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

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)

. 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 ...

Commentary on Tarkasaṅgraha of Annambhaṭṭa, active 17th century, treatise on the fundamentals of Nyaya philosophy.

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)

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)

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)