We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.

Tarski [5] showed that for any set X, its set w(X) of well-orderable subsets has cardinality strictly greater than that of X, even in the absence of the axiom of choice. We construct a Fraenkel-Mostowski model in which there is an infinite strictly descending sequence under the relation |w (X)| = |Y|. This contrasts with the corresponding situation for power sets, where use of Hartogs' ℵ-function easily establishes that there can be no infinite descending sequence under the relation |P(X)| = (...) |Y|. (shrink)

We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.

"...T S Eliot was unimpressed by Freud. Eliot preferred the more approachable Roger Vittoz. It was only Scofield Thayer, who in his prolonged therapy with Sigmund Freud can be said to have brought anything Freudian in the classically psychoanalytic sense to Modernism." This is from the review. The review of the book is contrarian as the book under review is. The salient points of the book are interrogated in this review.

In contemporary discussion of the philosophy of religion, or for that matter of any branch of philosophy, the names of Whitehead and Wittgenstein are not often linked. Whitehead's later work is, for the most part, treated as a rather specialized interest, an attractively under-cultivated field for the enterprising thesis-writer perhaps, but well away from the main centres of current philosophical activity. And what he has to say about specifically religious or theological issues 1 becomes simply one ramification of an ingenious (...) but somewhat eccentric system. Nonetheless, there is at least this much justification for considering it in relation to the much more influential and widely discussed views of Wittgenstein. Whitehead has some original things to say about God, Wittgenstein some original reasons for thinking that Whitehead's brand of originality is here radically misplaced. And the possibility or otherwise of such theological originality is an issue of very considerable importance for the philosophy of religion. (shrink)

Laland and colleagues have sought to challenge the proximate–ultimate distinction claiming that it imposes a unidirectional model of causation, is limited in its capacity to account for complex biological phenomena, and hinders progress in biology. In this article the core of their argument is critically analyzed. It is claimed that contrary to their claims Laland et al. rely upon the proximate–ultimate distinction to make their points and that their alternative conception of reciprocal causation refers to phenomena that were already accounted (...) for by standard theory. (shrink)

What is a natural kind? As we shall see, the concept of a natural kind has a long history. Many of the interesting doctrines can be detected in Aristotle, were revived by Locke and Leibniz, and have again become fashionable in recent years. Equally there has been agreement about certain paradigm examples: the kinds oak, stickleback and gold are natural kinds, and the kinds table, nation and banknote are not. Sadly agreement does not extend much further. It is impossible to (...) discover a single consistent doctrine in the literature, and different discussions focus on different doctrines without writers or readers being aware of the fact. In this paper I shall attempt to find a defensible distinction between natural and non-natural kinds. (shrink)

. Ill BERGSONS THEORY OF ART . . .141 THE PHILOSOPHY OF INTENSIVE MANIFOLDS I I CINDERS ..... 215 APPENDICES A. REFLECTIONS ON VIOLENCE . . 249 B. PLAN FOR A ...

Accepted quantum description is stochastic, yet history is nonstochastic, i.e., not representable by a probability distribution. Therefore ordinary quantum mechanics is unsuited to describe history. This is a limitation of the accepted quantum theory, rather than a failing of mechanics in general. To remove the limitation, it would be desirable to find a form of quantum mechanics that describes the future stochastically and the past nonstochastically. For this purpose it proves sufficient to introduce into quantum mechanics, by means of a (...) perfected formal correspondence, certain analogs of the classical initial-condition constants. Through the restoration of such parameters at the quantum level one accomplishes a natural accommodation of time anisotropy, wave-function reduction, and “event” description by quantum mechanical equations of motion alone, without the need for extra postulates (e.g., a projection postulate). This requires a complete restructuring of quantum measurement theory. (shrink)

Cognitive Development and Acquisition of Language.