We study the computational complexity of the universal and quasi-equational theories of classes of bounded distributive lattices with a negation operation, i.e., a unary operation satisfying a subset of the properties of the Boolean negation. The upper bounds are obtained through the use of partial algebras. The lower bounds are either inherited from the equational theory of bounded distributive lattices or obtained through a reduction of a global satisfiability problem for a suitable system of propositional modal logic.

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.

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)

One of the most extensive yet least conclusive methodological debates within religious studies revolves around the question of what, precisely, the phenomenology of religion is and what contribution it can make to the study of religion. I do not intend to answer this important question here. To do so satisfactorily would require a range of historical, philosophical and methodological inquiry which would go quite beyond the bounds of a single article. My intention in this paper is, by comparison, unambitious. It (...) is to take one view of what phenomenology of religion is and to consider an area outside that usually explored by students of religion which can, nonetheless, shed some light on how religions might be studied in a way which is in accordance with the phenomenology of religion so understood. What follows will offer an answer to the question of what contribution one particular understanding of phenomenology might make to the study of religion, but no attempt will be made to establish whether or not this particular understanding ought to be regarded as normative. (shrink)

Christology seems to fall fairly clearly into two divisions. The first is concerned with the truth of the two propositions: ‘Christ is God’ and ‘Christ is a man’. The second is concerned with the mutual compatibility of these propositions. The first part of Christology tends to confine itself to what is sometimes called ‘positive theology’: that is to say, it is largely given over to examining the Jons revelationis —let us not prejudge currently burning issues by asking what this is—to (...) see what evidence can be found for the truth of these propositions. Clearly, the methods used will be above all those of New Testament exegesis. The second part of Christology will necessarily consist entirely of that speculative theology which is contrasted with positive theology. Even if the earliest speculation on this topic is to be found in the New Testament itself and thus becomes fair game for the exegetes, any attempt to relate the primary truths, ‘Christ is God’ and ‘Christ is a man’, to eachother is a work of reflection, and in the terminology I am using speculative. (shrink)

"This edition, which replaces the original Loeb edition..., offers text, translation, and annotation that are fully current with modern scholarship"--Front flap of dust jacket, volume 1.

This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, (...) the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties). (shrink)

_Verificationism_ is the first comprehensive history of a concept that dominated philosophy and scientific methodology between the 1930s and the 1960s. The verificationist principle - the concept that a belief with no connection to experience is spurious - is the most sophisticated version of empiricism. More flexible ideas of verification are now being rehabilitated by a number of philosophers. C.J. Misak surveys the precursors, the main proponents and the rehabilitators. Unlike traditional studies, she follows verificationist theory beyond the demise of (...) positivism to examine its reappearance in the work of modern philosophers. Most interestingly, she argues that despite feminism's strenuous opposition to positivism, verificationist thought is at the heart of much of contemporary feminist philosophy. _Verificationism_ is an excellent assessment of a major and influential system of thought. (shrink)

In his celebrated masterpiece, Symposium, Plato imagines a high-society dinner-party in Athens in 416 BC at which the guests - including the comic poet Aristophanes and, of course, Plato's mentor Socrates - each deliver a short speech in praise of love. The sequence of dazzling speeches culminates in Socrates' famous account of the views of Diotima, a prophetess who taught him that love is our means of trying to attain goodness. And then into the party bursts the drunken Alcibiades, the (...) most popular and notorious Athenian of the time, who insists on praising Socrates himself rather than love, and gives us a brilliant sketch of this enigmatic character. The power, humour, and pathos of Plato's creation engages the reader on every page. This new translation is complemented by full explanatory notes and an illuminating introduction. (shrink)

Kant asserts that we cannot represent to ourselves the non-existence of space. In his discussion of the Ontological Argument he maintains that there is nothing whose non-existence is inconceivable. He thus seems to contradict himself. If the non-existence of space is unthinkable, so is the non-existence of a part of space — a place. Indicating a particular place, we might say "There are no objects there", but it would be nonsense to say "There doesn't exist". We can say, as Aristotle (...) saw, "There is a place where there was water and where there is now air"; but to do so is to bind an adverbial variable with a quantifier, not to attach "exists" to the name of a place. To assert of a place, or of space, that it exists or that it does not exist would be nonsense, and the unthinkable in that sense is not something whose negation is, as Kant thought, a necessary truth. (shrink)

This essay looks into the paradoxical friendship of Jacques Maritain, a Catholic philosopher, and Saul Alinsky, a radical community organizer. Commentators Bernard Doering and Charles Curran have used the fact of this friendship to draw the erroneous conclusion that Maritain approved of Alinsky’s philosophy. However, a closer look at their respective writings shows that Maritain and Alinsky retained profound disagreements on basic philosophical issues. Particular attention is paid to Maritain’s letter in response to Alinsky’s Rules for Radicals, in which Maritain (...) raised objections to many of Alinsky’s ideas. Thus, Maritain didnot compromise his Christian worldview. (shrink)

Kengo Miyazono, in his work Delusions and Beliefs, defends a teleo-functional account of delusions. In my contribution to this symposium, I question one of Miyazono’s motivations for appealing to teleo-functionalism over its main rival, dry-functionalism. Miyazono suggests that teleo-functionalism, unlike dry-functionalism, can account for the compatibility of the theses (i) that delusions are genuine doxastic states (doxasticism about delusions) and (ii) that delusions do not perform the typical causal roles of beliefs (the causal difference thesis). I argue, however, that there (...) are also ways for dry-functionalism to account for this compatibility. If what I have to say is correct, then Miyazono is perhaps too hasty—at least in one important respect—to opt for teleo-functionalism over dry-functionalism. Dry-functionalism has an equally good chance of satisfying some of Miyazono’s explanatory goals. (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.

Ash, C.J., Generalizations of enumeration reducibility using recursive infinitary propositional sentences, Annals of Pure and Applied Logic 58 173–184. We consider the relation between sets A and B that for every set S if A is Σ0α in S then B is Σ0β in S. We show that this is equivalent to the condition that B is definable from A in a particular way involving recursive infinitary propositional sentences. When α = β = 1, this condition is that B is (...) enumeration reducible to A. We establish further generalizations involving infinitely many sets and ordinals. (shrink)