In 1977, R. B. Angell presented a logic for <span class='Hi'>analytic</span> containment, a notion of relevant implication stronger than Anderson and Belnap's entailment. In this paper I provide for the first time the logic of first degree <span class='Hi'>analytic</span> containment, as presented in [2] and [3], with a semantical characterization—leaving higher degree systems for future investigations. The semantical framework I introduce for this purpose involves a special sort of truth-predicates, which apply to pairs of collections of formulas instead of individual (...) formulas, and which behave in some respects like Gentzen's sequents. This semantics captures very general properties of the truth-functional connectives, and for that reason it may be used to model a vast range of logics. I briefly illustrate the point with classical consequence and Anderson and Belnap's tautological entailments. (shrink)
Editorial 40 Content Type Journal Article Category Editorial Pages 1-2 DOI 10.1007/s10698-012-9148-y Authors Eric R. Scerri, Department of Chemistry and Biochemistry, UCLA, Los Angeles, CA 90095, USA Journal Foundations of Chemistry Online ISSN 1572-8463 Print ISSN 1386-4238.
Abstract The Los Angeles riots illustrate how a pluralistic society can come apart once its members lose faith in its moral character. The cynicism and despair so evident in our cities challenge moral educators to nurture in the coming generation a belief and hope in the transformative power of democratic institutions. Effective democratic moral education requires that teachers provide experience in democratic problem?solving. In this article we use examples from two Just Community programmes in urban settings, the recently established YES (...) program and the Cluster School, to illustrate how democratic participation can enkindle democratic faith and foster integration across racial and social class divisions. (shrink)
The subject of this investigation is the role of conventions in the formulation of Thomas Reid's theory of the geometry of vision, which he calls the 'geometry of visibles'. In particular, we will examine the work of N. Daniels and R. Angell who have alleged that, respectively, Reid's 'geometry of visibles' and the geometry of the visual field are non-Euclidean. As will be demonstrated, however, the construction of any geometry of vision is subject to a choice of conventions regarding the (...) construction and assignment of its various properties, especially metric properties, and this fact undermines the claim for a unique non-Euclidean status for the geometry of vision. Finally, a suggestion is offered for trying to reconcile Reid's direct realist theory of perception with his geometry of visibles.While Thomas Reid is well-known as the leading exponent of the Scottish 'common-sense' school of philosophy, his role in the history of geometry has only recently been drawing the attention of the scholarly community. In particular, several influential works, by N. Daniels and R. B. Angell, have claimed Reid as the discoverer of non-Euclidean geometry; an achievement, moreover, that pre-dates the geometries of Lobachevsky, Bolyai, and Gauss by over a half century. Reid's alleged discovery appears within the context of his analysis of the geometry of the visual field, which he dubs the 'geometry of visibles'. In summarizing the importance of Reid's philosophy in this area, Daniels is led to conclude that 'there can remain little doubt that Reid intends the geometry of visibles to be an alternative to Euclidean geometry'; while Angell, similarly inspired by Reid, draws a much stronger inference: 'The geometry which precisely and naturally fits the actual configurations of the visual field is a non-Euclidean, two-dimensional, elliptical geometry. In substance, this thesis was advanced by Thomas Reid in 1764 ...' The significance of these findings has not gone unnoticed in mathematical and scientific circles, moreover, for Reid's name is beginning to appear more frequently in historical surveys of the development of geometry and the theories of space.Implicit in the recent work on Reid's 'geometry of visibles', or GOV, one can discern two closely related but distinct arguments: first, that Reid did in fact formulate a non-Euclidean geometry, and second, that the GOV is non-Euclidean. This essay will investigate mainly the latter claim, although a lengthy discussion will be accorded to the first. Overall, in contrast to the optimistic reports of a non-Euclidean GOV, it will be argued that there is a great deal of conceptual freedom in the construction of any geometry pertaining to the visual field. Rather than single out a non-Euclidean structure as the only geometry consistent with visual phenomena, an examination of Reid, Daniels, and Angell will reveal the crucial role of geometric 'conventions', especially of the metric sort, in the formulation of the GOV (where a 'metric' can be simply defined as a system for determining distances, the measures of angles, etc.). Consequently, while a non-Euclidean geometry is consistent with Reid's GOV, it is only one of many different geometrical structures that a GOV can possess. Angell's theory that the GOV can only be construed as non-Euclidean, is thus incorrect. After an exploration of Reid's theory and the alleged non-Euclidean nature of the GOV, in respectively, the focus will turn to the tacit role of conventionalism in Daniels' reconstruction of Reid's GOV argument, and in the contemporary treatment of a non-Euclidean visual geometry offered by Angell (). Finally, in the conclusion, a suggestion will be offered for a possible reconstruction of Reid's GOV that does not violate his avowed 'direct realist' theory of perception, since this epistemological thesis largely prompted his formulation of the GOV. (shrink)
We study a range of issues connected with the idea of replacing one formula by another in a fixed (linguistic) context. The replacement core of a consequence relation ⊢ is the relation holding between a set of formulas { A 1 , ..., A m , ...} and a formula B when for every context C (·), we have C ( A 1 ), ..., C ( A m ), ... ⊢ C ( B ). Section 1 looks at some (...) differences between which inferences are lost on passing to the replacement cores of the classical and intuitionistic consequence relations. For example, we find that while the inference from A and B to , sanctioned by both these initial consequence relations, is retained on passage to the replacement core in the classical case, it is lost in the intuitionistic case. Further discussion of these two (and some other) logics occupies Sections 3 and 4. Section 2 looks at the m = 1 case, describing A as replaceable by B according to ⊢ when B is a consequence of A by the replacement core of ⊢, and inquiring as to which choices of ⊢ render this induced replaceability relation symmetric. Section 5 investigates further conceptual refinements— such as a contrast between horizontal and vertical replaceability—suggested by some work of R. B. Angell and R. Harrop (and a comment on the latter by T. J. Smiley) in the 1950s and 1960s. Appendix 1 examines a related aspect of term-for-term replacement in connection with identity in predicate logic. Appendix 2 is a repository for proofs which would otherwise clutter up Section 3. (shrink)
Troubadour of truth, by R. E. Brennan.--Reflections on necessity and contingency, by Jacques Maritain.--Intellectual cognition, by Rudolf Allers.--The problem of truth, J. K. Ryan.--The ontolgical roots of Thomism, by Hilary Carpeuter.--The role of habitus in the Thomistic metaphysics of potency and act, by V. J. Bourke.--The nature of the angels, by J. O. Riedl.--The dilemma of being and unity, by A. C. Pegis.--Prudence, the incommunicable wisdom, by C. J. O'Neil.--A question about law, by M. J. Adler.--The economic philosophy of Aquinas, (...) by J. A. Ryan.--Beyond the crisis of liberalism, by Y. R. Simon.--The fate of representative government, by Walter Farrell.--The Thomistic concept of education, by R. J. Slavin.--The perennial theme of beauty, by Immanuel Chapman.--Epilogue, by H. T. Schwartz.--Bibliography (p.[363]-419). (shrink)
Nozick's genetic supermarket has arrived on the wings of angels brought to us by Ron Harris, the founder of ronsangels.com. How should we respond to this and other options that will soon be beckoning? To assist us in answering these questions, I shall begin by considering a technique that has been with us for some time, but has the effect of changing the nature of children. Understanding the basis on which this technique can be supported may help us to grapple (...) with the more difficult question of what we should do about newer options that also change the nature of our children. It is not, however, my aim here to deal with all the objections that could be urged against these options. My purpose is the narrower one of developing a clear understanding of the central values at stake. (shrink)
