Hemeroteca de la sección ‘Leyes’

A Final Solution to the Mind-Body Problem by Quantum Language

Por • 17 ago, 2017 • Category: Leyes

Recently we proposed “quantum language”, which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes = Kant epistemology. And further we believe that quantum language is the only scientifically successful theory in dualistic idealism. If this turn is regarded as progress in the history of western philosophy (i.e., if “philosophical progress” is defined by “approaching to quantum language”), we should study the linguistic mind-body problem more than the epistemological mind-body problem. In this paper, we show that to solve the mind-body problem and to propose “measurement axiom” in quantum language are equivalent. Since our approach is always within dualistic idealism, we believe that our linguistic answer is the only true solution to the mind-body problema.

A mathematically derived theory of truth and its properties

Por • 3 ago, 2017 • Category: Leyes

Hannes Leitgeb formulated in his paper ‘What Theories of Truth Should be Like (but Cannot be) eight norms for theories of truth, and stated in p.8: “In the best of all (epistemically) possible worlds, some theory of truth would satisfy all of those norms at the same time. Unfortunately, we do not inhabit such a world.” In the present paper a theory of truth is derived mathematically. That theory is shown to satisfy well all those eight norms. Thus the choice over truth theories which don’t satisfy all those norms, or logic different from the classical one (cf., e.g., Section 2 of Leitgeb’s paper) seems not to be necessary. This makes the present trend to accept the choice over ‘alternative’ truths or facts less plausible.

The unreasonable power of the lifting property in elementary mathematics

Por • 28 jul, 2017 • Category: Leyes

We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing that many standard elementary notions of abstract topology can be defined by applying the lifting property to simple morphisms of finite topological spaces. Examples in topology include the notions of: compact, discrete, connected, and totally disconnected spaces, dense image, induced topology, and separation axioms. Examples in algebra include: finite groups being nilpotent, solvable, torsion-free, p-groups, and prime-to-p groups; injective and projective modules; injective, surjective, and split homomorphisms. We include some speculations on the wider significance of this.

Logic of gauge

Por • 16 jul, 2017 • Category: Leyes

The logic of gauge theory is considered by tracing its development from general relativity to Yang-Mills theory, through Weyl’s two gauge theories. A handful of elements—which for want of better terms can be called emph geometrical justice, emph matter wave, emph second clock effect, emph twice too many energy levels—are enough to produce Weyl’s second theory; and from there, all that’s needed to reach the Yang-Mills formalism is a emph non-Abelian structure group (say SU(N)).

A mathematical characterization of confidence as valid belief

Por • 5 jul, 2017 • Category: Leyes

Confidence is a fundamental concept in statistics, but there is a tendency to misinterpret it as probability. In this paper, I argue that an intuitively and mathematically more appropriate interpretation of confidence is through belief/plausibility functions, in particular, those that satisfy a certain validity property. Given their close connection with confidence, it is natural to ask how a valid belief/plausibility function can be constructed directly. The inferential model (IM) framework provides such a construction, and here I prove a complete-class theorem stating that, for every nominal confidence region, there exists a valid IM whose plausibility regions are contained by the given confidence region. This characterization has implications for statistics understanding and communication, and highlights the importance of belief functions and the IM framework.

Drowning by numbers: topology and physics in fluid dynamics

Por • 2 jul, 2017 • Category: Leyes

Since its very beginnings, topology has forged strong links with physics and the last Nobel prize in physics, awarded in 2016 to Thouless, Haldane and Kosterlitz ” for theoretical discoveries of topological phase transitions and topological phases of matter”, confirmed that these connections have been maintained up to contemporary physics. To give some (very) selected illustrations of what is, and still will be, a cross fertilization between topology and physics, hydrodynamics provides a natural domain through the common theme offered by the notion of vortex, relevant both in classical (S 2) and in quantum fluids (S 3). Before getting into the details, I will sketch in S 1 a general perspective from which this intertwining between topology and physics can be appreciated: the old dichotomy between discreteness and continuity, first dealing with antithetic thesis, eventually appears to be made of two complementary sides of a single coin.

Extracting Geometry from Quantum Spacetime: Obstacles down the road

Por • 29 jun, 2017 • Category: Leyes

Any acceptable quantum gravity theory must allow us to recover the classical spacetime in the appropriate limit. Moreover, the spacetime geometrical notions should be intrinsically tied to the behavior of the matter that probes them. We consider some difficulties that would be confronted in attempting such an enterprise. The problems we uncover seem to go beyond the technical level to the point of questioning the overall feasibility of the project. The main issue is related to the fact that, in the quantum theory, it is impossible to assign a trajectory to a physical object, and, on the other hand, according to the basic tenets of the geometrization of gravity, it is precisely the trajectories of free localized objects that define the spacetime geometry.

Equivalence-principle Analog of the Gravitational Redshift

Por • 24 jun, 2017 • Category: Leyes

What happens when two synchronized clocks on a rigid beam are both given the exact same acceleration profile? Will they remain synchronized? What if we use a rigid-rod Rindler acceleration profile? The special relativity prediction surprises many people. This experimental setup is the special-relativity analog of the gravitational redshift. Just like two clocks higher and lower in a gravitational field lose synchronization, one sees a loss of synchronization in these clocks with `identical’ acceleration profiles. To the best of our knowledge this equivalence principle analog has never been directly measured, and current experimental techniques are sensitive enough to measure it. We discuss the origin of the essential physics behind this synchronization loss, and some special conditions which simplify its experimental observation.

Making Metric Temporal Logic Rational

Por • 13 jun, 2017 • Category: Leyes

We study an extension of MTL in pointwise time with rational expression guarded modality RatI (re) where re is a rational expression over subformulae. We study the decidability and expressiveness of this extension called RatMTL, as well as its fragment SfrMTL where only star-free rational expressions are allowed. Using the technique of temporal projections, we show that RatMTL has decidable satisfiability by giving an equisatisfiable reduction to MTL. We also identify a subclass of RatMTL for which our equi-satisfiable reduction gives rise to formulae of MITL, yielding elementary decidability. As our second main result, we show a tight automaton-logic connection between SfrMTL and partially ordered (or very weak) 1-clock alternating timed autómata

Introduction to Lambda Calculus

Por • 30 may, 2017 • Category: Leyes

Introduction Some history Leibniz had as ideal the following. (1) Create a ‘universal language’ in which all possible problems can be stated. (2) Find a decision method to solve all the problems stated in the universal language. If one restricts oneself to mathematical problems, point (1) of Leibniz’ ideal is fulfilled by taking some form of set theory formulated in the language of first order predicate logic. This was the situation after Frege and Russell (or Zermelo). Point (2) of Leibniz’ ideal became an important philosophical question. ‘Can one solve all problems formulated in the universal language?’ It seems not, but it is not clear how to prove that. This question became known as the Entscheidungsproblem. In 1936 the Entscheidungsproblem was solved in the negative independently by Alonzo Church and Alan Turing. In order to do so, they needed a formalisation of the intuitive notion of ‘decidable’, or what is equivalent ‘computable’. Church and Turing did this in two different ways by introducing two models of computation.