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)

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...

Cet article expose la critique de Maimon du principe kantien de causalité. Pour ce faire, nous considérerons les deux niveaux sur lesquels cette critique se développe, l’un formel et l’autre matériel. Au premier niveau, Maimon soulève trois objections au jugement hypothétique, relativement à son origine, sa fonction et sa modalité. Selon le deuxième, Maimon développe deux objections, dont la première concerne en général la démonstration kantienne de la validité des catégories, tandis que la seconde concerne en particulier celle du principe (...) de causalité. Cela nous permettra de mieux comprendre le sens de ses deux objections fondamentales contre la philosophie kantienne, formulées à travers les questions quid juris? et quid facti? (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...

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)

Irrational debt decisions at the individual level may harm collective welfare. For this reason, regulators are committed to encourage information-based behaviours in order to enhance likelihood of appropriate indebtedness. We analyse, with a diff-in-diff estimator, the Italian case offered by the Legislative Decree that reformed the consumer credit market adopting European Directive 2008/48/ec, and that reinforced the mandatory information acquisition, jointly asked to lenders and borrowers, before granting/receiving consumer credit. By using micro-data on 60.000 consumer credit borrowers, in total, randomly (...) sampled from the most relevant Italian Credit Bureau, our findings support that, in the medium term, the new consumer credit regulation has improved borrowers’ repayment ability, enhancing the quality of credit distribution. Nevertheless, a simplistic ‘better information-better behaviour’ relationship cannot be assured. This success is likely due to conjunct adaptation of behaviours, with shared responsibilities experienced on both the demand and offer side of the consumer credit marketplace. (shrink)

This study investigates the risk and return characteristics of impact investing in the public equity market. We use a unique hand-collected dataset of 50 US listed firms whose product (or service) addresses at least one of the global social and environmental challenges, as defined by the United Nations Social Development Goals (SDGs). We designate such firms Impact Firms, and we compare their financial performance to a matched sample of Non-Impact Firms in the time span 2002–2019. Our results show that Impact (...) and Non-Impact Firms have similar level of financial performance and both volatility and systemic risk over the entire sample period. At the same time, Impact Firms show a slightly lower negative skewness of the returns over the entire sample period, but not during crisis periods. However, compared to matched Non-Impact Firms, Impact Firms outperform during periods of market crisis, generating a valuable dampening of downside risk. (shrink)

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)

This article investigates the intense debate on the figure of “Chinese public intellectuals,” which has gained increasing importance, both inside and outside Mainland China, during the last decade. The climax was reached in the year 2004, when the debate on the search for and against a role for the “public intellectuals” became the litmus test of the intellectual intersections between the State actors and the public. Through a close reading of the crucial documents, this article critically engages with the terminology (...) and the interpretive paradigms employed. Thus the article highlights the contribution of the scholars examined to a dialogue on the role of critical thinking within China as well as globally. In fact, the exploration of the diversity of contemporary Chinese thought on the topic of “public intellectuals” can be inscribed within the framework of the following questions: How is the social category of “public intellectuals” used and why? And, ultimately, what does it really means to be an intellectual for the public in China today? In this sense, the article sheds light on the indigenous and foreign understandings of “public” and “intellectual.”. (shrink)

How does the advancement of the sciences relate to the ways in which their founding figures are remembered? According to the stark picture painted by Alfred N. Whitehead in 1917, “the establishment of a reverential attitude towards any statement made by a classical author” had barred the progress of logic for several centuries: “Scholars became commentators on truths too fragile to bear translation. A science which hesitates to forget its founders is lost”. In the eyes of many critics, Sigmund Freud's (...) psychoanalysis may well be an example of such a lost cause. From the founding book The Interpretation of Dreams to his very last statements, Freud never ceased to affirm that psychoanalysis was a science: “What else can it be?”. Yet not only the fact that he has become one of the classic authors of the twentieth century, but also a number of very specific traits of psychoanalytic institutions have nourished the suspicion that Freud was less the founder of a science than of a sort of quasi-religious movement, a secular sect thriving on a personality cult. (shrink)

We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to $\mathrm {ATR_0}$ from the point of view of reverse mathematics, there is not a canonical way to phrase them as multivalued functions. We identify eight different multivalued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility. In particular one of our functions turns out to be strictly (...) stronger than any previously studied multivalued functions arising from statements around $\mathrm {ATR}_0$. (shrink)