-- Douglas Kellner, University of Texas, Austin.

Machine generated contents note: 1. The Computability Concept;2. General Recursive Functions;3. Programs and Machines;4. Recursive Enumerability;5. Connections to Logic;6. Degrees of Unsolvability;7. Polynomial-Time Computability;Appendix: Mathspeak;Appendix: Countability;Appendix: Decadic Notation;.

Both and agree that there are universals—that qualities are universals. To say that the quality white is a universal is to say, in part, that one and the same thing is connected in some way to both Plato and Socrates and accounts for the truth of the sentences "Plato is white" and "Socrates is white." To put it another way, the term "white" in both sentences refers to the same entity. What arguments are there for such a view? Russell elegantly (...) put forth the classic argument in "On the Relations of Universals to Particulars." To deny universals is to assert that the quality attributed to Socrates is not one and the same with the quality attributed to Plato. The quality "in" each is numerically distinct and, furthermore, no one thing accounts for these distinct qualities being of the same kind. [I mention this latter point since one might, on a version of, hold that there are particular qualities as well as universal qualities. The former account for the whiteness of particular patches; the latter for such particular whitenesses being just that.] One must then hold that such particular qualities are related in some way, since they are the entities in virtue of which we truly assert that both things are white. One must then specify such a relation. The obvious point is that such a relation will either be taken as a universal or a particular instance. If a particular then the original problem recurs when we introduce a third white patch or a pair of black patches. If admitted as a universal then the view finally accepts universals, albeit relational ones. No other alternative can answer the original question—to account for Socrates and Plato having the same color. That is, no alternative acknowledging only individuals—that denies the two patches are connected, in some way, to one and the same entity—can prevent the recurrence of exactly the same kind of question we started out with. Let us consider the case of particulars. One may argue that just as universals account for the sameness of quality, something must account for the difference of two patches which, conceivably, have all their nonrelational qualities in common. This something, the ground of numerical difference, is considered to be a substratum which stands in a unique relation or connection with universals to form or constitute facts and the things we started out with, Plato and Socrates. These ordinary things are thought of as composed of a substratum and universals connected together. Facts about such things may be composed of the substratum and one universal. The facts are about the things since the same substratum is a constituent of both sorts of entities. Such substrata account for the difference of the two patches; for there being two and not one thing. These substrata, in turn, are held to be simply different. At this point one may balk. If substrata are held to be simply different, why bother with them at all? Why not hold that Socrates and Plato are composites, not classes, of universals, and that they are different composites of the same universals? They just simply differ. If substrata can simply differ, why may not composites of universals simply differ? The proponent of substrata must retort that since Plato and Socrates are composite entities they cannot simply differ but must be held to differ in a constituent. Only simple entities can simply differ. Let me call this assertion the axiom of difference. The first point to note is that it is a necessary assumption in the argument to establish the need for substrata in an adequate ontology. We must then inquire why some accept, implicitly or explicitly, such an axiom. (shrink)

Education for peace.--Education in things.--Culture and education in a world order.--The moral significance of aesthetic education.--The education of free men.

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Music and listening, music and consciousness -- Conceptualizing consciousness -- The phenomenology of everyday music listening experiences -- Absorption, dissociation and trancing -- Musical and non-musical trancing in daily life -- Imaginative involvement -- Musical and non-musical trancing : similarities and differences -- Experiencing life and art : ethological and evolutionary perspectives on -- Transformations of consciousness -- Everyday music listening experiences reframed.

A consideration of the unity of a class or kind as including its member or instances.