My interest in gathering together a collection of this sort was generated by a fortuitous combination of historical studies under Professor Keith Lehrer and studies in cognitive science under Professor R. Michael Harnish at the University of Arizona. Work on the volume began there while I was an instructor in the Department of Linguistics and was greatly encouraged by participants in the Faculty Seminar on Cognitive Science chaired by Professor Lance J. Rips. I wish to express my appreciation to all (...) of these and to many other individuals with whom I discussed the possibility of contribution to this work. I am especially grateful to the authors of the essays included here, as they showed more patience than I could have hoped for in seeing me through a number of uncertain stages in development of the project. My thanks are also due to my colleague Charles Reid for assistance in reviewing submissions, to Tim McFadden for computer resources, and again, to Keith Lehrer for continuing advice in arrangements for publication. Financial support for manuscript preparation was provided in part under University Research Grant No. 617 from the University Research Council, Youngstown State University. (shrink)

The author sets forth that, especially in later Platonism, some aspects should be noted different from those which are usually considered as being characteristic of Plato's philosophy : in later Platonism the stress is laid on the fact that the visible world is an image of the invisible as perfect as it could possibly be ; soul is superior to body, but not separated from it ; and in the visible world an element of identity is fundamentally admitted. In Parm. (...) and Soph, motion is introduced into the intelligible world. The main theses of Platonism as a whole are : the existence of a transcendent intelligible world, the existence of an analogy between this intelligible world and ours. It neither can be said that modern philosophy as a whole rejects these theses, nor that Antiquity as a whole accepted them. Aristotle and the schools after him rejected the (first thesis, sceptics denied the second ; Neoplatonism restored them both. During the Middle Ages they were generally accepted ; only Occam denied the principle of analogy. So did Kant, and neopositivism seems to have accepted this heritage, when it holds that metaphysics have no sense. On the other hand, the « existentialism » of the school of Sartre denies that an eternal essence of things would precede their concrete existence ; and by this doctrine the first point of Platonism is denied as well. Against these modern philosophers others do accept the first principles of Platonism, and Plato's own attitude towards the materialistic philosophy of nature of his time authorizes the opinion that, on the point in question, Plato would not change his position if he lived in our days. (shrink)

A biresiduation algebra is a 〈/,\,1〉-subreduct of an integral residuated lattice. These algebras arise as algebraic models of the implicational fragment of the Full Lambek Calculus with weakening. We axiomatize the quasi-variety B of biresiduation algebras using a construction for integral residuated lattices. We define a filter of a biresiduation algebra and show that the lattice of filters is isomorphic to the lattice of B-congruences and that these lattices are distributive. We give a finite basis of terms for generating filters (...) and use this to characterize the subvarieties of B with EDPC and also the discriminator varieties. A variety generated by a finite biresiduation algebra is shown to be a subvariety of B. The lattice of subvarieties of B is investigated; we show that there are precisely three finitely generated covers of the atom. (shrink)

We study the computational complexity of the universal theory of residuated ordered groupoids, which are algebraic structures corresponding to Nonassociative Lambek Calculus. We prove that the universal theory is co $$\textsf {NP}$$ -complete which, as we observe, is the lowest possible complexity for a universal theory of a non-trivial class of structures. The universal theories of the classes of unital and integral residuated ordered groupoids are also shown to be co $$\textsf {NP}$$ -complete. We also prove the co $$\textsf {NP}$$ (...) -completeness of the universal theory of classes of residuated algebras, algebraic structures corresponding to Generalized Lambek Calculus. (shrink)

In a discussion-note in Mind, Father P. M. Farrell, O.P., gave an account, in what he admitted to be an embarrassingly brief compass, of the Thomist doctrine concerning evil. There is one sentence in this discussion which at first glance appears paradoxical. Father Farrell has been arguing that a universe containing ‘corruptible good’ as well as incorruptible is better than one containing ‘incorruptible good’ only. He continues: ‘If, however, they are to manifest this corruptible good, they must be corruptible and (...) they must sometimes corrupt.’ The final words, despite Father Farrell's italics, strike one as expressing, not a self-evident truth, but a non sequitur. The fact that I am capable of committing murder does not entail that I will at some time commit it. It is not immediately obvious that a similar entailment holds in the case of corruption and corruptibility. (shrink)

We re-express a previous general result in a way which seems easier to remember, using the terminology of infinite games. We show how this can be applied to construct recursive linear orderings, showing, for example, that if there is a ▵ 0 2β + 1 linear ordering of type τ, then there is a recursive ordering of type ω β · τ.

PLATO: PROTAGORAS, trans, with Notes by C. C. W. Taylor. Clarendon Press: O.U.P., 1976. vii+230 pp. £7.50 cloth, £3.75 paper.

C. J. F. Williams; VI*—Is Identity a Relation?, Proceedings of the Aristotelian Society, Volume 80, Issue 1, 1 June 1980, Pages 81–100, https://doi.org/10.1093/.