This thesis is devoted to the exploration of the complexity of some mathematical problems using the framework of computable analysis and descriptive set theory. We will especially focus on Weihrauch reducibility as a means to compare the uniform computational strength of problems. After a short introduction of the relevant background notions, we investigate the uniform computational content of problems arising from theorems that lie at the higher levels of the reverse mathematics hierarchy.We first analyze the strength of the open and (...) clopen Ramsey theorems. Since there is not a canonical way to phrase these theorems as multi-valued functions, we identify eight different multi-valued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility.We then discuss some new operators on multi-valued functions and study their algebraic properties and the relations with other previously studied operators on problems. In particular, we study the first-order part and the deterministic part of a problem f, capturing the Weihrauch degree of the strongest multi-valued problem that is reducible to f and that, respectively, has codomain $\mathbb {N}$ or is single-valued.These notions proved to be extremely useful when exploring the Weihrauch degree of the problem $\mathsf {DS}$ of computing descending sequences in ill-founded linear orders. They allow us to show that $\mathsf {DS}$, and the Weihrauch equivalent problem $\mathsf {BS}$ of finding bad sequences through non-well quasi-orders, while being very “hard” to solve, are rather weak in terms of uniform computational strength. We then generalize $\mathsf {DS}$ and $\mathsf {BS}$ by considering $\boldsymbol {\Gamma }$ -presented orders, where $\boldsymbol {\Gamma }$ is a Borel pointclass or $\boldsymbol {\Delta }^1_1$, $\boldsymbol {\Sigma }^1_1$, $\boldsymbol {\Pi }^1_1$. We study the obtained $\mathsf {DS}$ -hierarchy and $\mathsf {BS}$ -hierarchy of problems in comparison with the Baire hierarchy and show that they do not collapse at any finite level.Finally, we work in the context of geometric measure theory and we focus on the characterization, from the point of view of descriptive set theory, of some conditions involving the notions of Hausdorff/Fourier dimension and Salem sets. We first work in the hyperspace $\mathbf {K}$ of compact subsets of $[0,1]$ and show that the closed Salem sets form a $\boldsymbol {\Pi }^0_3$ -complete family. This is done by characterizing the complexity of the family of sets having sufficiently large Hausdorff or Fourier dimension. We also show that the complexity does not change if we increase the dimension of the ambient space and work in $\mathbf {K}$. We also generalize the results by relaxing the compactness of the ambient space and show that the closed Salem sets are still $\boldsymbol {\Pi }^0_3$ -complete when we endow $\mathbf {F}$ with the Fell topology. A similar result holds also for the Vietoris topology.We conclude by analyzing the same notions from the point of view of effective descriptive set theory and Type-2 Theory of Effectivity, and show that the complexities remain the same also in the lightface case. In particular, we show that the family of all the closed Salem sets is $\Pi ^0_3$ -complete. We furthermore characterize the Weihrauch degree of the functions computing Hausdorff and Fourier dimension of closed sets.prepared by Manlio Valenti.E-mail:[email protected]. (shrink)

Inhaltsverzeichnis/Table of Contents:IntroductionAntónio ZILHÃO: Folk-Psychology, Rationality and Human ActionJoão BRANQUINHO: The Problem of Cognitive DynamicsJ.P. MONTEIRO: Hume, Induction and Single ExperimentsMarco RUFFINO: The Primacy of Concepts and the Priority of Judgments in Frege's LogicJoão Vergílio Gallerani CUTER: Die unanwendbare Arithmetik des TractatusSílvio PINTO: Wittgenstein's Anti-PlatonismFernando FERREIRA: A Substitutional Framework for Arithmetical ValidityJ.R. CROCA & R.N. MOREIRA: Indeterminism Versus CausalismLuíz MONIZ PEREIRA: The Logical Impingement of Artifical Intelligence.

INCONTINENCE, HONOURING SUNK COSTS AND RATIONALITY According to a basic principle of rationality, the decision to engage in a course of action should be determined solely by the analysis of its consequences. Thus, considerations associated with previous use of resources should have no bearing on an agent’s decision-making process. Frequently, however, agents persist carrying on an activity they themselves judge to be nonoptimal under the circumstances because they have already allocated resources to that activity. When this is the case, agents (...) are said to be honouring sunk costs. Honouring sunk costs is thus typically viewed as irrational economic behaviour. Two striking findings of the psychological literature on the sunk cost effect are that it is, in general, not lessened by having taken previously courses in economics, and that agents who did take such courses and that do honour sunk costs seem to be frequently aware of a cognitive dissonance in their behaviour. Davidson’s account of the possibility conditions of incontinent action renders continent action materially unfeasible. The very idea of incontinent action becomes thus a hollow one. I’ll present an alternative description of these possibility conditions that renders continent action materially feasible, and both, continent and incontinent action, cognitively plausible. In a nutshell, my proposal rests upon the drawing of an essential cognitive contrast between explicit processes of deliberative reasoning and lower level heuristic procedures. I conclude the paper arguing that my redescription of incontinent action accounts for the above mentioned cognitive dissonance effect better than the alternatives and that viewing at least an important subset of behaviours of honouring sunk costs as incontinent actions will enable us to consider them as peculiar manifestations of a more general and meaningful pattern in human behaviour. (shrink)

The aim of this article is to identify the main factors of the current crisis of the nation-state and to demonstrate how many of the voids left by this crisis are filled by religions. The main characteristic of the nation-state is the principle of sovereignty. The apogee of the nation-state is the political form of industrialization. National identity is possible only when the state proves to its citizens that the fact of being a member of it carries benefits and privileges (...) and will always bring more. Today, the majority of nation-states, in particular the oldest great powers, no longer have this capability. The weakening of the nation-state began at the end of the 19th century. The first wave of globalization multiplied the cases of reciprocal interferences and trespassed on the theoretical impermeability of the sovereign states. The outcome of the First World War, with the creation of the first supranational body, and much more the outcome of the Second World War, were two important steps of this crisis. The birth of the United Nations, and of other supranational bodies, as well as the creation of the first court called to judge an entire political class, were an assault on the principle of sovereignty. The second wave of globalization, characterized by the free circulation of goods, money, people and cultures, did the rest. Moreover, the countries that ‘invented’ the principle of sovereignty are today in relative decline as new powers are emerging. The nation-state is no longer able to keep its promises. The less effective states become at offering their citizens both meaning and social services, the more do religions tend to reoccupy the public stage. The less national and political legitimacy they have, the more powers use the religious tool against one another. (shrink)

Nel nostro mondo occidentale e urbanizzato i bambini subiscono forme di segregazione e controllo, al pari di altre categorie sociali altrettanto ‘scomode', perché ostacolano il cosiddetto ‘ordine morale del profitto e del consumo'. La casa, la scuola, i luoghi strutturati e sorvegliati delle attivitÀ del tempo libero, vengono presentati come il rifugio contro i pericoli della strada che č perciň interdetta ai bambini con ogni mezzo, compreso il coprifuoco. Ma la libera fruizione di uno spazio pubblico fatto di strade, piazze, (...) slarghi, aree vuote e marginali, č invece fondamentale per lo sviluppo delle capacitÀ sociali dei bambini. Uno dei tre principi della Carta ONU dei Diritti dell'infanzia, quello alla partecipazione e all'autonomia, č violato. (shrink)

Inquieta anche il fatto che i nuovi giardini tendano ad assomigliare in modo impressionante a quei “rendering”, anch’essi uno standard, che si trovano esposti nelle vetrine delle sempre più numerose agenzie immobiliari che impestano la periferia diffusa. Ne avevo una vicino a casa qualche trasloco fa, quando abitavo in un appartamento di due stanze con bagno nel quartiere di Santa Lucia.Vitaliano Trevisan, Tristissimi giardini, pp. 46-47 Dopo la mela biblica consumata in un giardino terrestre...

Inquieta anche il fatto che i nuovi giardini tendano ad assomigliare in modo impressionante a quei “rendering”, anch’essi uno standard, che si trovano esposti nelle vetrine delle sempre più numerose agenzie immobiliari che impestano la periferia diffusa. Ne avevo una vicino a casa qualche trasloco fa, quando abitavo in un appartamento di due stanze con bagno nel quartiere di Santa Lucia.Vitaliano Trevisan, Tristissimi giardini, pp. 46-47 Dopo la mela biblica consumata in un giardino terrestre...

Una prima parte del saggio sintetizza le linee principali di un recente libro dell’autore: Per un paradigma del corpo: una rifondazione filosofica dell’ecologia, Quodlibet, Macerata, 2019. Viene sostenuto un paradigma in cui corpo e biologia mantengano la loro irriducibilità nei confronti della cultura e in cui il cosiddetto “linguistic turn”, che ha dominato la filosofia del XX secolo, viene fortemente criticato; in coerenza con questo, la riflessione di Merleau-Ponty sul concetto di natura viene considerata lo strumento più adeguato e più (...) attuale per ripensare la questione ecologica; ne vengono esaminate le conseguenze nel campo della filosofia della tecnologia e del problema del soggetto. Una seconda parte del saggio, che si concentra sull’incontro che ebbe luogo nel 1961 fra Adorno e Merleau-Ponty, cerca di abbozzare un paradigma materialistico per l’ecologia, correggendo l’avvicinamento che alla fine della sua vita vi fu fra Merleau-Ponty e Heidegger. (shrink)

The emergence of ecology as a fundamental horizon not only of politics, but also of contemporary philosophy, pushes us to rethink the relationship that currents of thought such as Kuturkritik and phenomenology, especially the phenomenology of Maurice Merleau-Ponty, can maintain with it. After a preliminary consideration of post-structuralist and postmodern positions from this perspective, the essay focuses on the French philosopher, and in particular on his courses on Nature and on his elaboration of the Husserlian concept of Stiftung. This results (...) in Merleau-Ponty’s original position on the Kultur – Civilization alternative: critique of unlimited productivism, respect for the environment, and, at the same time, defense of the variety of cultures and traditions from a homogenizing globalization are valuable tools that his philosophy offers to the debates of our time. (shrink)

Caro leitor! Em busca de sempre mais apresentar reflexões consistentes e relevantes para o pensar teológico, em conexão com o mundo e às urgências da Igreja, a presente edição trás importantes temas que ajudam refletir a realidade humana à luz do mistério de Deus. Por isso, os artigos oferecidos nas mais variadas áreas, a saber: bíblico-teológica, dogmática, moral, pastoral, antropologia teológica, filosofia e eclesiologia, dão suporte científico e metodológico para a reflexão teológica. Antes de conferir as novidades desta edição, gostaria (...) de comunicar que esta Revista Eletrônica conquistou um espaço ainda maior de publicação, ao tornar-se indexada na base de dados do Directory of Open Access Journals (DOAJ). (shrink)

This article aims to propose some connections between the conceptions of poetry of the Mexican poet Octavio Paz and the German philosopher Martin Heidegger. Both see in poetry the element of recognition of the original condition of the human being, not as an interpretation, but as a perception and affectation of the existential reality of human beings. So that the event of the "poetic saying" is configured as a call to the possibility of glimpsing the being of each entity, inhabiting (...) oneself and, thus, learning to be with others, establishing the poetic field as the clearing of perception and of existential affectation. Poetic speech goes beyond the limits of language, creating and establishing meanings and representations to the affectations that poetry provides. Thus, through poetry man recognizes himself in his worldliness, in search of his own being and in his relationship with other beings. (shrink)

Columbia University Press's multivolume _Prison Notebooks_ is the only complete critical edition of Antonio Gramsci's seminal writings in English. Based on the authoritative Italian edition of Gramsci's work, _Quaderni del Carcere_, this comprehensive translation presents the intellectual as he ought to be read and understood, with critical notes that clarify Gramsci's history, culture, and sources; an index of names; and a contextualization of the thinker's ideas against his earlier writings and letters. This set includes notebooks 1 through 8 with (...) all attendant notes and materials and is an indispensible resource for scholars in the humanities and social sciences. (shrink)