We show that if κ is a weakly compact cardinal then the embeddability relation on trees of size κ is invariantly universal. This means that for every analytic quasi-order R on the generalized Cantor space View the MathML source there is an Lκ+κ-sentence φ such that the embeddability relation on its models of size κ, which are all trees, is Borel bi-reducible to R. In particular, this implies that the relation of embeddability on trees of size κ is complete for (...) analytic quasi-orders on View the MathML source. These facts generalize analogous results for κ=ω obtained in Louveau and Rosendal [17] and Friedman and Motto Ros [6], and it also partially extends a result from Baumgartner [3] concerning the structure of the embeddability relation on linear orders of size κ. (shrink)

We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in Alessandro Andretta and Donald A. Martin [1], Luca Motto Ros [6] and Luca Motto Ros. [5] e.g. to the projective levels.

Answering one of the main questions of [S.-D. Friedman, T. Hyttinen and V. Kulikov, Generalized descriptive set theory and classification theory, Mem. Amer. Math. Soc. 230 80, Chap. 7], we show that there is a tight connection between the depth of a classifiable shallow theory [Formula: see text] and the Borel rank of the isomorphism relation [Formula: see text] on its models of size [Formula: see text], for [Formula: see text] any cardinal satisfying [Formula: see text]. This is achieved by (...) establishing a link between said rank and the [Formula: see text]-Scott height of the [Formula: see text]-sized models of [Formula: see text], and yields to the following descriptive set-theoretical analog of Shelah’s Main Gap Theorem: Given a countable complete first-order theory [Formula: see text], either [Formula: see text] is Borel with a countable Borel rank, or it is not Borel at all. The dividing line between the two situations is the same as in Shelah’s theorem, namely that of classifiable shallow theories. We also provide a Borel reducibility version of the above theorem, discuss some limitations to the possible complexities of [Formula: see text], and provide a characterization of categoricity of [Formula: see text] in terms of the descriptive set-theoretical complexity of [Formula: see text]. (shrink)

We study Polish spaces for which a set of possible distances $A \subseteq R^+$ is fixed in advance. We determine, depending on the properties of A, the complexity of the collection of all Polish metric spaces with distances in A, obtaining also example of sets in some Wadge classes where not many natural examples are known. Moreover we describe the properties that A must have in order that all Polish spaces with distances in that set belong to a given class, (...) such as zero-dimensional, locally compact, etc. These results lead us to give a fairly complete description of the complexity, with respect to Borel reducibility and again depending on the properties of A, of the relations of isometry and isometric embeddability between these Polish spaces. (shrink)

In [9] we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of [9] allowing to deal with a larger class of notions of reduction (including, among others, the Baire class ξ functions).

We show that if Ƒ is any "well-behaved" subset of the Borei functions and we assume the Axiom of Determinacy then the hierarchy of degrees on $P(^\omega \omega )$ induced by Ƒ turns out to look like the Wadge hierarchy (which is the special case where Ƒ is the set of continuous functions).

Answering some of the main questions from [L. Motto Ros, The descriptive set-theoretical complexity of the embeddability relation on models of large size, Ann. Pure Appl. Logic164(12) (2013) 1454–1492], we show that whenever κ is a cardinal satisfying κ<κ=κ>ω, then the embeddability relation between κ-sized structures is strongly invariantly universal, and hence complete for (κ-)analytic quasi-orders. We also prove that in the above result we can further restrict our attention to various natural classes of structures, including (generalized) trees, graphs, (...) or groups. This fully generalizes to the uncountable case the main results of [A. Louveau and C. Rosendal, Complete analytic equivalence relations, Trans. Amer. Math. Soc.357(12) (2005) 4839–4866; S.-D. Friedman and L. Motto Ros, Analytic equivalence relations and bi-embeddability, J. Symbolic Logic76(1) (2011) 243–266; J. Williams, Universal countable Borel quasi-orders, J. Symbolic Logic79(3) (2014) 928–954; F. Calderoni and L. Motto Ros, Universality of group embeddability, Proc. Amer. Math. Soc.146 (2018) 1765–1780]. (shrink)

Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs (or on any class of countable structures consisting of the models of a sentence of L ω ₁ ω ) is far from complete (see [5, 2]). In (...) this article we strengthen the results of [5] by showing that not only does bi-embeddability give rise to analytic equivalence relations which are complete under Borel reducibility, but in fact any analytic equivalence relation is Borel equivalent to such a relation. This result and the techniques introduced answer questions raised in [5] about the comparison between isomorphism and bi-embeddability. Finally, as in [5] our results apply not only to classes of countable structures defined by sentences of ω ₁ ω , but also to discrete metric or ultrametric Polish spaces, compact metrizable topological spaces and separable Banach spaces, with various notions of embeddability appropriate for these classes, as well as to actions of Polish monoids. (shrink)

This thesis is divided into three parts, the first and second ones focused on combinatorics and classification problems on discrete and geometrical objects in the context of descriptive set theory, and the third one on generalized descriptive set theory at singular cardinals of countable cofinality.Descriptive Set Theory (briefly: DST) is the study of definable subsets of Polish spaces, i.e., separable completely metrizable spaces. One of the major branches of DST is Borel reducibility, successfully used in the last 30 years to (...) solve and compare many classification problems. One of our goals is the classification of knots, very familiar and tangible objects in everyday life, which also play an important role in modern mathematics. The study of knots and their properties is known as knot theory. Our plan is to gain insight into knots using discrete objects, such as linear and circular orders. This approach was already exploited in [6]. The first part of this work is therefore devoted to countable linear orders and the study of the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results. We also expand our research to the case of circular orders.Another objective of this first part is to extend the notion of convex embeddability on countable linear orders. We provide a family of quasi-orders of which embeddability is a particular case as well. We study these quasi-orders from a combinatorial point of view and analyse their complexity with respect to Borel reducibility. Furthermore, we extend the analysis of these quasi-orders to the set of uncountable linear orders.The second part of the project deals with classification problems on knots and $3$ -manifolds. The goal here is to apply the results obtained in the first part to the study of proper arcs and knots, establishing lower bounds for the complexity of some natural relations between these geometrical objects. We also obtain some combinatorial results which are particularly interesting when we restrict to the set of wild proper arcs and wild knots, classes which haven’t received much attention so far. These parts are included in the two preprints [4, 5] in collaboration with my supervisor Alberto Marcone, Luca Motto Ros (University of Torino), and Vadim Weinstein (University of Oulu).The second part of this work also includes the classification of non-compact $3$ -manifolds up to homeomorphism (the case of compact $3$ -manifolds has already been solved: indeed, there are only countably many $3$ -manifolds up to homeomorphism; see [7]), and that of Cantor sets of $\mathbb {R}^3$ up to conjugation (answering to Question 5.5 of [3]). Here we resort to algebraic tools. Stone duality gives a neat way to go back-and-forth between totally disconnected Polish spaces and countable Boolean algebras (see [1]). The main ingredient is the Stone space of all ultrafilters on a Boolean algebra. In this work we introduce a weaker concept which we call “blurry filter”. Using blurry filters instead of ultrafilters enables one to extend the class of spaces under consideration beyond totally disconnected. As an application of this method, we show that both homeomorphism on non-compact $3$ -manifolds and conjugation of Cantor sets in $\mathbb {R}^3$ are completely classifiable by countable structures. These results are part of an upcoming paper in collaboration with Vadim Weinstein.The last part of this thesis concerns the natural generalization of descriptive set theory that occurs when countable is replaced by uncountable, called Generalized Descriptive Set Theory (briefly: GDST). In particular, we focus on the case of GDST for a singular cardinal $\kappa $ of countable cofinality. The goal here is to study the generalizations of the Perfect Set Property and the Baire Property to subsets of spaces of higher cardinalities, like the power set $\mathcal {P}(\kappa )$. We consider the question under which large cardinal hypotheses classes of definable subsets of these spaces possess such regularity properties, focusing on rank-into-rank axioms, like I2, and classes of sets definable by $\Sigma _1$ -formulas with parameters from various collections of sets. The obtained results are included in [2], a joint work with my co-supervisor Vincenzo Dimonte and Philipp Lücke (University of Hamburg).Abstract prepared by Martina IannellaE-mail: martina.iannella@tuwien.ac.at.URL: https://air.uniud.it/handle/11390/1262824. (shrink)

Coeducación implica replantear todo el proceso de enseñanza-aprendizaje, y requiere un marco concreto de aplicación y evaluación. Contamos con desarrollo normativo, recursos y materiales en la materia, sin embargo, la escuela sigue reproduciendo sexismos. La Didáctica de las Ciencias Sociales incluye las competencias, saberes y estrategias óptimas para la coeducación; además, la etapa de Educación Infantil es clave en el proceso de socialización sin sesgos de género. Por todo lo expuesto, en esta investigación se analiza el Real Decreto 95/2022, de (...) 1 de febrero, por el que se establece la ordenación y las enseñanzas mínimas de la Educación Infantil, para identificar en qué medida la actual reforma educativa, basada en el aprendizaje competencial, garantiza una práctica escolar libre de sexismos. Se concluye con las siete competencias coeducativas básicas desde las que seguir desarrollando el marco. (shrink)

Charlotte Witt's finely crafted book offers an original and powerful account of social role normativity––the normativity of norms associated with social ro.

Wiesbaden: Harrassowitz 2013. 314 S., geb., € 42,00. ISBN 978‐3‐447‐10006‐9. Daniel Stolzenberg,­ Egyptian Oedipus: Athanasius Kircher and the Secrets of Antiquity, Chicago/London: University of Chicago Press 2013. XI, 307 S., Ill., $ 50,00. ISBN 978‐0‐226‐92414‐4.

del. 1. Od protofilozofskih klasikov do neokonfucianstva dinastije Song -- del. 2. Zaton tradicije in obdobje moderne.

Having initially not had the attention of Sartre or Heidegger, Merleau-Ponty's work is arguably now more widely influential than either of his two contemporaries. "Merleau-Ponty: Key Concepts" presents an accessible guide to the core ideas which structure Merleau-Ponty's thinking as well as to his influences and the value of his ideas to a wide range of disciplines. The first section of the book presents the context of Merleau-Ponty's thinking, the major debates of his time, particularly existentialism, phenomenology, the history of (...) philosophy and the philosophy of history and society. The second section outlines his major contributions and conceptual innovations. The final section focuses upon how his work has been taken up in other fields besides philosophy, notably in sociology, cognitive science, health studies, feminism and race theory. (shrink)

A 'self-refutation argument' is any argument which aims at showing that a certain thesis is self-refuting. This study was the first book-length treatment of ancient self-refutation and provides a unified account of what is distinctive in the ancient approach to the self-refutation argument, on the basis of close philological, logical and historical analysis of a variety of sources. It examines the logic, force and prospects of this original style of argumentation within the context of ancient philosophical debates, dispelling various misconceptions (...) concerning its nature and purpose and elucidating some important differences which exist both within the ancient approach to self-refutation and between that approach, as a whole, and some modern counterparts of it. In providing a comprehensive account of ancient self-refutation, the book advances our understanding of influential and debated texts and arguments from philosophers like Democritus, Plato, Aristotle, Epicurus, the Stoics, the Academic sceptics, the Pyrrhonists and Augustine. (shrink)

Dieses Buch schlägt - unter dem Titel "synthetischer Materialismus" - einen neuen Weg zur Klärung des Geist-Materie-Problems vor. Ausgangspunkt ist die These, dass wir als Betrachter der Welt frei sind, dieselben Gegenstände in unterschiedlich komplexe raum-zeitliche Zusammenhänge einzuordnen, und dass sich daraus unterschiedliche Möglichkeiten der Klassifikation von Gegenständen ergeben können: Wenn wir von "Lebewesen", "Handlungssubjekten" und "Personen" sprechen, und ihnen psychische Phänomene zuschreiben, nutzen wir den Umstand, dass die Konstellationen von Kohlehydraten, Eiweißen, Wasser und Nukleinsäuren, die jene Entitäten auch sind, (...) in einer besonderen Weise mit Teilen ihrer Vergangenheit, Gegenwart und Zukunft in Verbindung gebracht werden können. Der synthetische Materialismus vermag so zu zeigen, dass es zwischen einem ausschließlich "materialistischen" Verständnis der Welt und jenen Sichtweisen, innerhalb derer wir manche Komplexe von materiellen Phänomenen als Individuen mit ihnen selbst bewussten Empfindungen, Absichten und Überzeugungen verstehen, Übergänge gibt, die methodisch-wissenschaftlich nachvollzogen werden können und die nicht zu nutzen töricht wäre. (shrink)

Auf die Rede von Begriffen und vergleichbaren Entitäten, so behauptet Quine, könne man verzichten. Mit einer solchen Einstellung handelt Quine sich jedoch Schwierigkeiten ein, die z.B. an seinem Konzept des Setzens von Gegenständen sowie an seinem Verständnis von Existenzaussagen sichtbar werden (§ 1 und 2). Im Hintergrund jener Einstellung steht ein unzureichendes Verständnis der Funktion von Begriffen (§ 3). Zudem hat Quine bisher nicht zur Kenntnis genommen, daß Wittgenstein in seiner Spätphilosophie Vorschläge zum Verständnis der Rede von Begriffen entwickelt hat, (...) welche es erlauben, zahlreiche Defizite des neuzeitlichen Verständnisses von Begriffen zu beheben (§ 4). (shrink)

Este artículo analiza los factores que llevaron a personas sin activismo político previo a participar en la campaña del movimiento de la Plataforma de Afectados por la Hipoteca (PAH) la obra social de la PAH. El contexto del estudio es la crisis hipotecaria, con más de 580.000 ejecuciones hipotecarias en el Estado español entre 2009 y 2015. A través del análisis de entrevistas semi-estructuradas, los resultados muestran cómo los interlocutores construyen un relato legitimador de la desobediencia civil como última opción (...) en una serie de protestas por el derecho a la vivienda. Haber sido desahuciado, no tener dónde vivir y la incapacidad del Estado para ofrecer vivienda social son algunas de las razones justificativas expuestas por los entrevistados. Al final suelen mostrar su voluntad de cumplir con las obligaciones ciudadanas y pagar un alquiler social según sus ingresos. (shrink)

Many classically valid meta-inferences fail in a standard supervaluationist framework. This allegedly prevents supervaluationism from offering an account of good deductive reasoning. We provide a proof system for supervaluationist logic which includes supervaluationistically acceptable versions of the classical meta-inferences. The proof system emerges naturally by thinking of truth as licensing assertion, falsity as licensing negative assertion and lack of truth-value as licensing rejection and weak assertion. Moreover, the proof system respects well-known criteria for the admissibility of inference rules. Thus, supervaluationists (...) can provide an account of good deductive reasoning. Our proof system moreover brings to light how one can revise the standard supervaluationist framework to make room for higher-order vagueness. We prove that the resulting logic is sound and complete with respect to the consequence relation that preserves truth in a model of the non-normal modal logic _NT_. Finally, we extend our approach to a first-order setting and show that supervaluationism can treat vagueness in the same way at every order. The failure of conditional proof and other meta-inferences is a crucial ingredient in this treatment and hence should be embraced, not lamented. (shrink)

The Confucian revival which manifests itself in the modern Confucian current belongs to the most important streams of thought in contemporary Chinese philosophy. This book introduces this stream of thought by focusing on the second generation modern Confucians--Mou Zongsan, Tang Junyi, Xu Fuguan and Fang Dongmei. They argue that traditional Confucianism, as a specifically Chinese social, political, and moral system of thought can, if adapted to the modern era, serve as the foundation for an ethically meaningful modern life.

This book offers a critical introduction of Li Zhou’s ethics. Li, who is among the most influential contemporary Chinese philosophers, takes Chinese ethics as a basis for his elaborations on Western ideas, aiming to develop a new global ethics.

ABSTRACTLinguistic evidence supports the claim that certain, weak rejections are less specific than assertions. On the basis of this evidence, it has been argued that rejected sentences cannot be premisses and conclusions in inferences. We give examples of inferences with weakly rejected sentences as premisses and conclusions. We then propose a logic of weak rejection which accounts for the relevant phenomena and is motivated by principles of coherence in dialogue. We give a semantics for which this logic is sound and (...) complete, show that it axiomatizes the modal logic KD45 and prove that it still derives classical logic on its asserted fragment. Finally, we defend previous logics of strong rejection as being about the linguistically preferred interpretations of weak rejections. (shrink)

Jean-Paul Sartre is a man who lived half his life in the limelight of extreme notoriety. An intellectual who already in 1945 had to protest against attempts aimed at institutionalizing the writer, turning his works into 'national goods', exclaiming: 'it is not pleasant to be treated in one's lifetime as a public monument'. What must be equally unpleasant is to be constantly subjected to abuse. And the fact is that no writer in his lifetime has been the target of so (...) many attacks, from the most varied and rather powerful quarters, as Jean-Paul Sartre. What are the reasons? How should we approach the work of this man, our contemporary? (shrink)

Specific Chinese models for theories of knowledge were premised upon a structurally ordered external reality; since natural (or cosmic) order is organic, it naturally follows the 'flow' of structural patterns and operates in accordance with structural principles that regulate every existence. In this worldview, our mind is also structured in accordance with this all-embracing, but open, organic system. The axioms of our recognition and thought are therefore not arbitrary, but follow this rationally designed structure. The compatibility of both the cosmic (...) and mental structures is the basic precondition that enables humans to perceive and recognize external reality. The present study shows that this paradigm of structural epistemology can already be found in the earliest Chinese theories of knowledge. The introduction of Chinese models and their incorporation into Western discourses fills an important theoretical gap in the Western model of structuralism. This book offers an insight into epistemological systems that arose outside the discourses of the Euro-American tradition. It can thus help us to eliminate and supersede certain culturally conditioned prejudices as to the superiority and omnipresence of Western theoretical models, while demonstrating incontrovertibly that the results of Western discourses are by no means the only force driving theoretical innovation at the present time. (shrink)

Mindreading (or folk psychology, Theory of Mind, mentalizing) is the capacity to represent and reason about others’ mental states. The Simulation Theory (ST) is one of the main approaches to mindreading. ST draws on the common-sense idea that we represent and reason about others’ mental states by putting ourselves in their shoes. More precisely, we typically arrive at representing others’ mental states by simulating their mental states in our own mind. This entry offers a detailed analysis of ST, considers theoretical (...) arguments and empirical data in favour of and against it, discusses its philosophical implications, and illustrates some alternatives to it. (shrink)

When in classical formal logic the notions of deduction, valid inference and logical consequence are defined, causal language plays no role. The founder of western logic, Aristotle, identified ‘non-cause’, or ‘positing as cause what is not a cause’, as a logical fallacy. I argue that a systematic re-examination of Aristotle's analysis of NCF, and the related language of logical causality, in the Sophistical Refutations, Topics, Analytics and Rhetoric, helps us to understand his conception of. It reveals that Aristotle's syllogismhood is (...) non-monotonic, and thus narrower than classical validity as consisting in, or coextensive with, necessary truth-preservation. It also supports the conclusion that a syllogism is a form of relevant consequence: the premisses must be causes of the conclusion in the sense that they are not only sufficient but also necessary for the conclusion to follow. Close analysis of NCF also suggests that syllogistic relevance is not a semantic matter, but a syntactic.. (shrink)

This article examines Artaud's 1920s cinema texts, arguing that like other theorists writing at the time, Artaud envisaged the medium of cinema as capable of forging new types of corporeal experience, both through the types of bodies that were portrayed onscreen, and their relationship to the body of the audience, conceived as collective force rather than an individual spectator. It pays particular attention to Artaud's theories of corporeal materiality, and argues that these are relevant to more recent approaches to embodiment (...) and identification in film studies. Whilst Artaud never successfully put his own cinematic theories into practice, these are discussed in relation to Carl Theodor Dreyer's The Passion of Joan of Arc ( La Passion de Jeanne d'Arc , 1928), a film which puts distinctions between bodies into question in an unprecedented manner. Finally, through an analysis of the various different critical interpretations of Dreyer's film, the article considers the difficulties inherent in the notion of a universally intelligible affective body, arguing that there is a distinction to be made between a fascist appropriation of collective affect, and a type of body that overcomes the boundaries between self and other. (shrink)

This paper questions the introduction of national teaching strategy for all ages from five to eleven. It is proposed that the lack of developmentally appropriate practice in the early teaching of literacy is inappropriate and may be counter-productive to the long term goals of high literacy standards.

Henrich (1966) has contributed to the revival of philosophical debates on subjectivity and its irreducibility, starting from Fichte’s notion of "insight", and focusing his attention on the reflective model of self-consciousness. Subsequent studies have followed the same line from different perspectives, emphasizing the basic role of pre-reflective self-consciousness as the condition of possibility of conscious experience. The so-called ubiquity thesis has been developed through analysis of indexical thinking.

This appreciation outlines the life and work of Giulio Preti, a philosopher of the critical rationalist movement. His was a tormented and conflictual philosophical itinerary from his intellectual roots in 1930s Italy, via the philosophical journal Studi filosofici in the 1940s, to his major works Praxis and Empiricism and Rhetoric and Logic in the 1950s and 1960s. His anxiety about the ambiguity of contemporary reality, it is suggested, is also ours.

This paper discusses a relational modeling of measurement which is complementary to the standard representational point of view: by focusing on the experimental character of the measurand-related comparison between objects, this modeling emphasizes the role of the measuring systems as the devices which operatively perform such a comparison. The non-idealities of the operation are formalized in terms of non-transitivity of the substitutability relation between measured objects, due to the uncertainty on the measurand value remaining after the measurement. The metrological structure (...) of traceability is shown to be an effective solution to cope with the problem of the general non-transitivity of measurement results. A preliminary theory is introduced as a possible formalization for the presented model. (shrink)

Measurement in soft systems generally cannot exploit physical sensors as data acquisition devices. The emphasis in this case is instead on how to choose the appropriate indicators and to combine their values so to obtain an overall result, interpreted as the value of a property, i.e., the measurand, for the system under analysis. This paper aims at discussing the epistemological conditions of the claim that such a process is a measurement, and performance evaluation is the case introduced to support the (...) analysis, performed in systematic comparison with the paradigm of measurement of physical quantities. Some background questions arising here are: – Are the chosen indicators appropriate performance indicators? – Do such indicators convey complete and non-redundant information on performance? – Does the chosen combination rule generate results suitably interpretable as performance values? And enlarging the focus: – Does the obtained value specifically convey information on the system under analysis, instead of some different entity (typically including the subject who is evaluating)? Operatively: would different subjects evaluate the same system in the same way? i.e., is the obtained information objective? – Does the obtained value convey information that is interpretable in the same way by different subjects? Operatively: would different subjects who have agreed on a decision procedure make the same decision from the same performance information? i.e., is the obtained information intersubjective? Any well founded positive answers to these questions significantly support a structural interpretation of measurement encompassing both physical and soft measurement. (shrink)

Bd. 1. Antike, Spätantike und Mittelalter -- Bd. 2. Neuzeit -- Bd. 3. Moderne.