Reumen. Se describen las bases del muestreo conglomerado y muestreo sistemático. Se presentan lasecuaciones pertinentes y aquellas para la estimación del tamaño óptimo de muestreo para cada tipo demuestreo. Se demuestra la aplicación práctica de éstos clases de muestreo por medio de ejemplosreales.Palabras claves. Muestreo conglomerado, muestreo sistemático, tamaño óptimo de la muestra.. Cluster sampling and systematic sampling are described and their equations are provided.Real examples are given in order to show the applications of these types of samplings. Equations toestimate (...) optimal sample sizes are also noted.Keywords. Cluster sampling, optimal sample size, systematic sampling. (shrink)

Dans cet article, j’essaie de montrer que l’idée du langage comme calcul structure la philosophie de Wittgenstein dans le Big Typescript. Pour ce faire, je commence par mettre en relief les différences entre la conception du langage comme calcul dans le Tractatus, et sa reformulation dans le Big Typescript ; j’explique ensuite comment l’idée de l’autonomie de la grammaire est à la base de la conception de la « grammaire » ou du langage comme calcul. J’espère pouvoir montrer ainsi l’unité (...) de la philosophie de Wittgenstein aux alentours de 1932-1933. Il doit en ressortir que sa philosophie à l’époque du Big Typescript présente un intérêt en elle-même, quoiqu’il ne s’agisse pas encore de la philosophie des Recherches philosophiques.I aim at showing that the idea of language as a calculus is the central view that shapes Wittgenstein’s philosophy in the Big Typescript. In order to do so, I first contrast the conception of language as a calculus in the Tractatus with its reformulation in the BigTypescript ; then I explain how the idea of the autonomy of grammar grounds the conception of “grammar” or language as calculus. With this on hand, I give an overview of the unity of Wittgenstein’s philosophy around 1932-1933. It should become clear that his philosophy at the time is worth arguing for, even though it is not yet the philosophy of the PhilosophicalInvestigations. (shrink)

As the United States population ages, there is a growing group of aging, elderly, individuals who may consider "preemptive suicide"(Prado, 1998). Healthy aging patients who preemptively attempt to end their life by suicide and who have clearly expressed a desire not to have life -sustaining treatment present a clinical and public policy challenge. We describe the clinical, ethical, and medical-legal decision making issues that were raised in such a case that presented to an academic emergency department. We also review (...) and evaluate a decision making process that emergency physicians confront when faced with such a challenging and unusual situation. (shrink)

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

The idea of a 'logic of quantum mechanics' or quantum logic was originally suggested by Birkhoff and von Neumann in their pioneering paper [1936]. Since that time there has been much argument about whether, or in what sense, quantum 'logic' can be actually considered a true logic (see, e.g. Bell and Hallett [1982], Dummett [1976], Gardner [1971]) and, if so, how it is to be distinguished from classical logic. In this paper I put forward a simple and natural semantical framework (...) for quantum logic which reveals its difference from classical logic in a strikingly intuitive way, viz. through the fact that quantum logic admits (suitably formulated versions of) the characteristic quantum-mechanical notions of superposition and incompatibility of attributes. That is, precisely the features that distinguish quantum from classical physics also serve, within this framework, to distinguish quantum from classical logic. Some light is shed on the question of whether quantum logic is a genuine logical system by introducing a natural entailment relation for quantum-logical formulas with the implication symbol. The novelty is that, although implication behaves as it should (i.e. the 'deduction theorem' holds), the order of introduction of premises is significant. The fact that a reasonable entailment relation can be formulated for quantum logic supports the view that it is a genuine logical system and not merely an algebraic formalism. (shrink)

"Remarkable how well Bouwsma understood Wittgenstein's approach to philosophical problems and how intelligently he was able to recount Wittgenstein's discussions. The bits about sensation are especially good. And the asides about the other philosophers--e.g. Dewey, Russell, Anscombe--are, while not frivolous, gossipy and titillating." --Riley Wallihan, Western Oregon University.

Autobiographical memories typically give rise either to memory reports (“I remember going swimming”) or to first person past-tense judgements (“I went swimming”). This article focuses on first person past-tense judgements that are (epistemically) based on autobiographical memories. Some of these judgements have the IEM property of being immune to error through misidentification. This article offers an account of when and why first person past-tense judgements have the IEM property.

The infinitesimal methods commonly used in the 17th and 18th centuries to solve analytical problems had a great deal of elegance and intuitive appeal. But the notion of infinitesimal itself was flawed by contradictions. These arose as a result of attempting to representchange in terms ofstatic conceptions. Now, one may regard infinitesimals as the residual traces of change after the process of change has been terminated. The difficulty was that these residual traces could not logically coexist with the static quantities (...) traditionally employed by mathematics. The solution to this difficulty, as it turns out, is to regard these quantities asalso being subject to (a form of) change, for then they will have the same nature as the infinitesimals representing the residual traces of change, and will become,ipso facto, compatible with these latter.In fact, the category-theoretic models which realize the Principle of Infinitesimal Linearity may themselves be regarded as representations of a general concept of variation (cf. Bell (1986)). While the static set-theoretical models represent change or motion by making a detour through the actual (but static) infinite, the varying category-theoretic models enable such change to be representeddirectly, thus permitting the introduction of geometric infinitesimals and, as we have attempted to demonstrate in this paper, the virtually complete incorporation of the methods of the early calculus.It is surely a remarkable — even an ironic — fact that the contradiction between the flux of the objective world and the stasis of mathematical entities has found its resolution in category theory, a branch of mathematics commonly, and, as one now sees, mistakenly, regarded as the summit of gratuitous abstraction. (shrink)

We analyze Zorn's Lemma and some of its consequences for Boolean algebras in a constructive setting. We show that Zorn's Lemma is persistent in the sense that, if it holds in the underlying set theory, in a properly stated form it continues to hold in all intuitionistic type theories of a certain natural kind. (Observe that the axiom of choice cannot be persistent in this sense since it implies the law of excluded middle.) We also establish the persistence of some (...) familiar results in the theory of (complete) Boolean algebras--notably, the proposition that every complete Boolean algebra is an absolute subretract. This (almost) resolves a question of Banaschewski and Bhutani as to whether the Sikorski extension theorem for Boolean algebras is persistent. (shrink)

In Discourse Contextualism, Alex Silk defends a new contextualist account of expressions at the centre of recent debates over contextualism versus relativism, namely, gradable adjectives, taste predicates and epistemic and deontic modals ).1 1 The first part of the book, which lays out the view and shows how it explains the phenomena at issue in those debates, focuses on the case of epistemic modals. The second part of the book extends that account with Discourse Contextualist treatments of the remaining expressions. (...) Discourse Contextualism is truly impressive in its scope, fully engaging with the relevant literature in linguistics, philosophy of language and meta-ethics. It is clearly written, carefully argued and makes a very significant contribution to the literature on the debates over contextualism, relativism and expressivism. No short review could possibly do justice to Silk’s book in its entirety. Here, I focus on its most fleshed out case study, that of epistemic modals. But the whole book will be required reading for anyone engaged in any of these debates. (shrink)

Consider the following well-known result from the theory of normed linear spaces ([2], p. 80, 4(b)): (g) the unit ball of the (continuous) dual of a normed linear space over the reals has an extreme point. The standard proof of (~) uses the axiom of choice (AG); thus the implication AC~(w) can be proved in set theory. In this paper we show that this implication can be reversed, so that (*) is actually eq7I2valent to the axiom of choice. From this (...) we derive various corollaries, for example: the conjunction of the Boolean prime ideal theorem and the Krein-Milman theorem implies the axiom of choice, and the Krein-Milman theorem is not derivable from the Boolean prime ideal theorem. (shrink)

In this paper we construct the ortholattices arising in quantum logic starting from the phenomenologically plausible idea of a collection of ensembles subject to passing or failing various “tests.” A collection of ensembles forms a certain kind of preordered set with extra structure called anorthospace; we show that complete ortholattices arise as canonical completions of orthospaces in much the same way as arbitrary complete lattices arise as canonical completions of partially ordered sets. We also show that the canonical completion of (...) an orthospace of ensembles is naturally identifiable as the complete lattice of properties of the ensembles, thereby revealing exactlywhy ortholattices arise in the analysis of “tests” or experimental propositions. Finally, we axiomatize the hitherto implicit concept of “test” and show how they may be correlated with properties of ensembles. (shrink)

This paper critically evaluates Jonathan Lowe's arguments for his non-Cartesian substance dualism. Sections 1 and 2 set out the principal claims of NCSD. The unity argument proposed in Lowe is discussed in Section 3. Throughout his career Lowe offered spirited attacks on reductionism about the self. Section 4 evaluates the anti-reductionist argument that Lowe offers in Subjects of Experience, an argument based on the individuation of mental events. Lowe offers an inventive proposal that the semantic distinction between direct and indirect (...) reference delineates the metaphysical boundary between self and world, and uses this as a further argument against reductionism about the self. This proposal is discussed in Sections 5 and 6. (shrink)

RésuméLa notion de système joue un rôle essentiel en physique. Les difficulté actuelles de la physique théorique résident en grande partie dans cette notion même. A chaque étape du développement de la physique il a fallu imaginer un processus nouveau pour effacer partiellement la coupure introduite dans la description de l'univers par la considération d'un système. Nous examinons ici le dernier procédé ou théorie fonctionnelle du corpuscule, qui consiste à se servir, pour la représentation du corpuscule, d'une image plus complète (...) que celles utilisées jusqu'ici, celle d'une fonction u d'un espace fonctionnel séparable. (shrink)

Où se trouve le sérieux? L'auteur se pose cette question peu commune, et se met en quête d'une réponse. Il propose une articulation du sérieux selon les modes épistémologique, esthétique et éthique, pour l'approcher indirectement par le feint, le comique et le léger. Il s'attaque d'abord au problème que pose une quête du sérieux par le " feint ", ce qui le conduit à des interprétations originales du doute cartésien, du langage philosophique et de la connaissance scientifique : il distingue (...) le feint du fictif et du faux, mais constate aussi que le feint a tendance à se transformer en l'un ou en l'autre. L'auteur s'aventure ensuite dans le domaine esthétique où, à partir d'une critique de la théorie bergsonienne du rire, il développe sa propre interprétation du comique ; il soutient que la musique est l'art relativement le plus sérieux, mais que le sérieux comme tel est absent de l'art. Passant à la morale, il se voit obligé d'abord de s'expliquer avec les existentialistes français, ennemis déclarés du sérieux, puis, après une franche appréciation du sérieux de notre époque, d'admettre finalement que le léger y joue un rôle essentiel aussi. Distinguant en plus le sérieux du fanatique, l'auteur tente de préciser les rapports entre le sérieux et la foi, la Bible, et la pensée kierkegaardienne. Il conclut que la philosophie, et plus particulièrement la métaphysique, est le ressort du sérieux, mais que le philosophe est tenu par son sérieux même de chercher toujours plus loin. Le livre est écrit sous la forme de carnets, dans un style clair et engageant ; non dépourvu d'humour, il s'adresse à tout lecteur philosophiquement averti. (shrink)