Hemeroteca de la sección ‘Leyes’

Demolishing prejudices to get to the foundations

Por • 18 feb, 2018 • Category: Leyes

Commonly accepted views on foundations of science, either based on bottom-up construction or top-down reduction of fundamental entities are here rejected. We show how the current scientific methodology entails a certain kind of research for foundations of science, which are here regarded as insurmountable limitations. At the same time, this methodology allows to surpass the bounds classically accepted as fundamental, yet often based on mere “philosophical prejudices”. Practical examples are provided from quantum mechanics and biophysics.

Why Is There Something, Rather Than Nothing?

Por • 9 feb, 2018 • Category: Leyes

It seems natural to ask why the universe exists at all. Modern physics suggests that the universe can exist all by itself as a self-contained system, without anything external to create or sustain it. But there might not be an absolute answer to why it exists. I argue that any attempt to account for the existence of something rather than nothing must ultimately bottom out in a set of brute facts; the universe simply is, without ultimate cause or explanation.

The modal logic of arithmetic potentialism and the universal algorithm

Por • 5 feb, 2018 • Category: Leyes

Natural potentialist systems arise from the models of arithmetic when they are considered under their various natural extension concepts, such as end-extensions, arbitrary extension, Σ n -elementary extensions, conservative extensions and more. For these potentialist systems, I prove, a propositional modal assertion is valid in a model of arithmetic, with respect to assertions in the language of arithmetic with parameters, exactly when it is an assertion of S4. Meanwhile, with respect to sentences, the validities of a model are always between S4 and S5, and these bounds are sharp in that both endpoints are realized.

Higher Theory and the Three Problems of Physics

Por • 28 ene, 2018 • Category: Leyes

According to the Butterfield–Isham proposal, to understand quantum gravity we must revise the way we view the universe of mathematics. However, this paper demonstrates that the current elaborations of this programme neglect quantum interactions. The paper then introduces the Faddeev–Mickelsson anomaly which obstructs the renormalization of Yang–Mills theory, suggesting that to theorise on many-particle systems requires a many-topos view of mathematics itself: higher theory. As our main contribution, the topos theoretic framework is used to conceptualise the fact that there are principally three different quantisation problems, the differences of which have been ignored not just by topos physicists but by most philosophers of science. We further argue that if higher theory proves out to be necessary for understanding quantum gravity, its implications to philosophy will be foundational: higher theory challenges the propositional concept of truth and thus the very meaning of theorising in science.

Quantum Physics, Algorithmic Information Theory and the Riemanns Hypothesis

Por • 21 ene, 2018 • Category: Leyes

In the present work the Riemanns hypothesis (RH) is discussed from four different perspectives. In the first case, coherent states and the Stengers approximation to Riemann-zeta function are used to show that RH avoids an indeterminacy of the type 0/0 in the inner product of two coherent states. In the second case, the Hilber-Polya conjecture with a quantum circuit is considered. In the third case, randomness, entanglement and the Moebius function are used to discuss the RH. At last, in the fourth case, the RH is discussed by inverting the first derivative of the Chebyshev function. The results obtained reinforce the belief that the RH is true.

Relational Complexes

Por • 14 ene, 2018 • Category: Leyes

A theory of relations is presented that provides a detailed account of the logical structure of relational complexes. The theory draws a sharp distinction between relational complexes and relational states. A salient difference is that relational complexes belong to exactly one relation, whereas relational states may be shared by different relations. Relational complexes are conceived as structured perspectives on states ‘out there’ in reality. It is argued that only relational complexes have occurrences of objects, and that different complexes of the same relation may correspond to the same state.

Una revisión crítica de Dudas filosóficas. Ensayos sobre escepticismo antiguo, moderno y contemporáneo

Por • 9 ene, 2018 • Category: Leyes

El no filósofo parece, como dice Rossi, no dudar cuando se sienta en la silla o cuando declara que conversó con un amigo ayer en Coyoacán. Sería una arrogancia, dice Rossi, sostener la irrealidad de ese encuentro. Sin embargo, no han sido sólo los “no filósofos” los que se han mostrado reluctantes a las dudas, las cuales habría que espantar como a moscas molestas. Dudar de algunas cosas está prohibido incluso para los filósofos, no sólo para el “común de los mortales”. Un filósofo como Aristóteles (Ornelas y Cíntora 2013, p. 18) dijo alguna vez que sería una “falta de respeto” poner en duda el principio de no contradicción. Arrogancia, falta de respeto y petulancia parecen explicar también la ira del Dr. Samuel Johnson cuando, con el rostro y las ideas de Berkeley en su mente, dijo, pateando una piedra, ¡así lo refuto! Si la ira es una emoción, un concepto psicológico con contenido cognitivo, ¿estaría reflejando Johnson mediante su enojo la verdad inconmovible de un conjunto de creencias x tal que su puesta en cuestión resultaría de plano inadmisible?

On the Semantics of Intensionality and Intensional Recursion

Por • 1 ene, 2018 • Category: Leyes

Intensionality is a phenomenon that occurs in logic and computation. In the most general sense, a function is intensional if it operates at a level finer than (extensional) equality. This is a familiar setting for computer scientists, who often study different programs or processes that are interchangeable, i.e. extensionally equal, even though they are not implemented in the same way, so intensionally distinct. Concomitant with intensionality is the phenomenon of intensional recursion, which refers to the ability of a program to have access to its own code. In computability theory, intensional recursion is enabled by Kleene’s Second Recursion Theorem. This thesis is concerned with the crafting of a logical toolkit through which these phenomena can be studied. Our main contribution is a framework in which mathematical and computational constructions can be considered either extensionally, i.e. as abstract values, or intensionally, i.e. as fine-grained descriptions of their construction. Once this is achieved, it may be used to analyse intensional recursion.

Probabilistic Spacetimes

Por • 21 dic, 2017 • Category: Leyes

Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a generalization is a possible application in the context of some quantum gravity approaches, particularly those using the path integral. It is argued that this model might be used to describe simplified geometry, resulting e.g. from discretization, while keeping the continuous manifold; or it may be used as an effective description of a probabilistic geometry resulting from a full-fledged quantum gravity computation.

Ways of Space-Making — The Early History of Space-Forms from Clifford to Hopf

Por • 14 dic, 2017 • Category: Leyes

At a certain moment in the history of geometry in the 19th century the perplexity was great: The spaces of the traditional geometries (Euclidean of course, spherical and elliptic, hyperbolic) got some “Doppelgänger” – spaces that were very similar to them but with strange qualities. Therefore, two questions raised: How to distinguish between the“traditional” or “real” spaces and their “fictional” Doppelgänger? Can we be sure that we live in traditional Euclidean space and not in one of his Doppelgänger? During this Story mathematicians learned how to produce spaces – there are many ways of space making!