What I wish to propose in the present paper is a new form of “career induction” for ambitious young logicians. The basic problem is this: if we look at the n-variable fragments of relevant propositional logics, at what point does undecidability begin? Focus, to be definite, on the logic R. John Slaney showed that the 0-variable fragment of R (where we allow the sentential con- stants t and f) contains exactly 3088 non-equivalent propositions, and so is clearly decidable. In the (...) opposite direction, I claimed in my paper of 1984 that the five variable fragment of R is undecidable. The proof given there was sketchy (to put the matter charitably), and a close examination reveals that although the result claimed is true, the proof given is incorrect. In the present paper, I give a detailed and (I hope) correct proof that the four variable fragments of the principal relevant logics are undecidable. This leaves open the question of the decidability of the n-variable fragments for n = 1, 2, 3. At what point does undecidability set in? (shrink)

Distributive bounded lattices with a dual homomorphism as unary operation, called Ockham algebras, were firstly studied by Berman (1977). The varieties of Boolean algebras, De Morgan algebras, Kleene algebras and Stone algebras are some of the well known subvarieties of Ockham algebra. In this paper, new results about the congruence lattice of Ockham algebras are given. From these results and Urquhart's representation theorem for Ockham algebras a complete characterization of the subdirectly irreducible Ockham algebras is obtained. These results are (...) particularized for a large number of subvarieties of Ockham algebras. For these subvarieties a full description of their subdirectly irreducible algebras is given as well. (shrink)

The title of this and proposed second volume presents the basic idea which unifies the wide variety of topics developed and investigated by the principal authors, major contributing authors, J. M. Dunn and Robert K. Meyer, and eleven other contributors. The other contributors are: J. R. Chidgey, J. A. Coffa, Dorthy L. Grover, Bas van Fraassen, H. Leblanc, Storrs McCall, A. Parks, G. Pottinger, R. Routley, A. Urquhart, and R. G. Wolf. From both the useful analytic table of contents (...) and from the section titles it is clear which contributing author has written each section. Chapter I, "The Pure Calculus of Entailment," suggests how logics of entailment are logics of relevance and necessity. When we explain why a large number of systems are investigated, it will be clear why we write of logics of entailment instead of the logic of entailment. The principal authors build a case in Chapter I, and elsewhere, that a genuinely valid formal inference, viz., a formal entailment, from a formula A to a formula B requires that A be relevant to B in addition to it being impossible that there be an interpretation making A true and B false. So, a claim that A entails B tells us, explicitly or implicitly, that A is relevant to B and that "if A then B" is necessarily true, i.e., A strictly implies B. Consequently since a logic of entailment presents allegedly unfalsifiable claims, i.e., theses, using entailment claims, a logic of entailment presents theses about relevance between antecedents and consequents and necessity. It should be noted that the systems of logic developed are for formal entailments; they may not be logics for material entailments such as: being a cube entails having six surfaces. (shrink)

After discussing in the first five sections the meaning and the difficulties of the principle of relativity we present a new sel of spacetime transformations between inertial systems (“inertial” transformations), based on three assumptions: (1) The two-way velocity of light is c in all inertial systems and in all directions; (2) Time dilation effects take place with the usual relativistic factor; (3) Clocks are synchronized in the way chosen by nature itself, e.g., in the Sagnac effect. We show that our (...) new transformation laws can explain the available experimental evidence in spite of the implied noninvariance of the one-way velocity of light. (shrink)

The Irish poet W. B. Yeats once wrote, with great sapience and perception: Nor dread, nor hope attend A dying animal; A man awaits his end Dreading and hoping all. That death has ever been a problem to man is attested as far back as we can trace our species in the archaeological record—indeed, it seems to have been a problem even for that immediate precursor of homo sapiens, the so-called Neanderthal Man; for he buried his dead.

My topic is a long-standing tension in the interpretation of religion. On the one hand, it seems undeniable — seems almost to go without saying — that liturgical and sacrificial practices, sacred dance, divination, procession and pilgrimage are intentional actions undertaken by persons. Yet there is a distinguished tradition in the study of religion according to which religious activity is typically caused by forces over which the agent has little or no control. Visible, latter-day members of this tradition include Hume, (...) Nietzsche, Marx, Durkheim, Freud, and, in some moods, Wittgenstein, but its roster is by no means limited to the religiously unmusical. (shrink)

Autobiography and Teacher Development in China investigates the roles of autobiography in teacher education, as several scholars in China recontextualize Western conceptions of teacher development, combining them with uniquely Chinese cultural conceptions to articulate a reconceptualization of teacher development that holds worldwide significance. Framed by the work of Zhang Hua and William F. Pinar, these theoretical and practical essays point to an internationally inflected reconceptualization of teachers' professional development, pre-service and in-service. This volume addresses multiple movements of teacher education reform (...) worldwide, focused on crafting a nationally distinctive course not only internationally, but also culturally, historically, and locally. (shrink)

In the Antiatticista, as we call the scanty excerpt of a lexicon of the second century A.D., so abbreviated as to be often unintelligible, we find on p. 86. 20 the following article: Γενέσια оσης тε έоρтς &lsqbтς&rsqb δημотελоũς 〈έν &rsquoΑθήνααις, ΒоB7δρоγιѿνоς ΠέμΠтηι, Γενέσια καλоυένμς, καθόтι øησί Φιλόχоρоς καί Σόλων έν тоȊς &rsquoΑξоσι, καί тς тоũ όνόμαтоς χρήσεως оσης &rsquoΕλλ:ηνικς, тί κιλúει μή μόνоν έΠ тς δημотελоũς έоρтς á»á καί έΠί тςίδίας έκáσтоυ тáσσεσθα&iota. What rouses our interest in this note (...) is not the domestic quarrel between the Atticists of a stricter and of a more lenient observance about the meaning and the use of the word, but the facts themselves, which in the present case are fortunately clear enough. The lexicographer knows two entirely different facts: a material fact, the existence of a State festival in Athens called Genesia and celebrated on the 5th of Boedromion; a linguistic fact, the ’Ελλινικǹ χασις which denotes by Γενέσια not this State festival but some private celebration. For the latter, it is important to observe that by &rsquoΕλλνικ χασις the lexicographer does not mean Hellenistic Greek nor the usage of his own day, but the occurrence of the word in those authors whom the strict Atticists do not take as models of style, or who are not held to be Attic writers: it is to such authors, at least, that the lexicographer appeals in the preceding gloss: he there quotes ΕριΠίδης “Іωνι for γενέθλια and Herodotos for γενέσια. The latter passage could be the evidence for his linguistic fact, that ‘Hellenic usage’ applies the word γενέσια to a private celebration. (shrink)

Objective: To pilot informed consent materials developed for Aboriginal parents in a vaccine trial, and evaluate their design and the informed consent process.Methods: Cross sectional quantitative and qualitative survey of 20 Aboriginal and 20 non-Aboriginal women in Alice Springs. Information about the proposed research was presented to Aboriginal participants by an Aboriginal researcher, using purpose designed verbal, visual, and written materials. Non-Aboriginal participants received standard materials developed by the sponsor. Questionnaires were used to evaluate recall and understanding immediately and five (...) days later. Qualitative analysis of Aboriginal participants’ interviews was performed.Results: There were no differences between the groups in understanding of diseases prevented by the vaccine, the potential risks of participating, or the voluntary nature of participation. Most Aboriginal participants had difficulty with the concept of a “licensed” versus “unlicensed” vaccine. The non-Aboriginal group had a good understanding of this. Aboriginal participants identified the use of the flipchart, along with a presentation by a doctor and Aboriginal health worker, as preferred delivery modes. Group presentations were preferred rather than one-on-one discussions. The use of the questionnaire posed considerable methodological difficulties.Conclusions: A one-off oral presentation to Aboriginal participants is unlikely to produce “informed consent”. Key but unfamiliar concepts require identification and particularly considered presentation. (shrink)

This chapter contains sections titled: Introduction Origins of the Contemporary Debate Historiographic Research and Writing Two Variants of Narrativist Philosophy of Historiography The Philosophical Approach The Transcendentalization of Narrativist Philosophy of Historiography Rhetorical Narrativist Philosophy Hayden White Conclusion Bibliography.

In the first part of this article, I raisequestions about Dworkin''s theory of theintrinsic value of life and about the adequacyof his proposal to understand abortion in termsof different ways of valuing life. In thesecond part of the article, I consider hisargument in ``The Philosophers'' Brief on AssistedSuicide'''', which claims that the distinctionbetween killing and letting die is morallyirrelevant, the distinction between intendingand foreseeing death can be morally relevantbut is not always so. I argue that thekilling/letting die distinction can be (...) relevantin the context of assisted suicide, but alsoshow when it is not. Then I consider why theintention/foresight distinction can be morallyirrelevant and conclude by presenting analternative argument for physician-assistedsuicide. (shrink)