Classical temples in ancient Greece show two deterministic illusionistic principles of architecture, which govern their functional design: geometric proportionalism and a set of illusion-strengthening rules in the proportionalism's stochastic margin. Animal morphology, in its mechanistic-deductive revival, applies just one architectural principle, which is not always satisfactory. Whether a Greek Classical situation occurs in the architecture of living structure is to be investigated by extreme testing with deductive methods.Three deductive methods for explanation of living structure in animal morphology are proposed: the (...) parts, the compromise, and the transformation deduction. The methods are based upon the systems concept for an organism, the flow chart for a functionalistic picture, and the network chart for a structuralistic picture, whereas the optimal design serves as the architectural principle for living structure. These methods show clearly the high explanatory power of deductive methods in morphology, but they also make one open end most explicit: neutral issues do exist. (shrink)

On what grounds will the rational man become a Christian? It is often assumed by many, especially non-Christians, that he will become a Christian if and only if he judges that the evidence available to him shows that it is more likely than not that the Christian theological system is true, that, in mathematical terms, on the evidence available to him, the probability of its truth is greater than half. It is the purpose of this paper to investigate whether or (...) not this is a necessary and sufficient condition for the rational man to adopt Christianity. (shrink)

Mr Olding's recent attack on my exposition of the argument from design gives me an opportunity to defend the central theses of my original article. My article pointed out that there were arguments from design of two types—those which take as their premisses regularities of copresence and those which take as their premisses regularities of succession. I sought to defend an argument of the second type. One merit of such an argument is that there is no doubt about the truth (...) of its premisses. Almost all objects in the world behave in a highly regular way describable by scientific laws. Further, any scientific explanation of such a regularity must invoke some more general regularity. The most general regularities of all are, as such, scientifically inexplicable. The question arises whether there is a possible explanation of another kind which can be provided for them, and whether their occurrence gives any or much support to that explanation. I urged that we do explain some phenomena by explanation of an entirely different kind from the scientific. We explain states of affairs by the action of agents who bring them about intentionally of their own choice. Regularities of succession, as well as other phenomena may be explained in this way. Explanation of this kind I will term intentional explanation. Intentional explanation of some phenomenon E consists in adducing an agent A who brought E about of his own choice and a further end G which, he believed, would be forwarded by the production of E. (shrink)

Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour (...) as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided. (shrink)

In this paper we consider the classes of all continuous $\mathcal {L}$ -(pre-)structures for a continuous first-order signature $\mathcal {L}$. We characterize the moduli of continuity for which the classes of finite, countable, or all continuous $\mathcal {L}$ -(pre-)structures have the amalgamation property. We also characterize when Urysohn continuous $\mathcal {L}$ -(pre)-structures exist, establish that certain classes of finite continuous $\mathcal {L}$ -structures are countable Fraïssé classes, prove the coherent EPPA for these classes of finite continuous $\mathcal {L}$ -structures, and (...) show that actions by automorphisms on finite $\mathcal {L}$ -structures also form a Fraïssé class. As consequences, we have that the automorphism group of the Urysohn continuous $\mathcal {L}$ -structure is a universal Polish group and that Hall’s universal locally finite group is contained in the automorphism group of the Urysohn continuous $\mathcal {L}$ -structure as a dense subgroup. (shrink)

We tend to assume that our map of the intellectual disciplines is valid cross-culturally. G. E. R. Lloyd challenges this in relation to eight main areas of human endeavour, namely philosophy, mathematics, history, medicine, art, law, religion, and science, by examining how the disciplines were conceived and developed in different times and places.

It is obvious that A.P. attached importance to chronology and considered it his business to supply his sketch of Athienian constitutional development, at every stage, with such chronological indications as were available. Thus his account of Peisistratos largely follows Herodotus , but with the addition of a more detailed chronology of the tyrant's comings and goings . From the archonship of Solon to that of Xenainetos he has constructed what is evidently intended to be a continuous chronological chain, by marking (...) the intervals between events. (shrink)

Since these notes were written, news has come of the finding at Troizen of an inscription purporting to bear a decree proposed by Themistokles in 480, which is relevant to Part II above, pp. 33–35. If this new evience is valid, it would appear to confirm the view expressed there to some extent.