Pure Type Systems, PTSs, were introduced as a generalization of the type systems of Barendregt's lambda cube and were designed to provide a foundation for actual proof assistants which will verify proofs. Systems of illative combinatory logic or lambda calculus, ICLs, were introduced by Curry and Church as a foundation for logic and mathematics. In an earlier paper we considered two changes to the rules of the PTSs which made these rules more like ICL rules. This led to four kinds (...) of PTSs. Most importantly PTSs are about statements of the form M:A, where M is a term and A a type. In ICLs there are no explicit types and the statements are terms. In this paper we show that for each of the four forms of PTS there is an equivalent form of ICL, sometimes if certain conditions hold. (shrink)

On the History of Modern Philosophy is a key transitional text in the history of European philosophy. In it, F. W. J. Schelling surveys philosophy from Descartes to German Idealism and shows why the Idealist project is ultimately doomed to failure. The lectures trace the path of philosophy from Descartes through Spinoza, Leibniz, Kant, Fichte, Jacobi, to Hegel and Schelling's own work. The extensive critiques of Hegel prefigure many of the arguments to be found in Feuerbach, Kierkegaard, Marx, Nietzsche, Heidegger, (...) and Derrida. This is the first English translation of On the History of Modern Philosophy. In his introduction Andrew Bowie sets the work in the context of Schelling's career and clarifies its philosophical issues. The translation will be of special interest to philosophers, intellectual historians, literary theorists, and theologians. (shrink)

Gilberto Freyre, the great Brazilian historian and sociologist, described Brazil as a ‘racial paradise’, a place where different races and nationalities have come to live together in a sort of ‘racial democracy’. The literature on this topic has become extensive as anthropologists, social scientists and historians felt the need to either prove or disprove such a claim. The argument that Brazil is a racial paradise or democracy is certainly romantic, even utopian; but it is true that Brazil has not experienced (...) the sort of racial friction that has been found in places such as South Africa (e.g. apartheid) or the USA (e.g. segregation laws). This article analyses interculturalism and non-formal education in Brazilian society from the perspective of Martin Buber's philosophy of dialogue and demonstrates some of the advantages interculturalism has over multiculturalism. We further suggest that the example of modern and contemporary Brazil follows Martin Buber in ‘pointing the way’ for other countries and for other societies and cultures. (shrink)

W. J. Mander provides a brief introduction to and critical assessment of the thought of the greatest of the British Idealist philosophers, F. H. Bradley (1846-1924), whose work has been largely neglected in this century. After a general introduction to Bradley's metaphysics and its logical foundations, Mander shows that much of Bradley's philosophy has been seriously misunderstood. Mander argues that any adequate treatment of Bradley's thought must take full account of his unique dual inheritance from the traditions of British empiricism (...) and Hegelian rationalism. The scholarship of recent years is assessed, and new interpretations are offered of Bradley's views about truth, predication, and relations, and of his arguments for idealism. (shrink)

F. H. Bradley did not write extensively or systematically on the philosophy of religion, and much of what he did write has the character of either tentative speculation or the pre-emptive rebuttal of potential misinterpretations that might threaten his general philosophical position. ‘I admit that on this subject I never had much to say’ he warns. But such a remark should not discourage us from considering his views on this topic, since the disclaimer is typically Bradleian, and more reflective of (...) his high standards for what is required in order to claim to have something to say about some matter than of any genuine lack of opinion. On closer inspection we find that he has, scattered throughout his work, a great many important things to say about this subject. (shrink)

Let S denote the variety of Sugihara algebras. We prove that the lattice (K) of subquasivarieties of a given quasivariety K S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice (S) is not modular.

Life, work, and influences -- Life -- Work -- Influences -- Metaphysics -- The intelligible world -- The existence of the intelligible world -- The intelligible and the divine world -- The intelligible and the natural world -- Knowledge -- Mind and body -- The souls of animals -- Knowledge : thought and souls -- Knowledge : God -- Mediate knowledge : external world -- Discussion and assessment of Norris's theory -- Was Norris an idealist? -- Faith and reason -- (...) The Socinian controversy -- Faith -- Reason -- Above reason and contrary to reason -- The measure of truth -- Faith and reason -- Malebranche -- Descartes -- Locke -- Love -- The theory of love -- The regulation of love -- The measure of divine love -- Controversy with Locke -- Norris's criticisms of Locke -- Locke's responses -- Concluding comments. (shrink)

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is (...) a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras. (shrink)

What precisely, W. J. T. Mitchell asks, are pictures (and theories of pictures) doing now, in the late twentieth century, when the power of the visual is said to be greater than ever before, and the "pictorial turn" supplants the "linguistic turn" in the study of culture? This book by one of America's leading theorists of visual representation offers a rich account of the interplay between the visible and the readable across culture, from literature to visual art to the mass (...) media. (shrink)

The purpose of this article is to introduce the reader to some intellectual origins of Simone Weil’s philosophy through a summary of and comment on her Lectures on Philosophy given when she was a teacher at a girls’ school at Roanne in the Loire region of central France. The article provides a comment on Simone Weil’s Lectures on Philosophy. There is a brief Introduction followed by a summary of Weil’s life which indicates her various interest as a religious thinker, mystic, (...) anarchist, and political activist and some of the important academic commentaries on these aspects of her life and work. The source of the Lectures on Philosophy edited by her pupil Anne Reynaud-Guérithault is then discussed followed by a detailed summary of and comment on the Lectures themselves. They are grouped under five headings which are considered in turn. These are: The materialist point of view; after the discovery of mind; politics and social theory; ethics and aesthetics; miscellaneous topics and essay plans. There is a further discussion of Simone Weil’s later philosophical thought which shows that what she published reveals classical learning and intellectual quality, but also the several antimonies with which she struggled in her thinking, the two major influences on her thought being Ancient Greece and Christianity. There is a short Conclusion and Bibliography. (shrink)

This paper argues that a strong thesis of divine providence, whereby God is understood as in complete control of all things, entails pantheism, the thesis that the universe is not ontologically distinct from God. In normal discourse, we distinguish a plan from, on the one hand, the state of affairs which realizes that plan—its execution or expression—and, on the other hand, the person or group whose plan it is. However, with respect to an omnipotent God who displays complete providence, neither (...) of these two distinctions holds. We cannot separate person from plan, or plan from world, and in consequence, neither can we separate person from world, ergo pantheism. Accordingly, the argument of this paper comes in two parts maintaining, first, the impossibility of distinguishing between God’s plan and its execution and, second, the impossibility of distinguishing God himself from his plan. (shrink)

What are the limits of Left Wittgensteinianism's point- and need-based account of conceptual change? Based upon Wittgenstein's account of certainty and the riverbed analogy for conceptual change in On Certainty, the question is raised whether Queloz and Cueni's redevelopment of Left Wittgensteinianism can account for the multiplicitous forms of change these concepts are subject to. I argue that Left Wittgensteinianism can only partially do so, because it overemphasises the role of criticism-driven conceptual change, due to its focus on the reason-based (...) contingency of the practices of a local ‘we’. In response, it is argued that Left Wittgensteinianism should be fortified with (i) gradual changes to concepts' sociocultural constraints that concept-users are unaware of and (ii) evolutionary and environmental changes to the biological determinants of natural constraints of conceptual cores. In the end, there are conceptual practices like holding for certain that are generally, and fully contingent, but simultaneously inevitable not only for ‘us’ but also for many other delimitations of ‘we’. Subsequently, the compatibility of this Wittgensteinian account of conceptual change with pragmatic genealogy is discussed. It is concluded that thinking about conceptual changes to practices cannot be about the possibility of criticism alone nor succeed without the inclusion thereof. (shrink)

A well-known result, going back to the twenties, states that, under some reasonable assumptions, any logic can be characterized as the set of formulas satisfied by a matrix 〈,F〉, whereis an algebra of the appropriate type, andFa subset of the domain of, called the set of designated elements. In particular, every quasi-classical modal logic—a set of modal formulas, containing the smallest classical modal logicE, which is closed under the inference rules of substitution and modus ponens—is characterized by such a matrix, (...) wherenow is a modal algebra, andFis a filter of. If the modal logic is in fact normal, then we can do away with the filter; we can study normal modal logics in the setting of varieties of modal algebras. This point of view was adopted already quite explicitly in McKinsey and Tarski [8]. The observation that the lattice of normal modal logics is dually isomorphic to the lattice of subvarieties of a variety of modal algebras paved the road for an algebraic study of normal modal logics. The algebraic approach made available some general results from Universal Algebra, notably those obtained by Jónsson [6], and thereby was able to contribute new insights in the realm of normal modal logics [2], [3], [4], [10].The requirement that a modal logic be normal is rather a severe one, however, and many of the systems which have been considered in the literature do not meet it. For instance, of the five celebrated modal systems, S1–S5, introduced by Lewis, S4 and S5 are the only normal ones, while only SI fails to be quasi-classical. The purpose of this paper is to generalize the algebraic approach so as to be applicable not just to normal modal logics, but to quasi-classical modal logics in general. (shrink)

Modal logics are studied in their algebraic disguise of varieties of so-called modal algebras. This enables us to apply strong results of a universal algebraic nature, notably those obtained by B. Jonsson. It is shown that the degree of incompleteness with respect to Kripke semantics of any modal logic containing the axiom □ p → p or containing an axiom of the form $\square^mp \leftrightarrow\square^{m + 1}p$ for some natural number m is 2 ℵ 0 . Furthermore, we show that (...) there exists an immediate predecessor of classical logic (axiomatized by $p \leftrightarrow \square p$ ) which is not characterized by any finite algebra. The existence of modal logics having 2 ℵ 0 immediate predecessors is established. In contrast with these results we prove that the lattice of extensions of S4 behaves much better: a logic extending S4 is characterized by a finite algebra iff it has finitely many extensions and any such logic has only finitely many immediate predecessors, all of which are characterized by a finite algebra. (shrink)

W. J. Mander presents the first ever synoptic history of British Idealism, the school of thought which dominated English-language philosophy from the 1860s to the early 20th century. He restores to its proper place this neglected period of philosophy, introducing the exponents of Idealism and explaining its distinctive concepts and doctrines.

W. J. Mander presents a history of metaphysics in nineteenth-century Britain. He traces the story of the development and interplay of three great schools of thought, the agnostics, the empiricists, and the idealists, and their different responses to the idea of an ultimate but unknowable way that things really are in themselves.