Hemeroteca de la sección ‘Ambiente’

Decoherence, quantum Darwinism, and the generic emergence of our objective classical reality

Por • 8 dic, 2018 • Category: Ambiente

In this article I aim to provide an intuitive and non-technical introduction to decoherence and quantum Darwinism. Together these theories explain how our classical reality emerges from an underlying quantum mechanical description. Here I focus on two aspects of this and explain, firstly, how decoherence can tell us why we never see macroscopic superpositions, such as dead-and-alive cats, in our classical surroundings; and secondly I describe and then provide a resolution to the so-called preferred basis problem. I then introduce recent results demonstrating that certain aspects of classicality are generic phenomena that emerge from the basic mathematical structure of quantum mechanics. This is in stark contrast to previous work in this field that focused on specific models that cannot realistically be scaled up to explicitly answer questions about the macroscopic world. Finally, I demonstrate how decoherence and quantum Darwinism can shed significant light on the measurement problem, and I discuss the implications for how we should interpret quantum mechanics.

Posibilidades de generalización de las lógicas cuánticas

Por • 3 dic, 2018 • Category: Ambiente

En un trabajo anterior (Crítica, IX (1977), n? 27, p. 49) dimos algunas evidencias en favor de la siguiente tesis: el valor epistemológico de las lógicas cuánticas reside en considerarlas como teorías (o, por abuso de lenguaje, como modelos para teorías), más que como cálculos lógicos propiamente dichos. Los cálculos lógico-cuánticos de proposiciones (p.e., Kalmbach [9]) o de predicados de primer orden [p.e., Dishkant [3]), tienen un interés intrínseco propio para el especialista en lógicas no clásicas, pero lo que da significado metodológico a las familias de estructuras llamadas “lógicas” cuánticas es su carácter modelístico, el cual está fundamentado en (y es analizado con ayuda de) la lógica habitual

On Hegel’s Critique of the Noumenal in Kant

Por • 17 nov, 2018 • Category: Ambiente

Damien Booth’s article “Hegel’s Philosophy of Physics and Kant’s Noumena” addresses Hegel’s critique of Kant concerning the positing of the noumena, the realm beyond the sensible, which for Hegel results in entanglements and contradiction, Kantian antinomies that the dialectic could resolve. While the article appears to be an exposition of the contradiction of Kant’s noumena and its critique in Hegel, Booth turns to Adorno and Heidegger to accentuate the relevance of Kant’s modern project of philosophy and Hegel’s critique.

Realism about the Wave Function

Por • 10 nov, 2018 • Category: Ambiente

A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review and compare several realist interpretations of the wave function. They fall into three categories: ontological interpretations, nomological interpretations, and the emph{sui generis} interpretation. For simplicity, I will focus on non-relativistic quantum mechanics.

Probability Logic: A Model Theoretic Perspective

Por • 1 nov, 2018 • Category: Ambiente

In this paper (propositional) probability logic (PL) is investigated from model theoretic point of view. First of all, the ultraproduct construction is adapted for σ-additive probability models, and subsequently when this class of models is considered it is shown that the compactness property holds with respect to a fragment of PL called basic probability logic (BPL). On the other hand, when dealing with finitely-additive probability models, one may extend the compactness property for a larger fragment of probability logic, namely positive probability logic (PPL).

Pruebas entimemáticas y pruebas canónicas en la geometría plana de Euclides

Por • 30 oct, 2018 • Category: Ambiente

Dado que la aplicación del Postulado I.2 no es uniforme en Elementos, ¿de qué manera debería ser aplicado en la geometría plana de Euclides? Además de legitimar la pregunta misma desde la perspectiva de una filosofía de la práctica matemática, nos proponemos esbozar una perspectiva general de análisis conceptual de textos matemáticos que involucra una noción ampliada de la teoría matemática como sistema de autorizaciones o potestades y una noción de prueba que depende del auditorio.

A survey of paraconsistent logics

Por • 12 oct, 2018 • Category: Ambiente

A survey of paraconsistent logics that are prominent representatives of the different approaches that have been followed to develop paraconsistent logics is provided. The paraconsistent logics that will be discussed are an enrichment of Priest’s logic LP, the logic RM3 from the school of relevance logic, da Costa’s logics Cn, Jaskowski’s logic D2, and Subrahmanian’s logics Ptau. A deontic logic based on the first of these logics will be discussed as well. Moreover, some proposed adaptations of the AGM theory of belief revision to paraconsistent logics will be mentioned.

Topological order and Emergence

Por • 28 sep, 2018 • Category: Ambiente

Topologically ordered systems play a prominent role in current research in condensed matter physics; examples include systems that exhibit the quantum Hall effect, topological insulators, and topological superconductors. These systems possess properties that are characterized by topological invariants, exhibit phase transitions that cannot be characterized by spontaneous symmetry breaking, and exhibit order that cannot be characterized in terms of a local order parameter. They thus fall outside the scope of the Landau–Ginsburg theory of phase transitions, which, arguably, has informed much of the discussion, in both the physics and philosophy literature, of emergence in condensed matter systems. Nevertheless, some authors have claimed that topologically ordered systems exhibit emergence.

Infinitary propositional relevant languages with absurdity

Por • 25 sep, 2018 • Category: Ambiente

Analogues of Scott’s isomorphism theorem, Karp’s theorem as well as results on lack of compactness and strong completeness are established for infinitary propositional relevant logics. An “interpolation theorem” (of a particular sort introduced by Barwise and van Benthem) for the infinitary quantificational boolean logic L∞ω holds. This yields a preservation result characterizing the expressive power of infinitary relevant languages with absurdity using the model-theoretic relation of relevant directed bisimulation as well as a Beth definability property.

A Brief Introduction to the Lambda Calculus

Por • 19 sep, 2018 • Category: Ambiente

When you first learned about functions, they were most likely introduced as abstractions of expressions. For example, consider the expression 2 + 3, which can be immediately evaluated by the rules of elementary arithmetic to give value 5. We can abstract, i.e., generalize the notion of “adding 3 to 2” to that of “adding 3 to something,” giving rise the function f : x 7→ x + 3. We can then apply this function to other arguments, e.g., f(4) = 4 + 3 = 7. This style of function definition is intentional—functions are defined by specifying an intended means of evaluation. Later, you may have been encouraged to think of functions extensionally, i.e., as sets of ordered pairs, e.g. f = {(x, y) : y = x + 3}. Such an approach conveys substantial metamathematical advantages, but it comes at a terrible cost—functions are no longer things that you can compute with. The lambda calculus [Chu41] returns to the notion of functions as abstractions of expressions. Abstraction is accomplished by the eponymous lambda (λ), by means of which we could define the function f as λx. x + 3. An abstraction may be applied to an argument,