This is a study of S. Kripke’s notion of fulfilment. Motivated by Paris-Harrington statement, Kripke was looking for a proof of Gödel’s Incompleteness Theorem which was model-theoretic, natural (without self-reference), and easy. Fulfilment gives a versatile tool for both Proof and Model Theory. We begin with short proofs to a number of classical results. With two new results: there is an easily definable subring R of the primitive recursive functions such that for any non-principal ultrafilter D on ω, R/D is a recursively saturated model of Peano arithmetic; and for any r.e. theory T and for any given r.e. set, we can feasibly find a Σ01 formula which semi-represents it in T. We then give a version of Herbrand’s Theorem, and of the Hilbert-Ackermann method of proving consistency

This article aims to develop a new account of scientific explanation for computer simulations. To this end, two questions are answered: what is the explanatory relation for computer simulations? and what kind of epistemic gain should be expected? For several reasons tailored to the benefits and needs of computer simulations, these questions are better answered within the unificationist model of scientific explanation. Unlike previous efforts in the literature, I submit that the explanatory relation is between the simulation model and the results of the simulation. I also argue that our epistemic gain goes beyond the unificationist account, encompassing a practical dimension as well.

The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the “shape of the universe.” More specifically, our aim is to consider, without a claim to completeness, the origin of Riemannian geometry, which is indispensable to the description of the space of the universe as a “generalized curved space.”

We study a dynamic game in which information arrives gradually as long as a principal funds research, and an agent takes an action in each period. In equilibrium, the principal’s patience is the key determinant of her information provision: the lower her discount rate, the more eagerly she funds. When she is sufficiently patient, her information provision and value function are well-approximated by the ‘Bayesian persuasion’ model. If the conflict of interest is purely belief-based and information is valuable, then she provides full information if she is patient.

The concept of the physical state of a system is ubiquitous in physics but is usually presented in terms of specific cases. For example, the state of a point particle of mass m is completely characterized by its position and momentum. There is a tendency to consider such states as “real”, i.e., as physical properties of a system. This rarely causes problems in classical physics but the notion of real quantum states has contributed mightily to the philosophical conundrums associated with quantum mechanics. The Einstein-Rosen-Podolsky paradox is a prime example. In fact, quantum states are not physical properties of a system but rather subjective descriptions that depend on the information available to a particular observer.

Compelling evidence against a heedless group theory generalization of pairwise comparisons elements is provided by means of counter-examples and mathematical reasoning. The lack of acceptable semantics for selected groups (with negative and complex numbers) and implications are analyzed. This study also provides examples and mathematical reasoning indicating why inconsistency indicators for pairwise comparisons require normalization. Methodological inconsistencies in using group theory for pairwise comparisons should be made public to the scientific community for further discussion and research.

A un pensar castrado, sin aristas, que no corre el riesgo del pensamiento libre sino que está condicionado por mil prejuicios y preconceptos que esta cultura mediática y sus pseudo pensadores nos imponen todos los días por los mass media. No puedo dejar de referirme a Heidegger y a aquello que leímos cientos de veces acerca de la existencia impropia en Ser y Tiempo (parágrafo 35): las habladurías, esto es, el hablar por hablar; la avidez de novedades y la ambigüedad. Tenemos que derrotar esa existencia impropia que nos quieren imponer y la mejor y única forma es pensando con cabeza propia y no con la de otro. Apoyándonos en nuestra tradición filosófica que es riquísima, con autores de primer nivel y de una enjundia poco común. También en investigadores, que los hay muy buenos, aunque son los menos. No hay que escamotear la realidad aun cuando no nos convenga, pues la realidad, como enseñaba el viejo Aristóteles, es un conflicto de potencia y acto. Y por eso, no es solo lo que es, sino también lo que puede ser.

The standard notion of formal theory, in Logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion by allowing one to take both assertions and denials on a par. This novel notion of theory is based on a bilateralist approach to consequence operators, which we hereby introduce, and whose main properties we investigate in the present paper.

Recently we proposed “quantum language” (or, “the linguistic Copenhagen interpretation of quantum mechanics”), which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes = Kant epistemology. We believe that quantum language is not only the scientific final goal of dualistic idealism but also the language in which science is written. Hence there is a reason to want to clarify, from the quantum linguistic point of view, the following problems: “brain in a vat argument”, “the Cogito proposition”, “five-minute hypothesis”, “only the present exists”, “Copernican revolution”, “McTaggart’s paradox”, and so on.

This article discusses some well-known historical developments in the theory of electronic and liquid structure. As topics in physical chemistry, they vacillate without warning between experimental facts and technical theoretical and mathematical details. The topics have been chosen specifically to highlight the debate between local structural and field theoretical models. Note that we have also presented the two topics in an idiosyncratic way to highlight their similarities. Both histories trace their roots to the Herapath/Maxwell/Boltzmann conception of a continuous density (or probability distribution) of discrete molecules, and stretch all the way to the present day, remaining lively research areas that are even in communication on several points.