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.

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.

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.

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 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 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.

‘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)

I submit that epistemic progress in key areas of contemporary academic philosophy has been compromised by politically correct ideology. First, guided by an evolutionary account of ideology, results from social and cognitive psychology and formal philosophical methods, I expose evidence for political bias in contemporary Western academia and sketch a formalization for the contents of beliefs from the PC worldview taken to be of core importance, the theory of social oppression and the thesis of anthropological mental egalitarianism. Then, aided by (...) discussions from contemporary epistemology on epistemic values, I model the problem of epistemic appraisal using the frameworks of multi-objective optimization theory and multi-criteria decision analysis and apply it to politically correct philosophy. I conclude that philosophy guided by politically correct values is bound to produce constructs that are less truth-conducive and that spurious values which are ideologically motivated should be abandoned. Objections to my framework stemming from contextual empiricism, the feminine voice in ethics and political philosophy are considered. I conclude by prescribing the epistemic value of empirical adequacy, the contextual value of political diversity and the moral virtue of moral courage to reverse unwarranted trends in academic philosophy due to PC ideology. (shrink)

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.

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)

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.

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.

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.

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)

The main objective of this work is to understand the daily practices of user management in post-reformist devices in the Brazilian mental health field. Through Foucault's genealogical work on government practices, understood as forms of conducting the behavior of others, it is possible to open a possible field for the study of the practices of psi knowledge, considering them as forms of management that act by through the free and natural acts of individuals. More specifically, our goal is to examine (...) day-to-day practices on some reformist devices such as CAPS through user files. Basically, two driving models have been found in the new devices: 1) Cases with frank intervention of production of commitments and agreements with users, seeking the entry of this to varied activities and political leadership ; 2) Cases with little response from the user, in which the forms of conduction are implemented by policies of inclusion of family members and close reference characters in the management of the patient's life. (shrink)

We analyze N. C. A. da Costa and F. A. Doria’s “exotic formalization” of the conjecture P = NP [3–7]. For any standard axiomatic PA extension T and any number-theoretic sentence ${\varphi }$ , we let ${\varphi ^{\star} := \varphi \vee \lnot \mathsf{Con}\left( \mathsf{T}\right)}$ and prove the following “exotic” inferences 1–3. 1. ${\mathsf{T}+\varphi ^{\star}}$ is consistent, if so is T, 2. ${\mathsf{T}+\varphi}$ is consistent, provided that ${\mathsf{T}+\varphi ^{\star}}$ is ω-consistent, 3. ${\mathsf{T}+\varphi}$ is consistent, provided that T is consistent and (...) has the same provably total recursive functions as ${\mathsf{T}+\left( \varphi \leftrightarrow \varphi ^{\star }\right) }$ . Furthermore we show that 1–3 continue to hold for ${\varphi ^{\star} := \varphi _{S} :=\varphi \vee \lnot S}$ , where ${S=\forall x\exists yR\left( x,y\right)}$ is any ${\Pi _{2}^{0}}$ sentence satisfying: 4. ${\left( \forall n\in \omega \right) \left( \mathsf{T}\vdash S_{x}\left[ \underline{n}\right] \right) }$ , 5. ${\mathsf{Con}\left( \mathsf{T}\right) \Rightarrow \mathsf{T}\nvdash S}$ . We observe that if ${\varphi :=\left[ \mathsf{P}=\mathsf{NP}\right] }$ and ${S:= \left[\digamma total\right] }$ , where ${\digamma=\digamma _{\mathsf{T}}}$ is da Costa-Doria “exotic” function with respect to T, then 4, 5 are satisfied for most familiar (presumably) consistent T in question, while ${\varphi _{S}}$ becomes equivalent to da Costa-Doria “exotic formalization” ${\left[ \mathsf{P}=\mathsf{NP}\right]^{\digamma}}$ . Moreover, the corresponding “exotic” inferences 1–3 generalize analogous da Costa-Doria results. Hence these “exotic” inferences are universal for all number-theoretic sentences and not characteristic to the conjecture P = NP. Nor do they infer relative consistency of P = NP (see Conclusion 15 in the text). (shrink)

L'histoire des femmes depuis la Seconde Guerre mondiale est bien plus développée en Italie qu'en France. Le dernier ouvrage d'Anna Rossi-Doria nous en fournit une preuve supplémentaire. S'appuyant sur ses recherches personnelles, mais aussi sur une solide bibliographie, l'auteure s'interroge sur les multiples facettes du droit de vote féminin. Le décret qui institue le droit de vote féminin présente bien des similarités avec l'ordonnance française. Comme en France, celui-ci ne résulte..

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)