A study in philosophical logic of the meaning of 'true'. Dr Williams demonstrates the shortcomings of various analyses which interpret 'true' as a predicate or truth as a relational property, and clears up a number of important points about propositions, quantification, definite descriptions and correspondence. This 'deflationary metaphysics' is interwoven with a positive theory of his own, which seeks to develop ideas about the late Arthur Prior. The work is marked throughout by great clarity, precision and thoroughness.

entirety to contemporary readers." --Book Jacket.

In this paper thecanonicalmodal logics, a kind of complete modal logics introduced in K. Fine [4] and R. I. Goldblatt [5], will be characterized semantically using the concept of anultrafilter extension, an operation on frames inspired by the algebraic theory of modal logic. Theorem 8 of R. I. Goldblatt and S. K. Thomason [6] characterizing the modally definable Σ⊿-elementary classes of frames will follow as a corollary. A second corollary is Theorem 2 of [4] which states that any complete modal (...) logic defining a Σ⊿-elementary class of frames is canonical.The main tool in obtaining these results is the duality between modal algebras and general frames developed in R. I. Goldblatt [5]. The relevant notions and results from this theory will be stated in §2. The concept of a canonical modal logic is introduced and motivated in §3, which also contains the above-mentioned theorems. In §4, a kind of appendix to the preceding discussion, preservation of first-order sentences under ultrafilter extensions is discussed.The modal language to be considered here has an infinite supply of proposition letters, a propositional constant ⊥, the usual Boolean operators ¬, ∨, ∨, →, and ↔ —with ¬ and ∨ regarded as primitives—and the two unary modal operators ◇ and □ — ◇ being regarded as primitive. Modal formulas will be denoted by lower case Greek letters, sets of formulas by Greek capitals. (shrink)

In the modal literature various notions of "completeness" have been studied for normal modal logics. Four of these are defined here, viz. completeness, first-order completeness, canonicity and possession of the finite model property -- and their connections are studied. Up to one important exception, all possible inclusion relations are either proved or disproved. Hopefully, this helps to establish some order in the jungle of concepts concerning modal logics. In the course of the exposition, the interesting properties of first-order definability and (...) preservation under ultrafilter extensions are introduced and studied as well. (shrink)

Bernard Lonergan devoted much of his life's work to developing a generalized method of inquiry, an integrated view which would overcome the fragmentation of knowledge in our time. In Topics in Education Lonergan adapts that concern to the practical needs of educators. Traditionalist and modernist notions of education are both criticized. Lonergan attempts to work out, in the context of the human good and the 'new learning,' the rudiments of a philosophy of education based on his well-known discovery of norms (...) in the unfolding of intelligent, reasonable, and responsible consciousness. He explores how the scientific revolution has changed ways of understanding reality, and examines the implications of this revolution for education. Topics in Education, the first publication of his 1959 lectures, follows Lonergan on his early explorations of human development, studies the theories ofJean Piaget and others, and concludes with his own original ideas in the realms of ethics, art, and history. Bernard Lonergan (1904-1984), a professor of theology, taught at Regis College, Harvard University, and Boston College. An established author known for his Insight and Method in Theology, Lonergan received numerous honorary doctorates, was a Companion of the Order of Canada in 1971 and was named as an original members of the International Theological Commission by Pope Paul VI. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

‘Hoplites are troops who take their name from their shields’. ‘The individual infantryman took his name, hoplites, from the hoplon or shield’. Such is the orthodox view. This paper will endeavour to show that its basis is inadequate. Rather, we shall argue, hoplites took their name from their arms and armour as a whole, their hopla in that all-encompassing sense; so that the original and essential meaning of the word hoplite was nothing more than ‘armed man’.

In response to a suggestion in the Class. Rev. , the two MSS. of the Liber Glossarum preserved at Tours have recently been examined. Since they had not been seen by Goetz when he published his excerpts, the following short descriptions may be added to the introduction of Vol. V. of the Corpus Glossariorum Latinorum: 1. Tours, Bibliothèque de Ville, MS. No. 850; end of the ninth century; foll. 493, of which 1, 491, 492 are mere corners; cmm. 49 by (...) 29. The last item is an Isidore gloss, Zatenen.-gemmam. Gaps due to loss of folia occur between Abiectus and Abdolet; Dextera manus and Dialogus; Faber and Impulitum; Res diuinae and Samsacus. There are no corrections except between folia 197 and 300, where a thirteenth-century hand has checked the MS. by means of another copy of the Lib. Gloss. The items are drawn up in two columns, and the alphabetical arrangement agrees for the most part with that of Vat. Pal. lat. 1773. Marginal indications of the sources of the items are numerous except between Profanum and Remeantes; where two or three neighbouring items come from the same source, the marginal mark is repeated; and towards the end of the MS., where the scribe takes to writing two items in the same line, the indication is also carefully transferred. This is important in view of Goetz' theory that the source of an unlabelled item is that given by the last preceding label. (shrink)

In Corp. Gloss. Lat. V. 435–490 Goetz published excerpts from the A A glossary. Further interesting items were published by C. Theander in Eranos XXIII 51–61, 167–176. The complete glossary is now being prepared for the press, and Professor W. M. Lindsay has kindly communicated to me some of the new items which may possibly contain quotations from classical authors. The most interesting of them is the following: MA 2 ‘Mabortia res quae ad pugnam pertinet unde moenia funduntur vel res (...) Martia.’. (shrink)