aristotle's Metaphysics is immensely difficult. Nor does being a philosophers' philosopher imply that an ordinary man cannot enjoy the writings, or many of them. Plato invented and exhausted a form: (...) no one else has written such dialogues. So someone with no philosophical bent, or who has left his philosophical curiosity far behind may still enjoy reading some of them. (shrink)

This considerably revised second edition of Wittgenstein's 1914-16 notebooks contains a new appendix with photographs of Wittgenstein's original work, a new preface by Elizabeth Anscombe, and a useful index by E.D. Klemke. Corrections have been made throughout the text, and notes have been added, making this the definitive edition of the notebooks. The writings intersperse Wittgenstein's technical logical notations with his thoughts on the meaning of life, happiness, and death. "When the first edition of this collection of remarks appeared in (...) 1961 we were provided with a glimpse of the workings of Wittgenstein's mind during the period when the seminal ideas of the _Tractatus Logico-Philosophicus_ were being worked out. This second edition provided the occasion to be struck anew by the breadth, rigor, and above all the restlessness of that mind."—T. Michael McNulty, S. J., _The Modern Schoolman_. (shrink)

I discuss the treatment by Chisholm of the problem posed by the fact that one can produce some neuro-physiological changes by moving a limb, namely the ones which cause the motions. I concentrate largely on the treatment Chisholm gave to this question before Person and Object, and I compare it with von Wright's discussion of it, I conclude that there are correct elements about both but that both are unsatisfactory, Chisholm's because it entails that we must know something which we (...) manifestly need not know when we move. (shrink)

I discuss the treatment by Chisholm of the problem posed by the fact that one can produce some neuro-physiological changes by moving a limb, namely the ones which cause the motions. I concentrate largely on the treatment Chisholm gave to this question before Person and Object, and I compare it with von Wright's discussion of it, I conclude that there are correct elements about both but that both are unsatisfactory, Chisholm's because it entails that we must know something which we (...) manifestly need not know when we move. (shrink)

Let us say that any (Turing) degree d > 0 satisfies the minimal complementation property (MCP) if for every degree 0 < a < d there exists a minimal degree b < d such that a ∨ b = d (and therefore a ∧ b = 0). We show that every degree d ≥ 0′ satisfies MCP. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

I discuss the treatment by Chisholm of the problem posed by the fact that one can produce some neuro-physiological changes by moving a limb, namely the ones which cause the motions. I concentrate largely on the treatment Chisholm gave to this question before Person and Object, and I compare it with von Wright's discussion of it, I conclude that there are correct elements about both but that both are unsatisfactory, Chisholm's because it entails that we must know something which we (...) manifestly need not know when we move. (shrink)

Ludwig Wittgenstein was born in 1889, son of parents of Jewish extraction but not Jewish religion. Asked how his family came by the name ‘Wittgenstein’ Ludwig said they had been court Jews to the princely family and so had taken the name when Jews were required by law to have European-style names. The father, Karl, was a Protestant, the mother a Catholic. The Jewish blood was sufficient to bring the family later on into danger under Hitler's Nuremberg Laws. They did (...) not think of themselves as Jews or belong to the Jewish community in Vienna. The children were brought up sort-of Catholic though so far as I know only the eldest, Hermine, towards the end of her life, took this seriously and made a profession of faith before friends and household. At 9 years of age Ludwig and Paul, a year or two older than Ludwig, talked together and decided that their religion was all nonsense. Paul became a pianist of some fame, but soon after his debut in Vienna he became a wounded prisoner on the Russian front and his arm was lopped off by a surgeon who did not know he was a pianist. (shrink)