I propose to show in this paper how Bosanquet’s aesthetics, in certain of its aspects, conditions William Temple’s reflection on art — a reflection which occupies a central position in Temple’s “Christo-centric metaphysics,” and which finds expression particularly in Mens Creatrix. Bosanquet’s influence becomes still more evident if we compare Temple’s position with the philosophy of art which R.G. Collingwood delineated in the initial phase of his thought, above all in Speculum Mentis and Outlines of a Philosophy of Art.

By using some classical reasoning we show that any countably presented formal topology, namely, a formal topology with a countable axiom set, is spatial.

O Argumento da Terra Gêmea Moral (ATGM) é o desafio semântico central para o Realismo Moral Naturalista (RMN). À fim de evitar tal problema, os defensores do RMN têm articulado uma série de réplicas ao ATGM. Neste artigo, abordo algumas dessas réplicas e defendo a tese de que elas não refutam o ATGM. Considero duas propostas em específico: o Argumento da Tradução, de D. Copp, e o Argumento do Fim da Investigação Moral, de A. Viggiano. Apresento essas objeções, mostro em (...) que sentido pretendem responder ao ATGM e argumento que cada uma delas é vulnerável a vários problemas. Concluo que os ataques de Copp e Viggiano ao ATGM devem ser recusados e que o desafio semântico ao RMN persiste. (shrink)

By means of models in toposes of C-sets (where C is a small category), necessary conditions are found for the minimum quantified extension of a propositional (intermediate, modal) logic to be complete with respect to Kripke semantics; in particular, many well-known systems turn out to be incomplete.

We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras.

We prove a generalization of the hyper-game theorem by using an abstract version of inductively generated formal topology. As applications we show proofs for Cantor theorem, uncountability of the set of functions from N to N and Gödel theorem which use no diagonal argument.

http://dx.doi.org/10.5007/1808-1711.2008v12n1p49 The aim of this article is to offer a rejoinder to an argument against scientific realism put forward by van Fraassen, based on theoretical considerations regarding microphysics. At a certain stage of his general attack to scientific realism, van Fraassen argues, in contrast to what realists typically hold, that empirical regularities should sometimes be regarded as “brute facts”, which do not ask for explanation in terms of deeper, unobservable mechanisms. The argument from microphysics formulated by van Fraassen is based (...) on the claim that in microphysics the demand for explanation leads to a demand for the so-called hidden-variable theories, which “runs contrary to at least one major school of thought in twentieth-century physics”. It is shown here that this argument does not represent an insurmountable obstacle to scientific realism, not even when a series of important theoretical and experimental results against hidden-variable theories — and not merely a conflict with a certain school of thought—is taken into account. (shrink)

We show that some common varieties of modal K4-algebras have finitary unification type, thus providing effective best solutions for equations in free algebras. Applications to admissible inference rules are immediate.

En este artículo, discuto la metodología filosófica frente a los límites del sentido y de la racionalidad. Empiezo con la concepción según la cual el filósofo debería resignarse a exhibir el sinsentido de otros filósofos, pero finalmente tendría que callarse, ya que su propio discurso necesariamente sobrepasa los límites de la racionalidad. En seguida, propongo una metodología interpretativa para la filosofía en un intento de caracterizar mejor estos límites y evitar el silencio que inviabilizaría todo el discurso filosófico. Finalmente, busco (...) reconciliar la metodología filosófica interpretativa con la irracionalidad interna del filósofo apelando a una división de su mente entre el sentido común y una segunda agencia que está destinada a sobrepasarlo. Dicha esquizofrenia de la filosofía sería la única manera de entender su tarea recurrente de trazar de manera segura los límites de nuestra comprensión cotidiana del mundo. (shrink)

We analyze some extensions of Martin-Löf 's constructive type theory by means of extensional set constructors and we show that often the most natural requirements over them lead to classical logic or even to inconsistency.

There is an important research tradition concerning the financial implications of social and environmental ethics. This study investigates the short- and long-term financial performance of ventures with explicit environmental commitments seeking to raise funds in equity crowdfunding (ECF) markets. Our results indicate that environmental orientation positively influences short-term funding performance, though only when accompanied by the costly signal of robust corporate governance mechanisms. In the long run, environmental orientation also positively impacts performance, albeit with only weak statistical significance when observed (...) alone. Governance again serves as a positive moderator, but its effect is less significant relative to the short term. However, environmental orientation does feature a strongly significant positive impact on long-run performance when combined with a successfully conducted initial ECF campaign. (shrink)

A. M. Pitts in [Pi] proved that HA op fp is a bi-Heyting category satisfying the Lawrence condition. We show that the embedding $\Phi: HA^\mathrm{op}_\mathrm{fp} \longrightarrow Sh(\mathbf{P_0,J_0})$ into the topos of sheaves, (P 0 is the category of finite rooted posets and open maps, J 0 the canonical topology on P 0 ) given by $H \longmapsto HA(H,\mathscr{D}(-)): \mathbf{P_0} \longrightarrow \text{Set}$ preserves the structure mentioned above, finite coproducts, and subobject classifier, it is also conservative. This whole structure on HA op (...) fp can be derived from that of Sh(P 0 ,J 0 ) via the embedding Φ. We also show that the equivalence relations in HA op fp are not effective in general. On the way to these results we establish a new kind of duality between HA op fp and a category of sheaves equipped with certain structure defined in terms of Ehrenfeucht games. Our methods are model-theoretic and combinatorial as opposed to proof-theoretic as in [Pi]. (shrink)

The logicD-J of the weak exluded middle with constant domains is proved to be incomplete with respect to Kripke semantics, by introducing models in presheaves on an arbitrary category. Additional incompleteness results are obtained for the modal systems with nested domains extendingQ-S4.1.

We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation fromS42 (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and.

This article suggests developing the concept of spiritual ecology into that of balanced spiritual ecosystems. Philosophies, theologies, education systems, political parties, and gender-based and ethnic identity politics need to be critiqued both from within and without so that they can finally contribute to the creation, maintenance and flourishing of balanced spiritual ecosystems.Contribution: Spiritual ecology is a concept on which converge different worldviews. This article recommends using balanced spiritual ecosystems, instead. The new concept could provoke further reflection on how our -ontologies (...) and communities co-exist and whether they do it organically and spiritually. This article befits HTS’s interest in ‘theology and nature’. (shrink)

Abstract.Formal topologies are today an established topic in the development of constructive mathematics. One of the main tools in formal topology is inductive generation since it allows to introduce inductive methods in topology. The problem of inductively generating formal topologies with a cover relation and a unary positivity predicate has been solved in [CSSV]. However, to deal both with open and closed subsets, a binary positivity predicate has to be considered. In this paper we will show how to adapt to (...) this framework the method used to generate inductively formal topologies with a unary positivity predicate; the main problem that one has to face in such a new setting is that, as a consequence of the lack of a complete formalization, both the cover relation and the positivity predicate can have proper axioms. (shrink)

Reflete-se sobre visões hegemônicas que, desde as primeiras elaborações imaginárias de um possível mundo ocidental no quarto século a.C., distorceram a imagem de povos africanos e sustentaram processos de colonização sob essa égide de pensamento.. Essas visões são fábulas, correspondendo a efabulações sobre a(s) África(s), africanos, descendentes. Existe um mundo fascinado há milênios por outro. Esse mundo fascinado e imaginado, o Ocidente, explorou e assumiu a narrativa sobre vários outros mundos, esmaecidos, rasurados, reinterpretados pela memória europeia, seja por traçados territoriais (...) ou da narrativa histórica. O Ocidental se contrapôs, assim, ao Oriental, também esmaecido. O que seriam Oriente e Ocidente? Assim como não existe raça, mas existe racismo, talvez não existam Ocidentes e Orientes, mas Ocidentalismos e Orientalismos. Cabe perguntar: sob esses imaginários, onde fica a África(s), que se situa e se perde entre os “ismos” elaborados, em lugar avesso à ideia de civilização, de não-Ocidente, de não-Oriente, de “um não-lugar”? Essa África imaginada enfeitiça o Ocidente e ao mesmo tempo é por ele metamorfoseada. O romance O Asno de Ouro, do africano Apuleio (Século II d. C.), servirá de pretexto para a reflexão sobre essa metamorfose. (shrink)

Sufficient syntactic conditions for canonicity in intermediate and intuitionistic modal logics are given. We present a new technique which does not require semantic first-order reduction and which is constructive in the sense that it works in an intuitionistic metatheory through a model without points which is classically isomorphic to the usual canonical model.

In this paper we present a general theory of normal forms, based on a categorial result for the free monoid construction. We shall use the theory mainly for proposictional modal logic, although it seems to have a wider range of applications. We shall formally represent normal forms as combinatorial objects, basically labelled trees and forests. This geometric conceptualization is implicit in and our approach will extend it to other cases and make it more direct: operations of a purely geometric and (...) combinatorial nature will be introduced in order to give a mathematical description of the basic logical/algebraic constructions .We begin by recalling the above-mentioned categorial construction: we need a careful inspection of it because in the various examples considered later we plan to deduce from it in a uniform way the normal forms and the description of finitely generated free algebras. This method always works whenever we can describe the category of algebras corresponding to the logic under consideration as a T-objects category. When this simple description seems not to be available, still the general theory might be of some interest, because a description of the category of algebras as a T-objects category plus equation is possible .The central part of the paper is more advanced and specific: we show how the general approach presented here can provide some insights even in the basic case of the modal system K. Section 4 contains a contribution to the theory of normal forms, namely the description of the uniform substitution. This result will enable us to give a duality theorem for the category of finitely generated free modal algebras and in Section 5 to provide a characterization of the collections of normal forms which happen to be normal forms for a logic, thus giving a description of the lattice of modal logics.Section 6 deals with some applications: we shall show how to use normal forms in order to prove for the modal system K the definability of higher-order propositional quantifiers and of the tense operator F .As to the prerequisites, the paper is almost self-contained. The reader is only assumed to have familiarity with standard techniques in algebraic logic ). Knowledge of the basic facts about adjoint functors is required too, see e.g. McLane or the appendix. (shrink)

We investigate finitarity of unification types in locally finite varieties of Heyting algebras, giving both positive and negative results. We make essential use of finite dualities within a conceptualization for E-unification theory 733–752) relying on the algebraic notion of a projective object.

In the literature, the nature of the relationships between memory processes and summary evaluations is still a debate. According to some theoretical approaches (e.g., “two-memory hypothesis”; Anderson, 1989) retrospective evaluations are based on the impression formed while attending to the to-be-assessed stimuli(on-line judgment) – no functional dependence between information retrieval and judgment is implied. Conversely, several theories entail that judgment must depend, at least in part, on memory processes (e.g., Dougherty, Gettys, & Ogden, 1999; Schwarz, 1998; Tversky & Kahneman, 1973). (...) The present study contributes to this debate by addressing two important issues. First, it shows how more comprehensive memory measures than those used previously (e.g., Hastie & Park, 1986) are necessary in order to detect a relationship between memory and retrospective evaluations. Secondly, it demonstrates how memory strategies influence the relationship between memory and judgment. Participants recalled lists of words, after having assessed each of them for their pleasantness. Results showed a clear association between memory and judgment, which was mediated by the individual strategies participants used to recall the items. (shrink)

This article argues that we cannot separate theology on the one hand and politics, law and economy on the other when trying to understand how to deal with religious and cultural diversity. Through an historical examination of the formation of the right to religious liberty in the West, it shows that the European secular state is still deeply indebted with its theological presuppositions. This conclusion explains why systems of religiously based personal regimes are much less widespread in Europe than in (...) other parts of the world. It also suggests that the best way to manage cultural and religious diversity in Europe consists in strengthening the pluralistic components of the European legal systems, as already shown by recent reforms in the field of family and commercial law. (shrink)

We characterize (both from a syntactic and an algebraic point of view) the normal K4-logics for which unification is filtering. We also give a sufficient semantic criterion for existence of most general unifiers, covering natural extensions of K4.2⁺ (i.e., of the modal system obtained from K4 by adding to it, as a further axiom schemata, the modal translation of the weak excluded middle principle).