We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

We conjecture that the existence of some fast-growing functions implies in a simple way the existence of some inaccessible cardinals. This note expands some previous work by the second author.

We expose the main ideas, concepts and results about Jakowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

Maps and territory suggest problems which have to do with the opening of pathways in some poorly explored domain.

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.

We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.

We give a overview of the main areas in theoretical physics, with emphasis on their relation to Lagrangian formalism in classical mechanics. This review covers classical mechanics; the road from classical mechanics to Schrodinger's quantum mechanics; electromagnetism, special and general relativity, and (very briefly) gauge field theory and the Higgs mechanism. We shun mathematical rigor in favor of a straightforward presentation.

We give a overview of the main areas in theoretical physics, with emphasis on their relation to Lagrangian formalism in classical mechanics. This review covers classical mechanics; the road from classical mechanics to Schrödinger’s quantum mechanics; electromagnetism, special and general relativity, and gauge field theory and the Higgs mechanism. We shun mathematical rigor in favor of a straightforward presentation.

Esta coletânea é uma homenagem aos 70 anos do professor Emmanuel Carneiro Leão. Reúne artigos de seus alunos, amigos e admiradores que foram atraídos pela abrangência e rigor de seu pensamento. A diversidade de temáticas, abordagens e premissas destes ensaios refletem bem a generosidade do espírito de Emmanuel Carneiro.

In 1962 Tibor Radó uncovered a monster hiding in the midst of innocent-looking Turing machines.

We show that the P 2 0 sentence, and explore some of theconsequences of that fact. This paper summarizes recent workby the author with N. C. A. da Costa on the P

Truth in Philosophy of Language

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Out of a folklore–like fact about the counterexample function to P=NP, a function which grows about as fast as the Busy Beaver function, we review the consequences of our exotic formalization for P=NP and then speculate about possible ways to extend our work.

We discuss Kunen’s algorithmic implementation of a proof for the Paris–Harrington theorem, and the author’s and da Costa’s proposed “exotic” formulation for the P = NP hypothesis. Out of those two examples we ponder the relation between mathematics within an axiomatic framework, and intuitive or informal mathematics.

This volume presents essays by pioneering thinkers including Tyler Burge, Gregory Chaitin, Daniel Dennett, Barry Mazur, Nicholas Humphrey, John Searle and Ian Stewart. Together they illuminate the Map/Territory Distinction that underlies at the foundation of the scientific method, thought and the very reality itself. It is imperative to distinguish Map from the Territory while analyzing any subject but we often mistake map for the territory. Meaning for the Reference. Computational tool for what it computes. Representations are handy and tempting that (...) we often end up committing the category error of over-marrying the representation with what is represented, so much so that the distinction between the former and the latter is lost. This error that has its roots in the pedagogy often generates a plethora of paradoxes/confusions which hinder the proper understanding of the subject. What are wave functions? Fields? Forces? Numbers? Sets? Classes? Operators? Functions? Alphabets and Sentences? Are they a part of our map? Or do they actually belong to the territory? Researcher, like a cartographer, clothes the reality by stitching multitudes of maps that simultaneously co-exist. A simple apple, for example, can be analyzed from several viewpoints beginning with evolution and biology, all the way down its microscopic quantum mechanical components. Is there a reality out there apart from these maps? How do these various maps interact/intermingle with each other to produce a coherent reality that we interact with? Or do they not? Does our brain uses its own internal maps to facilitate “physicist/mathematician” in us to construct the maps about the external territories in turn? If so, what is the nature of these internal maps? Are there meta-maps? Evolution definitely fences our perception and thereby our ability to construct maps, revealing to us only those aspects beneficial for our survival. But the question is, to what extent? Is there a way out of the metaphorical Platonic cave erected around us by the nature? While “Map is not the territory” as Alfred Korzybski remarked, join us in this journey to know more, while we inquire on the nature and the reality of the maps which try to map the reality out there. The book also includes a foreword by Sir Roger Penrose and an afterword by Dagfinn Follesdal. (shrink)

Este ensayo es consecuencia de las reflexiones que desde hace años realizamos en el Instituto de Paz y Conflictos de la Universidad de Granada y que nos ha obligado a hacer una deconstrucción crítica de algunos aspectos del pensamiento pacifista. Bien es cierto que la supervivencia de la especie ha sido posible porque la respuesta a la conflictividad ha sido, mayoritariamente, la búsqueda de equilibrios dinámicos y de armonía. Pero, a pesar de todo, perviven muchas grietas, rupturas, dadas por la (...) propia contingencia y fragilidad humanas. Estamos ante unos entes humanos fragmentados, violentados, lo que hace más difícil la búsqueda de la armonía o la paz. Estas dificultades son razones de peso para trabajar en el camino de una «desfragmentación» ontológica que sea útil para liberar nuestras fuerzas emancipadoras y creativas. Construir la visión integrada y unitaria de la Ciencia de los Seres Humanos es una tarea conjunta que interesa sobremanera a la Investigación para la Paz.This essay is a consequence of the reflections we have been conducting for several years at the Instituto de Paz y Conflictos of the University of Granada. These reflections have obliged us to undertake a critical deconstruction of a few aspects of pacifist thought. Although the survival of the species has been possible because the response to conflicts has been, principally, the search for dynamic equilibrium and harmony; on the other hand there remain many fissures, ruptures brought about by the own human contingency and fragility. We find ourselves before a fragmented and distorted human being, which makes the search for harmony or peace even more difficult. These difficulties are convincing reasons for working towards an ontological “defragmentation” which is useful to liberate our emancipating and creative forces. To build the integrated and united view of Human Sciences is a collective task which is of great interest for Peace Research. (shrink)

We propose a formalization of Meinong's theory of objects with the help of Hilbert's $\epsilon$-symbol and a paraconsistent logical system, with an eye towards its application in an axiomatization of the natural sciences.

We first show that a theorem by Cartan that generalizes the Frobenius integrability theorem allows us (given certain conditions) to obtain noncurvature solutions for the differential Bianchi conditions and for higher-degree similar relations. We then prove that there is no algorithmic procedure to determine, for a reasonable restricted algebra of functions on spacetime, whether a given connection form satisfies the preceding conditions. A parallel result gives a version of Gödel's first incompleteness theorem within an (axiomatized) theory of gauge fields.

I. WINCHESTER and K. BLACKWELL (eds.), Antinomies and paradoxes. Studies in Russell's early philosophy. Hamilton, Ontario: McMaster University Library Press, 1989. 248 pp. No price stated.

Traces the development of British philosopher Russell's (1872-1970) ideas on mathematics from the 1890s to the publication of his Principles of mathematics in 1903. Draws from Russell's unpublished manuscripts, correspondence, and published works to point out the influence of Hegel, Cantor, Whitehead, Peano, and others. No index. Annotation copyrighted by Book News, Inc., Portland, OR.

The main thesis of this paper is that some of the most important ideas and symbolic devices that made Russell's theory of descriptions possible were already present in writings by Frege and especially Peano that Russell knew well. The paper contains a detailed comparison between the relevant parts of Russell's theory--including manuscripts recently published--and some of Frege and Peano's insights, as well as a discussion of numerous possible objections that could be posed to the main claim. Even if Russell was (...) not actually influenced by those insights, the parallelism is close enough to be worth analyzing, especially in the case of Peano, whose writings are not very well known. (shrink)