A notion of resource-bounded Baire category is developed for the class PC[0,1] of all polynomial-time computable real-valued functions on the unit interval. The meager subsets of PC[0,1] are characterized in terms of resource-bounded Banach-Mazur games. This characterization is used to prove that, in the sense of Baire category, almost every function in PC[0,1] is nowhere differentiable. This is a complexity-theoretic extension of the analogous classical result that Banach proved for the class C[0, 1] in 1931.

Ennead I. 4. 3: Plotinus is arguing that happiness is fullness and completeness of life, and continues, according to the MSS. , οϋτω γρ ν οùδέ έπακτòν τò γαθòν ύπάρΧοι, ούδ' λλο τò ύποκείμενον άλλαΧόθεν γενόμενον παρέξει αύτò ν άγαθεναι. Mr. MacKenna translates the last phrase by ‘a life needing no foreign substance called in from a foreign realm to establish it in good ’; Ficinus by ‘neque aliud quicquam aliunde adueniens efficiet ut subiectum collocetur in bono.’ Ficinus is undoubtedly (...) right. τò ύποκειμέν means ‘the subject,’ which a few lines above has been identified with the λογικ ζωή. The passage should be corrected by writing τ, ύποκειμέν, dependent on γενόμενον, for τò úποκείμενον. (shrink)

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First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Intuitionists and classical logicians use in common a large number of the logical axioms, even though they supposedly mean different things by the logical connectives and quantifiers — conquans for short. But Wittgenstein says The meaning of a word is its use in the language. We prove that in a definite sense the intuitionistic axioms do indeed characterize the logical conquans, both for the intuitionist and the classical logician.

Woodger discusses what he claims to be haldane's misunderstandings about his article "what do we mean by unborn?" these include primarily the structure of woodger's definitions. (staff).

State of nature theories have a long history and play a lively role in contemporary work. Theories of this kind share certain nontrivial commitments. Among these are commitments to inclusion of a Lockean proviso among the principles of justice and to an assumption of invariance of political principles across changes of circumstances. In this article I want to look at those two commitments and bring to light what I believe are some important difficulties they engender. For nonpattern state of nature (...) theories, the justness of a society is marked by the conformance of the society to procedural principles. Distributions of resources and the like have no particular import for questions of justice. Whatever may later result, so long as it came about in accordance with the rules determined by the principles of justice, is itself just. The Lockean proviso is one of the principles of justice governing property and other rights of nonpattern theories of justice. The proviso hangs as a "shadow" over the results of the operation of the other (usual) principles of justice. It is intended to remedy a complaint which arises when the positions of those no longer at liberty to use some resource are worsened (1) by no longer being able to use freely what they previously were free to use and (2) in such a way that they fall below a "baseline." Following Locke, a traditional formulation of the proviso is to allow acquisition just so long as there is "enough and as good" left over for others. Section I concerns the relation of the Lockean proviso to pattern and nonpattern principles of justice, demonstrating that a Lockean proviso turns a nonpattern into a pattern theory of justice. Section II is about the relation of the Lockean proviso to the ideas revealed by an examination of a state of nature, suggesting reasons to reject ideal theories of justice. (shrink)

Orestes has returned to Argos, . For him to brandish at his father's murderers is natural there, where he is delivering a sort of general manifesto as to his aims, and where the strong word is justified and alleviated by the jingle with juxtaposed . But there is no reason for Orestes to go on insisting on the bloodthirstiness of these aims, and reads oddly in 100, where he is explaining soberly his plan of campaign.

This lecture is divided, roughly, into three parts. First, there is a general and perhaps rather simple-minded discussion of what are the ‘facts’ that social anthropologists study; is there anything special about these ‘facts’ which makes them different from other kinds of facts? It will be useful to start with the common-sense distinction between two kinds or, better, aspects of social facts; first—though neither is analytically prior to the other—and putting it very crudely, ‘what people do’, the aspect of social (...) interaction, and second, ‘what—and how—people think’, the conceptual, classifying, cognitive component of human culture. Now in reality, of course (and perhaps not so ‘of course’; people do tend to think of them as separate ‘things’), these two aspects are inextricably intertwined. But it is essential to distinguish them analytically, because each aspect gives rise to quite different kinds of problems of understanding for the social anthropologist. We shall see that the problem of how to be ‘objective’, and so to avoid ethnographic error, arises in both contexts, but in rather different forms in each. (shrink)

Professor Richmond's reply t o m y article on Palatine Apollo is argued with his usual enthusiasm and cogency. This reply to him, which has been delayed by my departure for Australia, must begin with an expression of the respect that I feel for an antagonist far more able and experienced than I can claim to be. Indeed, it was while lecturing on Ovid, Tristia 3 that I first met Professor Richmond's masterly article on the Augustan Palatium . From this (...) article my enthusiasm for the subject began, and I know that Professor Richmond has always welcomed discussion and argument about the famous Augustan temple of Apollo on the Palatine. I can but join him in urging any who may have been interested by our discussion to study his original article which contains much more besides a discussion of the site of Apollo's temple. (shrink)