In this article the author shows that we must distinguish between criterion as a characteristic in a definition and as a norm for truth and ethical values. He shows that we must accept a hierarchy of such criteria, But that this hierarchy is not absolute. He also discusses and solves the 'paradox of the publican'.

If we were to name the two greatest mathematicians of antiquity, we would probably choose Archimedes and Euclid. The first excelled in research, the second in synthesis or system. The synthesis or system is closely associated with the theory or philosophy of that subject; and Euclid's Elements, which has been characterized as “one of the noblest monuments of antiquity”, is the best concrete instance of the theory of mathematics according to the ancient Greeks. Now Aristotle had a theory of mathematics, (...) although he was not a practicing mathematician. It is the purpose of this article to show that the mathematical method according to Aristotle is superior to and more modern than that according to Euclid. For references to Aristotle's works we shall use pages and lines according to the standard Bekker's edition. By “a number” we shall mean a positive integer or a whole number. We proceed to a brief outline of Euclid's Elements. (shrink)

G. H. Bird; Discussions: Kantian Myths, Proceedings of the Aristotelian Society, Volume 96, Issue 1, 1 June 1996, Pages 245–252, https://doi.org/10.1093/aristot.

In this superb little book, written during World War II, historian, sociologist, and novelist H.G. Wells (1866-1946) contemplates the belief systems, prejudices, and institutions that have brought humankind to a dreadful impasse, where it stands at the brink of destruction - or of a new beginning. In his lucid summary of modern ideas concerning the fundamentals and ultimates of existence, Wells points out how absurd and outmoded religious beliefs, marked by intolerance, hatred, and exclusion, have poisoned human beings' relations with (...) the world and each other. These need to be replaced by a new social morality and a heightened sense of humankind's proper place in a dynamic universe. (shrink)

Explaining the persistence of populations is an important quest in ecology, and is a modern manifestation of the balance of nature metaphor. Increasingly, however, ecologists see populations (and ecological systems generally) as not being in equilibrium or balance. The portrayal of ecological systems as “non-equilibrium” is seen as a strong alternative to deterministic or equilibrium ecology, but this approach fails to provide much theoretical or practical guidance, and warrants formalisation at a more fundamental level. This is available in adaptation theory, (...) which allows population persistence to be explained as an epiphenomenon stemming from the maintenance, survival, movement and reproduction of individual organisms. These processes take place within a physicochemical and biotic environment that persists through structured annual cycles, but which is also spatiotemporally dynamic and subject to stochastic variation. The focus is thus shifted from the overproduction of offspring and the consequent density dependent population pressure thought to follow, to the adaptations and ecological circumstances that support those relatively few individuals that do survive. (shrink)

In "Realism and Reason" Hilary Putnam has offered an apparently strong argument that the position of metaphysical realism provides an incoherent model of the relation of a correct scientific theory to the world. However, although Putnam's attack upon the notion of the "intended" interpretation of a scientific theory is sound, it is shown here that realism may be formulated in such a way that the realist need make no appeal to any "intended" interpretation of such a theory. Consequently, it can (...) be shown that realism is immune to Putnam's criticism and that attempts at reformulating this criticism are not likely to meet with success. (shrink)