Several intrinsic/extrinsic distinctions amongst properties, current in the literature, are discussed and contrasted. The proponents of such distinctions tend to present them as competing, but it is suggested here that at least three of the relevant distinctions (including here that between non-relational and relational properties) arise out of separate perfectly legitimate intuitive considerations: though of course different proposed explications of the informal distinctions involved in any one case may well conflict. Special attention is paid to the question of whether a (...) single notion of property is capable of supporting the various distinctions. (shrink)

We consider the modal logic of non-contingency in a general setting, without making special assumptions about the accessibility relation. The basic logic in this setting is axiomatized, and some of its extensions are discussed, with special attention to the expressive weakness of the language whose sole modal primitive is non-contingency , by comparison with the usual language based on necessity.

This essay is a critical theological and pastoral study of the Working Document of the Second African Synod. The article engages the articles in the document which deal with the theme of reconciliation. This essay begins by exploring the Christological and ecclesiological foundations for an African theology of reconciliation as found in the working document. While engaging the significant aspects of the working document which relate to articulating an African theology of reconciliation, this essay shows the limitations of the document (...) in its historical and cultural analysis of the situation in Africa. Drawing from a phenomenological hermeneutical engagement with African history, cultural grammar, and Christ-centered African Christian imagination, the essay widens the scope of theological engagement with the task of reconciliation in Africa. It does a theological aesthetics of reconciliation in Africa, by integrating diverse cultural, ontological, and Christological symbols within the African world on vital participation and vital union. Through the inculturation of vital participation as analogous to Trinitarian Communion, the essay shows how the Church in Africa can deal with the ever-revolving cycle of violence, conflicts, and divisions in the churches and political institutions which have all hampered the mission of building relationship and God's kingdom in Africa. The essay concludes by recommending four pastoral approaches through which the Catholic Church in Africa can be both a reconciled community and an instrument for reconciliation in Africa. (shrink)

This paper considers the question: what becomes of the notion of a logic as a way of codifying valid arguments when the customary assumption is dropped that the premisses and conclusions of these arguments are statements from some single language? An elegant treatment of the notion of a logic, when this assumption is in force, is that provided by Dana Scott's theory of consequence relations; this treatment is appropriately generalized in the present paper to the case where we do not (...) make this assumption of linguistic homogeneity. Several applications of the resulting concept of a heterogeneous logic are suggested, but the main emphasis is on the formal development. One topic touched on is a certain contrast between the boolean and the intensional sentence-connectives in this more general setting. (shrink)

For the claim that the satisfaction of certain conditions is sufficient for the application of some concept to serve as part of the (`reductive') analysis of that concept, we require the conditions to be specified without employing that very concept. An account of the application conditions of a concept not meeting this requirement, we call analytically circular. For such a claim to be usable in determining the extension of the concept, however, such circularity may not matter, since if the concept (...) figures in a certain kind of intensional context in the specification of the conditions, the satisfaction of those conditions may not itself depend on the extension of the concept. We put this by saying that although analytically circular, the account may yet not be inferentially circular. (shrink)

For the claim that the satisfaction of certain conditions is sufficient for the application of some concept to serve as part of the (‘reductive’) analysis of that concept, we require the conditions to be specified without employing that very concept. An account of the application conditions of a concept not meeting this requirement, we call analytically circular. For such a claim to be usable in determining the extension of the concept, however, such circularity may not matter, since if the concept (...) figures in a certain kind of intensional context in the specification of the conditions, the satisfaction of those conditions may not itself depend on the extension of the concept. We put this by saying that although analytically circular, the account may yet not be inferentially circular. (shrink)

An account of desire as a species of belief may owe its appeal to the details of its proposal as to precisely what sort of beliefs desires are to be identified with, and its downfall may be due to those details it does provide. For example, it may be proposed that the desire that α is in fact the belief that it ought to be that α, or is morally good or desirable that it should be the case that α. (...) Here the appeal might be that of forging a link between the holding of a moral belief and the acknowledgment that one has a reason for acting a certain way; and the shortcoming of the suggestion is its evident implausibility: even if the ‘necessity’ direction could be established, having a desire hardly seems sufficient for the holding of any such belief. Again: it might be proposed, perhaps simply to bring some order into the realm of propositional attitudes by reducing some to others, that the belief with which we should identify a’s desire that α is a’s belief that he will or would be happy if α. This proposed identification can be seen to be incorrect by consideration of examples such as the following, due to J. Gosling. An aging and ailing parent might forego numerous pleasures in order that his children should reap the benefits of his saving and have a good start in life – perhaps by receiving an expensive education – after his impending death. Oearly he may want that they should so benefit even if he does not believe in an after-death existence in which he might come to know of, and so take pleasure in, his children’s subsequent well-being. So his wanting that they should prosper cannot consist in his believing that he will be happy if/when they do, since he has no expectation of even being in existence in that eventuality. As Gosling puts it, there is a clear difference between thinking that something’s coming about will bring one pleasure, on the one hand, and viewing the prospect of its coming about with pleasure, on the other. (shrink)

A.N. Prior once showed that on certain apparently reasonable assumptions, a thesis sometimes associated with the name of Hume to the effect that no set of factual statements can ever entail an evaluative statement, is quite untenable. We assume only that there is at least one statement of each kind, and that the negation of a factual statement is factual — a principle we may call ‘N'. Now consider the disjunction F V E of some factual with some evaluative statement. (...) Since the disjunction is entailed by F, a factual statement, it must, if principle H is correct, be classified as factual. But by N, ∽ F is also factual, and this together with F V E entails E, thus violating H since E was exhypothesi an evaluative statement. (shrink)

An account of desire as a species of belief may owe its appeal to the details of its proposal as to precisely what sort of beliefs desires are to be identified with, and its downfall may be due to those details it does provide. For example, it may be proposed that the desire that α is in fact the belief that it ought to be that α, or is morally good or desirable that it should be the case that α. (...) Here the appeal might be that of forging a link between the holding of a moral belief and the acknowledgment that one has a reason for acting a certain way; and the shortcoming of the suggestion is its evident implausibility: even if the ‘necessity’ direction could be established, having a desire hardly seems sufficient for the holding of any such belief. Again: it might be proposed, perhaps simply to bring some order into the realm of propositional attitudes by reducing some to others, that the belief with which we should identify a’s desire that α is a’s belief that he will or would be happy if α. This proposed identification can be seen to be incorrect by consideration of examples such as the following, due to J. Gosling. An aging and ailing parent might forego numerous pleasures in order that his children should reap the benefits of his saving and have a good start in life – perhaps by receiving an expensive education – after his impending death. Oearly he may want that they should so benefit even if he does not believe in an after-death existence in which he might come to know of, and so take pleasure in, his children’s subsequent well-being. So his wanting that they should prosper cannot consist in his believing that he will be happy if/when they do, since he has no expectation of even being in existence in that eventuality. As Gosling puts it, there is a clear difference between thinking that something’s coming about will bring one pleasure, on the one hand, and viewing the prospect of its coming about with pleasure, on the other. (shrink)

This paper is about a support information management system for a wind power producer having an energy storage system and participating in a day-ahead electricity market. Energy storage can play not only a leading role in mitigation of the effect of uncertainty faced by a WP producer, but also allow for conversion of wind energy into electric energy to be stored and then released at favourable hours. This storage provides capability for arbitrage, allowing an increase on profit of a WP (...) producer, but must be supported by a convenient problem formulation. The formulation proposed for the support information management system is based on an approach of stochasticity written as a mixed integer linear programming problem. WP and market prices are considered as stochastic processes represented by a set of scenarios. The charging/discharging of the ESS are considered dependent on scenarios of market prices and on scenarios of WP. The effectiveness of the proposed formulation is tested by comparison of case studies using data from the Iberian Electricity Market. The comparison is in favour of the proposed consideration of stochasticity. (shrink)

Extant semantic theories for languages containing vague expressions violate intuition by delivering the same verdict on two principles of classical propositional logic: the law of noncontradiction and the law of excluded middle. Supervaluational treatments render both valid; many-Valued treatments, Neither. The core of this paper presents a natural deduction system, Sound and complete with respect to a 'mixed' semantics which validates the law of noncontradiction but not the law of excluded middle.

A.N. Prior once showed that on certain apparently reasonable assumptions, a thesis sometimes associated with the name of Hume to the effect that no set of factual statements can ever entail an evaluative statement, is quite untenable. We assume only that there is at least one statement of each kind, and that the negation of a factual statement is factual — a principle we may call ‘N'. Now consider the disjunction F V E of some factual with some evaluative statement. (...) Since the disjunction is entailed by F, a factual statement, it must, if principle H is correct, be classified as factual. But by N, ∽ F is also factual, and this together with F V E entails E, thus violating H since E was exhypothesi an evaluative statement. (shrink)

SummaryIf you know you can recognise positive instances of a property, can you use this knowledge so as to be able to recognise also its negative instances? This is the question to be adressed.

Tarski 1968 makes a move in the course of providing an account of ?definitionally equivalent? classes of algebras with a businesslike lack of fanfare and commentary, the significance of which may accordingly be lost on the casual reader. In ?1 we present this move as a response to a certain difficulty in the received account of what it is to define a function symbol (or ?operation symbol?). This difficulty, which presents itself as a minor technicality needing to be got around (...) especially for the case of symbols for zero-place functions (for ?distinguished elements?), has repercussions?not widely recognised?for the account of functional completeness in sentential logic. A similarly stark comment in Church 1956 reveals an appreciation of this difficulty, though not every subsequent author on the topic has taken the point. We fill out this side of the picture in ?2. The discussion of functional completeness in ?2 is supplemented by some remarks on what is involved in defining a connective, which have been included in an Appendix. The emphasis throughout is on conceptual clarification rather than on proving theorems, and the main body of the paper may be regarded as an elaboration on the remarks just mentioned by Tarski and Church. The Appendix (?3) is intended to be similarly clarificatory, though this time with some corrective intent, of remarks made in and about Makinson 1973. (shrink)

An analogy between functional dependencies and implicational formulas of sentential logic has been discussed in the literature. We feel that a somewhat different connexion between dependency theory and sentential logic is suggested by the similarity between Armstrong's axioms for functional dependencies and Tarski's defining conditions for consequence relations, and we pursue aspects of this other analogy here for their theoretical interest. The analogy suggests, for example, a different semantic interpretation of consequence relations: instead of thinking ofB as a consequence of (...) a set of formulas {A1,...,A n} whenB is true on every assignment of truth-values on which eachA i is true, we can think of this relation as obtaining when every pair of truth-value assignments which give the same truth-values toA 1, the same truth-values toA 2,..., and the same truth-values toA n, also make the same assignment in respect ofB. We describe the former as the consequence relation inference-determined by the class of truth-value assignments (valuations) under consideration, and the latter as the consequence relation supervenience-determined by that class of assignments. Some comparisons will be made between these two notions. (shrink)