Journal of Mathematical Logic, Ahead of Print. Asperó and Schindler have completely solved the Axiom [math] vs. [math] problem. They have proved that if [math] holds then Axiom [math] holds, with no additional assumptions. The key question now concerns the relationship between [math] and Axiom [math]. This is because the foundational issues raised by the problem of Axiom [math] vs. [math] arguably persist in the problem of Axiom [math] vs. [math]. The first of our two main theorems is that Axiom (...) [math] is equivalent to Axiom [math], and as a corollary we show that Axiom [math] fails in all the known models of [math]. This suggests that [math] actually refutes Axiom [math]. Our second main theorem is that the [math] Conjecture holds assuming [math]. This is the strongest partial result known on this conjecture which is one of the central open problems of [math]-theory and [math]-logic. These results identify a fundamental asymmetry between the Continuum Hypothesis and any axiom which is both [math]-expressible and which implies [math], on the basis of generic absoluteness for the simplest of the nontrivial sentences of Third-Order Number Theory. These are the [math]-sentences with no parameters. Such sentences are those which simply assert the existence of a set [math] for which some property involving only quantification over [math] holds. (shrink)

This paper considers the relationship between G. H. von Wright's solution to the paradoxes of confirmation and his "Principal Theorem of Confirmation". The former utilizes the order of our knowledge of the qualities of confirming instances of an hypothesis; the latter states the way in which an instance contributes to the probability of an hypothesis. It is shown that these two, as stated by von Wright, are logically incompatible. Then the most thorough possible emendation of the paradoxes solution is considered, (...) and it is shown that this still prohibits use of the "Principal Theorem" to confirm hypotheses stating necessary causal conditions, and to confirm by deliberate experiment hypotheses stating sufficient causal conditions. It is concluded that any solution of the paradoxes must rest solely upon the relation of the data to the hypothesis involved. (shrink)

It is a truism to say that the study of ornithology has made great advances in the last fifty years, and that important problems affecting the classification of certain species and their distribution have been brought much closer to solution. Classical scholars, however, still tend to rely on the identifications of ancient Greek bird-names made by a few standard works such as D'Arcy Thompson's A Glossary of Greek Birds2 or O. Keller's Die antike Tierwelt , apparently unaware that much of (...) the ornithological information given there is now badly out of date, if not sheerly inaccurate. This brief paper aims protreptically to take four bird-names out of the Peripatetic corpus on natural history: and and to produce more precise identifications in the light of modern ornithological studies. (shrink)