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.

We state and comment our recent results on the incompleteness of elementary real analysis and their relevance for the axiomatized sciences.

Current mathematical models are notoriously unreliable in describing the time evolution of unexpected social phenomena, from financial crashes to revolution. Can such events be forecast? Can we compute probabilities about them? Can we model them? This book investigates and attempts to answer these questions through GOdel's two incompleteness theorems, and in doing so demonstrates how influential GOdel is in modern logical and mathematical thinking. Many mathematical models are applied to economics and social theory, while GOdel's theorems are able to predict (...) their limitations for more accurate analysis and understanding of national and international events. This unique discussion is written for graduate level mathematicians applying their research to the social sciences, including economics, social studies and philosophy, and also for formal logicians and philosophers of science. (shrink)

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.

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

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 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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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.

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.

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 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.

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)

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 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 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 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 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.

‘My name is Ephraïm Naana, I have already told you on one of these many occasions when you have come here before closing time to speak about my school. In my village, since you ask me, there are not all the things which are to be found on the market here, there are only those which grow there: mangoes, potatoes, maize, bananas, papayas. And my primary school teacher told me that in other places there might be even fewer things; he (...) said that in the market in Khartoum, in Sudan, the nation is vast but on the stalls there are only onions and white and red beans; and even though they were nicely arranged in piles, they were still only white beans, red beans and onions; and then he said that the world was big and that the hunger we experienced was not the worst of famines. (shrink)

. Introductory Remarks THEODOSIUS DOBZHANSKY The problems of reduction in biology are currently of considerable theoretical interest and practical ...

Partindo de dois modelos clássicos que fundamentaram a emergência do conceito do que entendemos hoje enquanto cidade, a polis e a civitas, este texto busca compreender e questionar a cidade contemporânea em sua condição metropolitana, marcada por políticas de imobilidade e sufocamento que demandam uma intensa produção de subjetividades. Trazendo pensadores dos campos da filosofia e da política como Giorgio Agamben, Massimo Cacciari e Vinícius NicastroHonesko, entre outros, nos propomos a pensar outras chaves de relações para o que denominamos cidade, (...) que sejam capazes de produzir modos de habitá-la para além da metrópole. Uma cidade outra, espaço de composição e transposição de mundos que não se encerre em si mesma; uma cidade ainda por vir.Palavras-chave: Cidade. Metrópole. Mundo. Política. Habitar. (shrink)

Should the philosophy of biology deal with organismic, or with molecular aspects , or with both ? We are, of course, not the first to appreciate the ...

Preference orderings assigned by coherent lower and upper conditional previsions are defined and they are considered to define maximal random variables and Bayes random variables. Sufficient conditions are given such that a random variable is maximal if and only if it is a Bayes random variable. In a metric space preference orderings represented by coherent lower and upper conditional previsions defined by Hausdorff inner and outer measures are given.

The moral enhancement of human beings is a constant theme in the history of humanity. Today, faced with the threats of a new, globalised world, concern over this matter is more pressing. For this reason, the use of biotechnology to make human beings more moral has been considered. However, this approach is dangerous and very controversial. The purpose of this article is to argue that the use of another new technology, AI, would be preferable to achieve this goal. Whilst several (...) proposals have been made on how to use AI for moral enhancement, we present an alternative that we argue to be superior to other proposals that have been developed. (shrink)

This article discusses some of the claims of the earlier and later versions of the Contemporary Theory of Metaphor (CTM) and addresses some of the criticism that has been leveled against it. It is argued that much of this criticism arises from common misconceptions as to the real claims made by the theory. However, CTM is still in need of further exploration and empirical support. In this connection, we identify some areas where research is still needed and supply our own (...) developments. We argue for a more complex classification of metaphor types, which takes into account various complementary taxonomic perspectives, including the nature of source and target and the genericity and complexity of the metaphoric operation. We also explore metaphor in relation to cognitive prominence and conceptual interaction issues. Finally, we deal with the problem of constraints on metaphor and make a proposal for three complementary kinds of constraint. (shrink)

Bravo, F. La dialéctica en Teilhard de Chardin.--Carías, R. El conocimiento de Dios en Max Scheler.--Cappelletti, A. J. El fuego y el logos en la filosofía de Heráclito.--Li Carrillo, V. Estructuralismo y antihumanismo.--Rosales, A. Martín Heidegger y la crisis de la filosofía transcendental.--Rosales, A. La crítica de Heidegger al idealismo moderno.--Rosales, A. El giro del pensamiento de Heidegger.

Can Artificial Intelligence be more effective than human instruction for the moral enhancement of people? The author argues that it only would be if the use of this technology were aimed at increasing the individual's capacity to reflectively decide for themselves, rather than at directly influencing behaviour. To support this, it is shown how a disregard for personal autonomy, in particular, invalidates the main proposals for applying new technologies, both biomedical and AI-based, to moral enhancement. As an alternative to these (...) proposals, this article proposes a virtual assistant that, through dialogue, neutrality and virtual reality technologies, can teach users to make better moral decisions on their own. The author concludes that, as long as certain precautions are taken in its design, such an assistant could do this better than a human instructor adopting the same educational methodology. (shrink)