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)

Il sansimonismo, sistema culturale della civiltà tecnologica, di A. Cattabiani.--Nota dell'Editore.--Introduzione.--Beniamino Constant.--I San-Simoniani.--Appendice: L'utopismo di Carlo Fourier.

On raconte qu'après la désignation comme Premier consul, Napoléon montra à des invités La Science de la législation de Gaetano Filangieri, le "jeune homme qui est notre maître à tous". Presque au même moment, ces volumes se trouvaient aussi sur le bureau de Benjamin Constant. La fortune et la circulation de cette oeuvre au sein de l'Europe des Lumières et du XIXe siècle sont l'objet de cet ouvrage, qui décrit les débats qu'elle a alimentés afin de comprendre pourquoi les hommes (...) de lettres et les politiques continuèrent à s'intéresser à ce classique de la pensée républicaine du XVIIIe siècle pour se fondre dans la nouvelle Europe du XIXe siècle."--Page 4 of cover. (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)

This selection of papers is concerned with the history of linguistics in Spain, dealing with the evolution of linguistic ideas from the Middle Ages and the European context of the linguistic debates in Spain to the 20th century, concluding with Malkiel's appraisal of Ramón Menéndez Pidal (1869-1968). The volume includes papers on Antonio Nebrija and Sanctius, probably the best-known grammarians of the Iberian peninsula, but - as the other papers suggest - there is much more to be known about (...) the Spanish linguistic traditions. The papers in this volume were previously published in Historiographia Linguistica XI:1/2 (1984). (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

In 1964, the young Walter Kasper (born in 1933) was granted by the Faculty of Catholic Theology at Tübingen the licence to teach dogmatic theology on the basis of a thesis on Philosophie und Theologie der Geschichte in der Spätphilosophie Schellings (Philosophy and Theology of History in Schelling’s Late Philosophy). Kasper’s interest in Schelling, himself a student at the Evangelisches Stift at Tübingen, thus originated in the context of his university studies in the school of J.R. Geiselmann and developed in (...) parallel with his theological education. For this reason, it is impossible to form a correct idea of Kasper and his whole theology unless one is willing to take into account this background, not least because he himself has always consciously and forcefully recognised this fact and seen in it his own centre of gravity. Kasper’s work and thought were shaped in a lasting manner during his university years. In fact, his entire academic oeuvre has been nurtured from this fecund origin so much so that he became one of the most well known names associated with the Catholic school at Tübingen to which he gave a new, creative impulse having himself been profoundly inspired by it. ‘He always emphasised his own roots not only as a teacher of theology and a member of the teaching faculty of this institution, but also as bishop’ and cardinal. The principal intention of the present article is precisely this: to return to this beginning and elucidate these decisive years for Kasper in broad outline by way of a relecture and interpretation of his book on The Absolute in History and the particular manner in which he interpreted the so-called second Schelling, an author whom he approached in the wake of Walter Schulz and at practically the same time as Xavier Tilliette. The analysis will subsequently move on into the more properly theological field. (shrink)

Antonio Rosmini (1797-1855) si profila come una delle vette filosofiche della prima metà dell'Ottocento europeo. La presente edizione di alcuni suoi inediti giovanili del 1813 (Delle laudi dell'amistà e il Dialogo tra Cieco e Lucillo), consente di gettare nuova luce sulla formazione di un intellettuale dell'epoca e sulla sua nascente sensibilità filosofico-letteraria: dalla ricerca dello stile linguistico all'esposizione delle numerose opere consultate, dal desiderio di condividere con gli altri le proprie passioni al conseguente riflettere sul senso dell'amore e dell'amicizia.

The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities (...) --qua part of a physical law-- highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature. (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...