Sergio F. Martinez

An interpretation of quantum mechanics that rejects hidden variables has to say something about the way measurement can be understood as a transformation on states of individual systems, and that leads to the core of the interpretive problems posed by Luders' projection rule: What, if any, is its physical content? In this paper I explore one suggestion which is implicit in usual interpretations of the rule and show that this view does not stand on solid ground. In the process, important aspects of the role played by the projection postulate in the conceptual structure of quantum mechanics will be clarified. It will be shown in particular that serious objections can be raised against the (often implicit) view that identifies the physical relation of compatibility preserved by Luders' rule with the relation of simultaneous measurability.

Usual derivations of Lilders's projection rule show that Liuders's rule is the rule required by quantum statistics to calculate the final state after an ideal (minimally disturbing) measurement. These derivations are at best inconclusive, however, when it comes to interpreting Liuders's rule as a description of individual state transformations. In this paper, I show a natural way of deriving Liiders's rule from well-motivated and explicit physical assumptions referring to individual systems. This requires, however, the introduction of a concept of individual state which is not standard.

The search for understanding is a major aim of science. Traditionally, understanding has been undervalued in the philosophy of science because of its psychological underpinnings; nowadays, however, it is widely recognized that epistemology cannot be divorced from psychology as sharp as traditional epistemology required. This eliminates the main obstacle to give scientific understanding due attention in philosophy of science. My aim in this paper is to describe an account of scientific understanding as an emergent feature of our mastering of different (causal) explanatory frameworks that takes place through the mastering of scientific practices. Different practices lead to different kinds of representations. Such representations are often heterogeneous. The integration of such representations constitute understanding.

La filosofía de la ciencia se desarrolló durante la primera mitad del siglo xx bajo el supuesto de que la ciencia podía caracterizarse por la estructura lógica tanto del conocimiento articulado en las teorías más exitosas como de sus explicaciones. En la segunda mitad del siglo xx se cuestiona fuertemente esa idea, pero se sigue asumiendo que la filosofía de la ciencia debe hacerse siguiendo los cánones de una epistemología fundamentalista que considera que el avance de la ciencia pasa por una ontología cada vez mas austera guiada por la idea de "mientras menos mejor". Desde esta perspectiva fundamentalista, el que las diferentes ciencias hablen de diferentes tipos de cosas es un obstáculo al entendimiento, producto de la imperfección del conocimiento actual. Este ideal nos invita a pensar que la epistemología debe hacerse reflexionando sobre el conocimiento articulado en nuestras teorías más austeras y nos compromete con propuestas reduccionistas problemáticas que no permiten explicar la diversidad de recursos epistémicos que de hecho utilizan los científicos. En este libro promovemos una epistemología que no sigue el lema de "mientras menos mejor", sino el de "organizar nuestros recursos epistémicos de manera que se genere entendimiento". Así, la misma estructura de las explicaciones y las prácticas (que incluye métodos y normas respecto de lo que se considera plausible y valioso) es lo que nos da la pauta para responder a la pregunta de qué es lo que hay. Esta estrategia epistémica nos obliga a hacer una filosofía de la ciencia muy cercana a la ciencia, reconociendo la pluralidad de sus métodos, objetivos y prácticas, sin reducir la filosofía de la ciencia a la sociología o a cualquier otra ciencia en particular.

This paper explores some of the philosophical difficulties involved in the task of clarifying the idea of an irreducible statistical law, by means of an analysis of the paradigmatic example of such a law in the Quantum theory.These are two alternative strategies that can be pursued in clarifying this question. One is to understand this irreductibility by means of one or another interpretation of the Quantum theory. But, as will be shown, the different interpretations of Quantum mechanics lead to radically different and fundamentally incompatible answers to the problem. The second strategy is to try to caracterize this irreducibility “directly”, via a proof of the impossibility of a hidden-variable extension of the statistical formalism of the theory. This strategy culminates with Bell’s theorem which indeed establishes the impossibility of constructing “Iocal” theories of hidden variables. This impossibility result, however, fails to provide us with a satisfying interpretation of the quantum irreductibility, rather, it merely shows how far we are from a solution to the problem.

The projection postulate is the source of a long standing controversy in the interpretation of the axiomatic foundations of quantum mechanics. In a sense which is made precise in chapter II the projection postulate is a mathematical theorem easily derivable within the mathematical framework of the theory. This theorem receives a clear and straightforward interpretation if Luders' rule is given only statistical significance. Under the assumption that an interpretation of quantum mechanics has to provide an account of the process of measurement as a change on the state of individual systems, however, additional interpretive assumptions are needed in order to arrive at a satisfactory interpretation of Luders' rule. ;I show in chapter III that there are serious problems with the usual interpretation by making explicit in a quantum logical framework the concept of individual state and minimal disturbance implicit in this view. In chapter IV I show that it is possible to formulate a natural interpretation of Luders' rule as a description of 'dispersion free' state transformations within a semantic framework that takes states of individual systems to be represented by Boolean ultrafilters , as opposed to the usual approach that takes individual states to be represented by lattice ultrafilters. This lay the ground for the clarification of several interpretive issues in the foundations of quantum mechanics. It is shown that Luders' rule can be justified as a description of individual state transformations without the need of imposing additional assumptions. The derivation of Luders' rule within the semantic framework of B-states shows an important connection between interpretation that take individual state to be 'relative' to experimental situations and the statistical structure of the theory

This paper explores some of the philosophical difficulties involved in the task of clarifying the idea of an irreducible statistical law, by means of an analysis of the paradigmatic example of such a law in the Quantum theory.These are two alternative strategies that can be pursued in clarifying this question. One is to understand this irreductibility by means of one or another interpretation of the Quantum theory. But, as will be shown, the different interpretations of Quantum mechanics lead to radically different and fundamentally incompatible answers to the problem. The second strategy is to try to caracterize this irreducibility “directly”, via a proof of the impossibility of a hidden-variable extension of the statistical formalism of the theory. This strategy culminates with Bell’s theorem which indeed establishes the impossibility of constructing “Iocal” theories of hidden variables. This impossibility result, however, fails to provide us with a satisfying interpretation of the quantum irreductibility, rather, it merely shows how far we are from a solution to the problem

RESUMEN: Una tendencia importante en la filosofía de la educación contemporánea toma de la sociología del conocimiento la manera de entender la naturaleza del conocimiento científico. Esta tendencia parte de una crítica al "cognitivismo" individualista, asociado con una concepción tradicional del conocimiento y defiende una posición consensualista según la cual el conocimiento es la búsqueda de consenso. El objetivo del trabajo es mostrar que los consensualistas asumen una falsa dicotomía. Contrario a lo que los consensualistas asumen la cognición puede entenderse a la vez como un logro social y como el resultado del ejercicio de capacidades individuals. Concluyo haciendo ver algunas consecuencias del abandono de esa dicotomía para entenderel papel de la autoridad en la educación.ABSTRACT: An important trend in contemporary philosophy of education follows a view of knowledge promoted by sociologists of knowledge. According to this view a critique of the cognitive individualism implicit in the traditional account of knowledge leads to "consensualism ", the view that knowledge is the search for consensus. The aim of this paper is to show that the consensualists assume a false dichotomy. Cognition can be understood both as a social achievement and as the display of individual capacities. I conclude by exploring some consequences of the abandoning of this dichotomy for our understanding of the role of authority in education.

En este texto se examina críticamente la teoría combinatoria de las representaciones científicas de Andoni Ibarra y Thomas Mormann. El núcleo de la crítica va dirigido a mostrar que una serie de estudios sobre la ciencia, que ellos mismos mencionan, sugiere que la clasificación en tipos de representaciones propuesta es problemática. Es más, esos mismos estudios muestran que por lo menos muchas representaciones tienen una dimensión histórica que parece imposible capturar por medio del tipo de formalismo propuesto. /// Ibarra and Mormann's combinatorial theory of scientific representations is subject to critical scrutiny. It is argued that the classification of types of representations offered cannot serve as a basis for an analysis of the variety of representations that happen to arise in science. Empirical studies on ways of representing used in science strongly suggest that a formal theory of representations of the kind proposed is not able to capture the historical dimension of the structure of representations.

There are (at least) two ways to think of the differences in basic concepts and typologies that one can find in the different scientific practices that constitute a research tradition. One is the fundamentalist view: the fewer the better. The other is a non-fundamentalist view of science whereby the integration of different concepts into the right abstraction grounds an explanation that is not grounded as the sum of the explanations supported by the parts. Integrative concepts are often associated with idealizations that can successfully set the stage for different phenomena to be compared or for explanations of different phenomena to be considered as jointly increasing our understanding of reality beyond that which each explanation provides separately. In this paper, our aim is to argue for the importance of the notions of an ?affordance? and ?scaffolding? as integrative concepts in the cognitive sciences. The integrational role of the concept of affordance is closely related with the capacity of affordances to generate the scaffoldings leading to the integration. The capacities of affordances that turn them into (stable) scaffoldings explain why such notions are often used interchangeably (as we shall see). On this basis, we aim to show that the concepts of affordance and scaffolding provide the sort of epistemic perspective that can overcome common complaints about the limits and unity of the cognitive sciences once claims about extended cognition are taken seriously

RESUMEN: Una tendencia importante en la filosofía de la educación contemporánea toma de la sociología del conocimiento la manera de entender la naturaleza del conocimiento científico. Esta tendencia parte de una crítica al "cognitivismo" individualista, asociado con una concepción tradicional del conocimiento y defiende una posición consensualista según la cual el conocimiento es la búsqueda de consenso. El objetivo del trabajo es mostrar que los consensualistas asumen una falsa dicotomía. Contrario a lo que los consensualistas asumen la cognición puede entenderse a la vez como un logro social y como el resultado del ejercicio de capacidades individuals. Concluyo haciendo ver algunas consecuencias del abandono de esa dicotomía para entenderel papel de la autoridad en la educación.ABSTRACT: An important trend in contemporary philosophy of education follows a view of knowledge promoted by sociologists of knowledge. According to this view a critique of the cognitive individualism implicit in the traditional account of knowledge leads to "consensualism ", the view that knowledge is the search for consensus. The aim of this paper is to show that the consensualists assume a false dichotomy. Cognition can be understood both as a social achievement and as the display of individual capacities. I conclude by exploring some consequences of the abandoning of this dichotomy for our understanding of the role of authority in education.