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)

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)

In poem 64 Catullus, as Fordyce points out in his edition, often has lines enclosed by a noun and its adjective, e.g.: 5 auratam optantes Colchis avertere pellem Very often, but not always, a syntactical unit is enclosed as well as the line. This is perhaps not surprising, considering the prevalence of punctuation at the end of the line in this poem. Nevertheless, an examination of the lines will show that when a noun and adjective1 enclose both line and syntactical (...) unit the fact that they enclose a syntactical unit can be regarded as a determinant of the word order. (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)

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)

To what extent does the fact that a philosopher, in order to communicate, is constrained to use the same language and the same concepts as other members of his society, inhibit him from developing genuinely original modes of thought? Section I of this paper outlines arguments for the view that any attempt at radical originality, of the kinds traditionally expected of philosophy, must involve misuse of these shared concepts. Section II, however, on the basis of an examination of what it (...) is for different members of a society to use the same concepts, argues that so doing does not rule out important differences over instantiations and logical interrelations. It then attempts to show that this latitude for difference is adequate to allow for certain kinds of philosophical originality, for example, that shown in the Whiteheadian philosophy of organism. (shrink)

Solon's fragments 9–11 are preserved in three late authors: frr. 9 and 11 by Diodoros Sikelos , 9.20.2, Plutarch , Solon 3.6 and 30.3 respectively, and Diogenes Laertios , 1.50 and 1.51 respectively; and fr. 10 by Diogenes Laertios alone, 1.49. They are all quoted in the context of Solon's reaction to Peisistratos. Stories on this theme were circulating by the time of the Aristotelian Athenaion Politeia , and Rhodes' scepticism about them is well founded. Its author did not garnish (...) his version of events with these poems, nor indeed with any Solonian utterance, and he explicitly states that myth-making on this subject had already resulted in two stories about Solon and Peisistratos which were chronologically impossible. (shrink)