We show that the join of two classical [respectively, regular, normal] modal logics employing distinct modal operators is a conservative extension of each of them.

Although we believe the results reported below to have direct philosophical import, we shall for the most part confine our remarks to the realm of mathematics. The reader is referred to [4] for a philosophically oriented discussion, comprehensible to mathematicians, of tense logic.The “minimal” tense logicT0is the system having connectives ∼, →,F(“at some future time”), andP(“at some past time”); the following axioms:(whereGandHabbreviate ∼F∼ and ∼P∼ respectively); and the following rules:(8) fromαandα → β, inferβ,(9) fromα, infer any substitution instance ofα,(10) fromα, (...) inferGα,(11) fromα, inferHα.A tense logic is a systemTwhose language is that ofT0and whose axioms and rules include (1)–(11). The axioms and rules ofTother than (1)–(11) are calledproperaxioms and rules.We shall investigate three systems of semantics for tense logics, i.e. three notions ofstructureand three relations ⊧ which stand between structures and formulas. One reads⊧αas “αis valid in.” A structureis amodelof a tense logicTif every formula provable inTis valid in. A semantics isadequateforTif the set of models ofTin the semantics is characteristic forT, i.e. if wheneverT ∀ αthen there is a modelofTin the semantics such that∀ α. Two structuresand, possibly from different semantics, are calledequivalent(∼) if exactly the same formulas are valid inas in. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume XX, Number 2, November 1994, pp. 261-287 Collingwood's Understanding of Hume S. K. WERTZ What was David Hume's reception in the British idealistic tradition? In this paper, I shall contribute a short chapter on this question by examining Hume's place in R. G. Collingwood's thought.1 Such an examination has been lacking in the literature, so what follows is a comprehensive study of Collingwood's use of Hume (...) throughout all of R.G.'s writings. I shall mainly focus on two main, unrelated discussions of Hume: first is the theory of the imagination which primarily occurs in The Principles of Art, and second is the set of relations between human nature and human history which is principally found in The Idea of History. These sections will be followed by a section on minor discussions and omissions and a conclusion. It is a common misconception that Collingwood (1889-1943) has little to offer Hume scholarship, and I wish to amend that here. Actually, Collingwood has good insights into the nature of the imagination and its role in human understanding, besides instructive thoughts on Hume on human nature and history, even though his discussion of the latter is flawed. This essay serves both historical and philosophical purposes. It is to sample Hume's place in early twentieth century British idealism at a time when he began to emerge as an important philosophical figure worthy of careful study. (By "idealism," I mean the philosophical movement which takes ideas to be an irreducible part of the world and whose program is opposed to both materialism and realism.) So Collingwood's portrait is historically interesting. But over and above this, it carries significant philosophical amendments, S. K. Wertz is at the Department of Philosophy, Texas Christian University, Box 30781, Fort Worth, TX 76129 USA. e-mail: [email protected] 262 S. K. Wertz criticisms, and suggestions about Hume's thought and the eighteenth century intellectual climate. Collingwood has mostly been studied as a philosopher of history or as an aesthetician, but not in toto from the perspective of one of the historical figures to whom he is deeply indebted. Such a view affords a portrait of Hume that is instructive and rewarding. The comparison of Hume and Collingwood lead us to finer appreciation of both philosophers. Let us first look at Collingwood's positive contribution. Imagination Collingwood begins his analysis by declaring his intentions: I shall...try to show that there are such things, to be with what Hume (whose account of them I shall take as my starting-point) called 'ideas' as distinct from 'impressions'. I shall try to show that there is a special activity of mind correlative to them, and that this is what we generally call imagination, as distinct from sensation on the one hand and intellect on the other. (PA 170-71, emphasis added) Why would Collingwood start with Hume's distinction between impressions and ideas? Undoubtedly, this means that Collingwood is willing to accept the validity of the distinction and to build on it. Isn't this a strange place for an idealist to begin? Not really. When we look at British philosophy at the turn of this century, we find idealists preoccupied with the distinction,2 so it is not extraordinary to find Collingwood utilizing it to some extent. Like most Oxford students of the time, Collingwood read Locke, Berkeley, and Hume in his undergraduate program. Consequently we find them in the problems he addresses. "It was Hume who first perceived the [Lockean] problem [of confusing sensation with imagination]," Collingwood attributes, "and tried to solve it by distinguishing ideas from impressions" (PA 200). In detail: He [Hume] was right when he laid it down that the immediate concern of thought is not with impressions but with ideas; that it is ideas, not impressions, that are associated with one another and thus built up into the fabric of knowledge; and that ideas, though 'derived' from impressions, are not mere relics of them like an after-taste of onions or an after-image of the sun (as Lockeans like Condillac supposed), but something different in kind: different, if not in what he... (shrink)

Seeks to provide a new direction for the advancement of political theory. This essay deals with the uneasy relationship between liberty and equality; the nature of democracy and the formation of political consensus; and the weakness of our understanding of class.

In verse twelve of the Tao Te Ching, Lao Tzu makes a curious claim about the five flavors; namely that they cause people not to taste or that they jade the palate. The five flavors are: sweet, sour, salt, bitter and spicy or hot as in 'heat'. To the Western mind, the claim, 'The five flavors cause them [persons] to not taste,' is counterintuitive; on the contrary, the presence of the five flavors in a dish or in a meal would (...) expand or enhance the senses and the palate, i.e., taste would be augmented by the five flavors. So what is the plausible meaning of the Taoistic claim? To answer this question, I look very briefly at the history of the doctrine of the five flavors and the history of Chinese cuisine. Lao Tzu probably has Confucian feasts in mind in making such a claim, but other interpretations are discussed. (shrink)

In his critique of aesthetic individualism, R.G. Collingwood provides an account of persons that anticipates the post-Wittgensteinians; notably, Peter Strawson, Daniel Dennett, and Annette Baier. According to this view, persons emerge in the midst of other persons. This process is always unfinished and ongoing throughout one's life. One difficulty with this perspective is the problem of firstness: if persons are essentially second persons or one's personhood is contingent upon other persons, how could there be a first person or early persons? (...) One solution to this problem is to employ the notion of family or community. This solution can be found in both Collingwood and Baier.After this discussion,we look at his autobiography for evidence of his own 'discoveries' of personhood. There is tension here because he was a rebel and a loner, but there were a few (but not many) good relationships that confirm or exemplify his view of persons in his own life. Also briefly addressed is how this view fits into his theories of history and art. (shrink)

R. G. Collingwood (1889–1943) had several arguments that analyzed race in history and anthropology. These appear mainly in Roman Britain (both in theory and practice of history), The Idea of History, and The Principles of History. This latter work, which is fairly new to Collingwood scholarship (1999), contains the most important arguments. Collingwood argued that race is grounded in the historical process and this includes a people's environment, more so than genetics or evolution. He used the nature of art as (...) an example in his main argument. This spills over in his view of anthropology—in particular physical anthropology that was influenced by John Beddoe. His view is contrasted with Claude Lévi-Strauss who held that physical anthropology is at the forefront of social or cultural anthropology which follows its lead. Whereas Collingwood held that in studying blood types, skulls, and bones, 'one does not get inside the object or recreate its object inside itself.' Consequently, cultural anthropology will always provide the key to racial considerations. What is revealed is that emotions and rationality are the same across cultures; also, that superiority/inferiority claims about race are mythical and lead us into darkness and superstition. (shrink)

A set S of degrees is said to be an initial segment if c ≤ d ∈ S→-c∈S. Shoenfield has shown that if P is the lattice of all subsets of a finite set then there is an initial segment of degrees isomorphic to P. Rosenstein [2] (independently) proved the same to hold of the lattice of all finite subsets of a countable set. We shall show that “countable set” may be replaced by “set of cardinality at most that of (...) the continuum.” This result is also an extension of [3, Corollary 2 to Theorem 15], which states that there is a sublattice of degrees isomorphic to the lattice of all finite subsets of 2N. (A sublattice of degrees is a subset closed under ∪ and ∩; an initial segment closed under ∪ is necessarily a sublattice, but not conversely.)It seems worth noting that the proof of the present result was preceded in time by our proof [4] of the analogous theorem for hyperdegrees, and is in fact an adaptation of that proof. Thus the present work has been influenced much more directly by the Gandy-Sacks forcing construction of a minimal hyperdegree [1] than by previous work on initial segments of degrees. (shrink)

We eat not only because it is necessary for us to, but also and much more because eating gives us pleasure.In this essay, I develop a case for G. W. Leibniz as our first modern food philosopher. It is in his theory of perception and in his culinary examples that I find the most convincing evidence, especially when I contrast them with Locke and Hume’s account of perception with reference to food. In the process, Leibniz expanded aesthetic perception to include (...) nature and food. He did not draw a distinction between ordinary or regular perception and aesthetic perception; perceiving smells and tastes are similar to perceiving colors—both have structures,2 but more on.. (shrink)

By focusing on the known details of Laonikos Chalkokondyles’ biography, on his relation to Byzantine historiographical tradition, by comparing his historical work to that of contemporary intellectuals living under the Ottomans as well as those in the west, examining his portrayal of Mehmed II, his adoption of a Herodotean model, the revival of Herodotus in the Renaissance more generally, and the reception of the ᾿Aπόδειξις in the fifteenth and sixteenth centuries, I argue that Laonikos was writing for an elite circle (...) of Byzantine émigrés and other intellectuals with access to classical Greek in the west, rather than for the post- Byzantine intellectuals associated with the Ottoman court. (shrink)