Marsilio Ficino (1433-1499) was one of the luminaries of the Florentine Renaissance and the scholar responsible for the revival of Platonism. The translator and interpreter of the works of both Plato and Plotinus as well as of various Hermetic and Neoplatonic texts, Ficino was also a musician, priest, magus and psychotherapist, an original philosopher and the author of a vast and important correspondence with the intellectual figures of his day including Lorenzo the Magnificent. Professor Allen has become the foremost interpreter (...) of Ficino's metaphysics and mythology, and the ancient sources they draw upon; and this collection of essays assembles his work on Ficino's complex interrogation of Platonic 'theology' as not only a preparation for Christianity but as an enduring medium for intellectuals to explore and to express Christian truths. (shrink)

The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have \ \cong^{d} {{\rm S}_{p}}}\), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices (...) satisfy the Jónsson–Kiefer property. (shrink)

We propose two principles of inductive reasoning related to how observed information is handled by conditioning, and justify why they may be said to represent aspects of rational reasoning. A partial classification is given of the probability functions which satisfy these principles.

We argue that the simplicity condition on a probability function on sentences of a predicate language L that it takes only finitely many values on the sentences of any finite sublanguage of L can be viewed as rational. We then go on to investigate consequences of this condition, linking it to the model theoretic notion of quantifier elimination.

In this paper, we study the lower semilattice of NP-subspaces of both the standard polynomial time representation and the tally polynomial time representation of a countably infinite dimensional vector space V∞ over a finite field F. We show that for both the standard and tally representation of V∞, there exists polynomial time subspaces U and W such that U + V is not recursive. We also study the NP analogues of simple and maximal subspaces. We show that the existence of (...) P-simple and NP-maximal subspaces is oracle dependent in both the tally and standard representations of V∞. This contrasts with the case of sets, where the existence of NP-simple sets is oracle dependent but NP-maximal sets do not exist. We also extend many results of Nerode and Remmel concerning the relationship of P bases and NP-subspaces in the tally representation of V∞ to the standard representation of V∞. (shrink)

While cetaceans clearly show social learning in a wide variety of contexts, to label this as hides more than it reveals: we need a taxonomy of culture to tease apart the differences rather than hiding them in a catch-all category.

The sixteen essays contained in this book were all written independently of each other and date back over a considerable period of time to 1956. Most of the essays have been previously published and are reprinted here with little or no change or additions. Only two were specially written for this volume. All but two deal with the theoretical as distinct from the practical dimensions of science. The two exceptions are a set of reflections on the morality of the atomic (...) bombing of Japan in World War II and an essay which sketches a framework for the consideration of issues in nursing as a practical discipline. (shrink)

Mayhew wants to rescue Aristotle from charges of misogynic ideology. Although there are residues of traditional Greek assumptions in the biological works, Mayhew holds Aristotle was not rationalizing from these ideas. Rationalization involves self-deception, evasion of truth, and the “desire to support some outlook, agenda, or position”. Mayhew will argue that Aristotle generalized from insufficient and flawed evidence, but that it was an honest attempt at scientific reasoning and not an attempt to show that women are inferior.