The complexity of equivalence relations has received much attention in the recent literature. The main tool for such endeavour is the following reducibility: given equivalence relations R and S on natural numbers, R is computably reducible to S if there is a computable function f:ω→ω that induces an injective map from R-equivalence classes to S-equivalence classes. In order to compare the complexity of equivalence relations which are computable, researchers considered also feasible variants of computable reducibility, such as the polynomial-time reducibility. (...) In this work, we explore Peq, the degree structure generated by primitive recursive reducibility on primitive recursive equivalence relations with infinitely many equivalence classes. In contrast with all other known degree structures on equivalence relations, we show that Peq has much more structure: e.g., we show that it is a dense distributive lattice. On the other hand, we also offer evidence of the intricacy of Peq, proving, e.g., that the structure is neither rigid nor homogeneous. (shrink)

We make some beginning observations about the category Eq of equivalence relations on the set of natural numbers, where a morphism between two equivalence relations R and S is a mapping from the set of R-equivalence classes to that of S-equivalence classes, which is induced by a computable function. We also consider some full subcategories of Eq, such as the category Eq(Σ01) of computably enumerable equivalence relations (called ceers), the category Eq(Π01) of co-computably enumerable equivalence relations, and the category Eq(Dark*) (...) whose objects are the so-called dark ceers plus the ceers with finitely many equivalence classes. Although in all these categories the monomorphisms coincide with the injective morphisms, we show that in Eq(Σ01) the epimorphisms coincide with the onto morphisms, but in Eq(Π01) there are epimorphisms that are not onto. Moreover, Eq, Eq(Σ01), and Eq(Dark*) are closed under finite products, binary coproducts, and coequalizers, but we give an example of two morphisms in Eq(Π01) whose coequalizer in Eq is not an object of Eq(Π01). (shrink)

This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same reducibility degree (under the notion of reducibility for equivalence relations usually called “computable reducibility”), or in the same isomorphism type (with the isomorphism induced by a computable function), or in the same strong isomorphism type (with the isomorphism induced by a computable permutation (...) of the natural numbers). We observe, e.g., that every ceer is isomorphic to the word problem of some c.e. semigroup, but (answering a question of Gao and Gerdes) not every ceer is in the same reducibility degree of the word problem of some finitely presented semigroup, nor is it in the same reducibility degree of some non‐periodic semigroup. We also show that the ceer provided by provable equivalence of Peano Arithmetic is in the same strong isomorphism type as the word problem of some non‐commutative and non‐Boolean c.e. ring. (shrink)

It is prima facie uncontroversial that the justification of an assertion amounts to a collection of other (inferentially related) assertions. In this paper, we point at a class of assertions, i.e. mathematical assertions, that appear to systematically flout this principle. To justify a mathematical assertion (e.g. a theorem) is to provide a proof—and proofs are sequences of directives. The claim is backed up by linguistic data on the use of imperatives in proofs, and by a pragmatic analysis of theorems and (...) their proofs. Proofs, we argue, are sequences of instructions whose performance inevitably gets one to truth. It follows that a felicitous theorem, i.e. a theorem that has been correctly proven, is a persuasive theorem. When it comes to mathematical assertions, there is no sharp distinction between illocutionary and perlocutionary success. (shrink)

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^0_2$$\end{document} sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice L. In (...) this paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy. In particular, we focus on the fuzzy n-c.e. sets which form the finite levels of this hierarchy. Intuitively, a fuzzy set is n-c.e. if its membership function can be approximated by changing monotonicity at most n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n-1$$\end{document} times. We prove that the Fuzzy Ershov Hierarchy does not collapse; that, in analogy with the classical case, each fuzzy n-c.e. set can be represented as a Boolean combination of fuzzy c.e. sets; but that, contrary to the classical case, the Fuzzy Ershov Hierarchy does not exhaust the class of all Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^0_2$$\end{document} fuzzy sets. (shrink)

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies limit computable sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice. In this paper, we combine the Ershov Hierarchy and fuzzy set (...) theory, by introducing and investigating the Fuzzy Ershov Hierarchy. (shrink)

We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the learning type InfEx_\iso, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures is InfEx_\iso-learnable if and only if the structures can be distinguished in terms of their \Sigma^2_inf-theories. We apply this characterization to familiar cases and we show the following: there is an infinite (...) learnable family of distributive lattices; no pair of Boolean algebras is learnable; no infinite family of linear orders is learnable. (shrink)

We investigate the complexity of embeddings between bi-embeddable structures. In analogy with categoricity spectra, we define the bi-embeddable categoricity spectrum of a structure A as the family of Turing degrees that compute embeddings between any computable bi-embeddable copies of A; the degree of bi-embeddable categoricity of A is the least degree in this spectrum (if it exists). We extend many known results about categoricity spectra to the case of bi-embeddability. In particular, we exhibit structures without degree of bi-embeddable categoricity, and (...) we show that every degree d.c.e above 0(α) for α a computable successor ordinal and 0(λ) for λ a computable limit ordinal is a degree of bi-embeddable categoricity. We also give examples of families of degrees that are not bi-embeddable categoricity spectra. (shrink)

We aim at providing a philosophical analysis of the notion of “proof by Church’s Thesis”, which is – in a nutshell – the conceptual device that permits to rely on informal methods when working in Computability Theory. This notion allows, in most cases, to not specify the background model of computation in which a given algorithm – or a construction – is framed. In pursuing such analysis, we carefully reconstruct the development of this notion (from Post to Rogers, to the (...) present days), and we focus on some classical constructions of the field, such as the construction of a simple set. Then, we make use of this focus in order to support the following encompassing claim (which opposes to a somehow commonly received view): the informal side of Computability, consisting of the large class of methods typically employed in the proofs of the field, is not fully reducible to its formal counterpart. (shrink)

This paper studies algorithmic learning theory applied to algebraic structures. In previous papers, we have defined our framework, where a learner, given a family of structures, receives larger and larger pieces of an arbitrary copy of a structure in the family and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. The learning is successful if there is a learner that eventually stabilizes to a correct conjecture. Here, we analyze the number of (...) mind changes that are needed to learn a given family K. We give a descriptive set-theoretic interpretation of such mind change complexity. We also study how bounding the Turing degree of learners affects the mind change complexity of a given family of algebraic structures. (shrink)

Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and bi-reducibility. These spectra provide a natural way of measuring the complexity of reductions between equivalence relations. We prove that any upward closed collection of Turing degrees with a countable basis can be realised as a reducibility spectrum or as a bi-reducibility spectrum. We show also that there is a reducibility (...) spectrum of computably enumerable equivalence relations with no countable basis and a reducibility spectrum of computably enumerable equivalence relations which is downward dense, thus has no basis. (shrink)

In this paper we argue, against a somewhat standard view, that pragmatic phenomena occur in mathematical language. We provide concrete examples supporting this thesis.

This paper is part of a project that is based on the notion of a dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In Amidei et al. (2016, Rev. Symb. Logic, 9, 1–26) and Amidei et al. (2016, Rev. Symb. Logic, 9, 299–324), we investigated the expressive and computational power of dialectical systems, and we compared them to a new class of systems, that of quasi-dialectical systems, that enrich Magari’s systems with a natural mechanism (...) of revision. In the present paper we consider a third class of systems, that of p-dialectical systems, that naturally combine features coming from the two other cases. We prove several results about p-dialectical systems and the sets that they represent. Then we focus on the completions of first-order theories. In doing so, we consider systems with connectives, i.e. systems that encode the rules of classical logic. We show that any consistent system with connectives represents the completion of a given theory. We prove that dialectical and q-dialectical systems coincide with respect to the completions that they can represent. Yet, p-dialectical systems are more powerful; we exhibit a p-dialectical system representing a completion of Peano Arithmetic that is neither dialectical nor q-dialectical. (shrink)

We study the algorithmic complexity of isomorphic embeddings between computable structures.

In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power that is needed to learn finite families of structures. In particular, we prove that, if a family of structures is both finite and learnable, then any oracle which computes the Halting set is able to achieve such a learning. On the other hand, we construct (...) a pair of structures which is learnable but no computable learner can learn it. (shrink)

In this short paper, we analyse whether assuming that mathematical objects are “thin” in Linnebo's sense simplifies the epistemology of mathematics. Towards this end, we introduce the notion of transparency and show that not all thin objects are transparent. We end by arguing that, far from being a weakness of thin objects, the lack of transparency of some thin objects is a fruitful characteristic mark of abstract mathematics.

We offer a novel picture of mathematical language from the perspective of speech act theory. There are distinct speech acts within mathematics, and, as we intend to show, distinct illocutionary force indicators as well. Even mathematics in its most formalized version cannot do without some such indicators. This goes against a certain orthodoxy both in contemporary philosophy of mathematics and in speech act theory. As we will comment, the recognition of distinct illocutionary acts within logic and mathematics and the incorporation (...) of illocutionary force indicators in the formal language for both goes back to Frege’s conception of these topics. We are, therefore, going back to a Fregean perspective. This paper is part of a larger project of applying contemporary speech act theory to the scientific language of mathematics in order to uncover the varieties and regular combinations of illocutionary acts present in it. For reasons of space, we here concentrate only on assertive and declarative acts within mathematics, leaving the investigation of other kinds of acts for a future occasion. (shrink)

In this paper we focus on the logicality of language, i.e. the idea that the language system contains a deductive device to exclude analytic constructions. Puzzling evidence for the logicality of language comes from acceptable contradictions and tautologies. The standard response in the literature involves assuming that the language system only accesses analyticities that are due to skeletons as opposed to standard logical forms. In this paper we submit evidence in support of alternative accounts of logicality, which reject the stipulation (...) of a natural logic and assume instead the meaning modulation of nonlogical terms. (shrink)

Computably enumerable equivalence relations received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility \. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the \ case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by \ on the \ equivalence relations. (...) A special focus of our work is on the existence of infima and suprema of c-degrees. (shrink)

The Friedman–Stanley jump, extensively studied by descriptive set theorists, is a fundamental tool for gauging the complexity of Borel isomorphism relations. This paper focuses on a natural computable analog of this jump operator for equivalence relations on $\omega $, written ${\dotplus }$, recently introduced by Clemens, Coskey, and Krakoff. We offer a thorough analysis of the computable Friedman–Stanley jump and its connections with the hierarchy of countable equivalence relations under the computable reducibility $\leq _c$. In particular, we show that this (...) jump gives benchmark equivalence relations going up the hyperarithmetic hierarchy and we unveil the complicated highness hierarchy that arises from ${\dotplus }$. (shrink)

We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, \ bi-embeddable categoricity, and degrees of bi-embeddable categoricity. These notions mirror the classical notions used to study the complexity of isomorphisms between structures. We show that the notions of \ bi-embeddable categoricity and relative \ bi-embeddable categoricity coincide for equivalence structures for \. We also prove that computable equivalence structures have degree of bi-embeddable categoricity \, or \. We furthermore obtain results (...) on the index set complexity of computable equivalence structure with respect to bi-embeddability. (shrink)

We examine the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ of equivalence relations on $\omega $ under computable reducibility. We examine when pairs of degrees have a least upper bound. In particular, we show that sufficiently incomparable pairs of degrees do not have a least upper bound but that some incomparable degrees do, and we characterize the degrees which have a least upper bound with every finite equivalence relation. We show that the natural classes of finite, light, and dark degrees are (...) definable in $\operatorname {\mathrm {\mathbf {ER}}}$. We show that every equivalence relation has continuum many self-full strong minimal covers, and that $\mathbf {d}\oplus \mathbf {\operatorname {\mathrm {\mathbf {Id}}}_1}$ needn’t be a strong minimal cover of a self-full degree $\mathbf {d}$. Finally, we show that the theory of the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ as well as the theories of the substructures of light degrees and of dark degrees are each computably isomorphic with second-order arithmetic. (shrink)

Mauro Basaure Cet article cherche à innover dans le cadre de la controverse sur le musée de la Mémoire et des Droits de l’homme du Chili : devrait-il ou non intégrer dans sa muséographie la période antérieure au 11 septembre 1973, c’est-à-dire le contexte du coup d’État? Je défends la thèse selon laquelle le MMDH peut intégrer une dimension contextuelle sans trahir sa mission, sa vision et sa fonction, tant qu’il répond à une approche de la notion de contexte-sans-causalité. (...) Selon moi, le grand problème de la critique venant de la droite politique – qui accuse le musée de ne pas remplir sa mission pédagogique, car il décontextualise le coup d’État – est que cette critique répond à une vision causale de la notion de contexte, ce qui la conduit à des contradictions insurmontables. Si, grâce à une muséographie bien réfléchie, le concept de contextualisation non causale était mis en oeuvre avec succès, ceci n’engendrerait pas une contradiction au sein du musée mais pourrait même le favoriser. La conviction que le coup d’État et ses atrocités n’ont ni causes ni antécédents et ne peuvent en avoir renforce la mission pédagogique du MMDH. (shrink)

The reception of Avicenna by medieval Jewish readers presents an underappreciated enigma. Despite the philosophical and scientific stature of Avicenna, his philosophical writings were relatively little studied in Jewish milieus, be it in Arabic or in Hebrew. In particular, Avicenna's philosophical writings are not among the “Hebräische Übersetzungen des Mittelalters” – only very few of them were translated into Hebrew. As an author associated with a definite corpus of writings, Avicenna hardly existed in Jewish philosophy in Hebrew. Paradoxically, however, some (...) of Avicenna's most distinctive ideas were widely known and embraced by Jewish philosophers. This is the phenomenon that we dub Avicennian knowledge without Avicenna. In contrast with the philosophical treatises, Avicenna's medical writings were widely and intensively studied by Jews, especially in Hebrew, and remained influential until at least the seventeenth century. The present article presents a comprehensive picture of Avicenna's reception within medieval Jewish cultures in both Arabic and Hebrew and tries to explain the Jews’ complex attitude to Avicenna.La réception d'Avicenne par les érudits juifs médiévaux présente une énigme dont on n'a pas encore pris toute la mesure. Malgré la grande stature scientifique et philosophique d'Avicenne, ses écrits philosophiques ont été peu connus des savants juifs, que ce soit en arabe ou en hébreu. Ils n'ont guère fait partie des “Hebräische Übersetzungen des Mittelalters” – peu seulement ont été traduits en hébreu. En tant qu’auteur associé à un corpus de textes, Avicenne n'existe presque pas dans la philosophie juive en hébreu. Paradoxalement cependant, certaines des idées les plus caractéristiques d'Avicenne étaient bien connues et acceptées par des philosophes juifs. Nous appelons ce phénomène savoir avicennien sans Avicenne. Contrairement aux écrits philosophiques, les ouvrages médicaux d'Avicenne, eux, étaient lus et utilisés par les juifs, notamment en traductions hébraïques, et ce jusqu'au xviie siècle. Cet article présente un tableau général de la réception d'Avicenne, en arabe et en hébreu, dans les différentes cultures juives et il tente d'expliquer l'attitude complexe des savants juifs vis-à-vis d'Avicenne.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.AVICENNA AMONG MEDIEVAL JEWS THE RECEPTION OF AVICENNA'S PHILOSOPHICAL, SCIENTIFIC AND MEDICAL WRITINGS IN JEWISH CULTURES, EAST AND WESTVolume 22, Issue 2Gad Freudenthal and Mauro Zonta DOI: https://doi.org/10.1017/S0957423912000033Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. AVICENNA AMONG MEDIEVAL JEWS THE RECEPTION OF AVICENNA'S PHILOSOPHICAL, SCIENTIFIC AND MEDICAL WRITINGS IN JEWISH CULTURES, EAST AND WESTVolume 22, Issue 2Gad Freudenthal and Mauro Zonta DOI: https://doi.org/10.1017/S0957423912000033Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. AVICENNA AMONG MEDIEVAL JEWS THE RECEPTION OF AVICENNA'S PHILOSOPHICAL, SCIENTIFIC AND MEDICAL WRITINGS IN JEWISH CULTURES, EAST AND WESTVolume 22, Issue 2Gad Freudenthal and Mauro Zonta DOI: https://doi.org/10.1017/S0957423912000033Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

Economic and sanitary crises have great repercussions on access to food and the health of the population. In this context, austerity policies can have devastating effects on social rights. The purpose of this essay is to reflect on the impact of various types of crises on the Human Right to Adequate Food and Nutrition (DHANA) and on Food and Nutritional Security (SAN) of vulnerable populations and to identify of public policies, programs and actions developed based on the relief of the (...) damage caused by the COVID-19 pandemic. From the collection of information carried out in a non-systematic way on government websites and scientific databases, documents were read in full, categorized, and critically analyzed. Three different contexts, Africa, Latin America, and Portugal, are presented by the authors who work in these realities, with the intention of contributing to mitigate the food problems that worsen and are derived from the pandemic situation. (shrink)

Franz Brentano was a leading philosopher and psychologist of the nineteenth century. Indeed, the impact of his scholarship was so great that he became synonymous with a school of thought and a new approach in scientific philosophy. The Brentano School stood against the Idealistic and post-Kantian German tradition and Brentano played a crucial role in the founding of Austrian philosophy. He had an enormous impact on the work of Husserl and Heidegger, as well as on Moore’s _Ethics_ and Stout and (...) Russell’s analysis of mind. In particular, situated between the phenomenology movement and the analytic tradition, the concept of intentionality was redefined by Brentano and has been—and remains—a key concept of twentieth- and twentieth-first century philosophy of mind. But Brentano not only reshaped philosophy of mind; he was also a remarkable and innovative thinker in several other fields of philosophy, and recent debate in metaethics, metaphysics, and the history of analytic philosophy shows a strong resurgence of interest in Brentano’s thought. Published to coincide with the centenary of Brentano’s death, this four-volume collection, a new title from Routledge Major Works, provides an essential intellectual tool for the exegetical evaluation of all aspects of Brentano’s work. Bringing together early reviews and reactions from his contemporaries—many of which have never before been translated into English—as well as the best critical assessments of Brentano’s work, this ‘mini library’ provides Brentano scholars, historians of philosophy and psychology, and phenomenologists, with a rigorous historical appraisal of Brentano’s thought and influence. Brentano’s relationships with Husserl, Heidegger, and the phenomenological tradition are examined in depth, alongside investigations of key themes from his work on Aristotle, medieval and modern philosophy, philosophy of mind, logic, ontology, ethics, aesthetics, philosophy of religion, and the philosophy of history. (shrink)

The aim of this article is to amend some misunderstandings about Franz Brentano's thesis of intentionality, defending a different interpretation from the current one about the nature of intentional object and intentional correlate, and proposing an analysis of the origin of this conceptual confusion. The main problem lies in his student Anton Marty's interpretation of the immanent object, paving the way for an immanentist reading of Brentano's theory of intentionality.

A partir de la afirmación en la que Ortega dice que el científico se aloja en el ser humano, el texto pretende, por un lado y desde una perspectiva fenomenológica, abordar el vínculo entre las ciencias naturales y las ciencias humanas y sociales y, por otro lado, analizar las consecuencias de las maneras en las que estos dos grupos de ciencias se han relacionado a fin de imaginar la posición que tanto las ciencias naturales como las humanas y sociales deben (...) ocupar. From a phenomenological perspective and begining with the statement from Ortega saying that a scientist lives inside a human being, this text has a twofold structure. First, the author analyzes the relationship among natural sciences and human and social sciences. Second, the author analyzes the consequences of the different ways in which bothsciences have interrelated, in order to imagine the place that either natural sciences, and social sciences and humanities, should occupy. (shrink)

El objetivo de este ensayo es primero honrar la memoria de Vicent Martínez Guzmán, destacando sus importantes contribuciones a la filosofía. Dada su relación con el autor, ha parecido lo más oportuno centrarse en la relación de su filosofía con la fenomenología puesto que otros colegas desentrañarán otras facetas. Para cumplir ese cometido el ensayo tiene cuatro partes. En la primera se hace una presentación de las etapas de la filosofía de nuestro autor. En la segunda se expone, con bastante (...) amplitud, por la importancia que tiene, la primera concepción de la fenomenología de Vicent Martínez Guzmán. El apartado tercero expone, aunque sea brevemente, por ser más conocido, el sentido fenomenológico de la filosofía para hacer las paces. Por fin, la cuarta comenta la posición de Vicent Martínez Guzmán respecto al ordoliberalismo de la Escuela de Friburgo, considerando la relación de este con la fenomenología husserliana.The aim of this essay is first of all to honor the memory of Vicent Martínez Guzmán, highlighting his important contributions to philosophy. Given its relationship with the author, it has seemed most appropriate to focus on the relationship of his philosophy with phenomenology since other colleagues will unravel other facets. To fulfill this task, the essay has four parts. In the first one, a presentation is made of the stages of our author's philosophy. In the second, the first conception of the phenomenology of Vicent Martínez Guzmán is exposed, quite widely, because of its importance. The third section exposes, even if briefly, for being better known, the phenomenological sense of “philosophy to make peace”. Finally, the fourth section comments on Vicent Martínez Guzmán’s position regarding the ordoliberalism of the Fribourg School, considering its relation to Husserlian phenomenology. (shrink)

In this paper, I pursue two main goals. The first is to raise three objections against Tom Roberts and Joel Krueger’s recent account of loneliness (2021). The second is to sketch an alternative, receptive account. Roberts and Krueger focus on loneliness conceived of as an occurrent emotion. According to their account, loneliness involves two components: (1) a pro-attitude (e.g., a desire) towards certain social goods and (2) an awareness that such goods “are missing and out of reach, either temporarily or (...) permanently” (p. 186). My first objection is that having a pair of pro-attitudes and cognitive states of the sort that Roberts and Krueger have in mind is neither sufficient nor necessary for an individual to experience loneliness. The second is that Roberts and Krueger’s account has trouble accounting for the unpleasant phenomenology of loneliness. The third is that their account has trouble demarcating loneliness from other negative emotions that one may experience within romantic, friendship or social relationships. Next, I sketch my own account of loneliness. According to the receptive theory (Tappolet 2022) to which I adhere, emotions are receptive experiences that non-conceptually represent their intentional objects as possessing specific evaluative properties. Accordingly, I argue that loneliness consists in a receptive experience that represents the absence of certain relational goods as bad in a particular way. I draw a distinction between the intentional object and the intentional locus of loneliness, and clarify the role that some of the individual’s pro-attitudes play in loneliness. I also show how a receptive account can explain the phenomenology of loneliness and demarcate it from other emotion types, and offer an account of degrees of loneliness, which distinguishes between the intensity and the centrality of episodes of loneliness. (shrink)

The year 2005 has been named the World Year of Physics in recognition of the 100th anniversary of Albert Einstein's "Miracle Year," in which he published four landmark papers which had deep and great influence on the last and the current century: quantum theory, general relativity, and statistical mechanics. Despite the enormous importance that Einstein’s discoveries played in these theories, most physicists adopt a version of quantum theory which is incompatible with the idea that motivated Einstein in the first place. (...) This seems to suggest that Einstein was fundamentally incapable of appreciating the `quantum revolution,’ and that his vision of physics as an attempt to reach a complete and comprehensive description of reality was ultimately impossible to obtain. Relativity theory has provided us with a picture of reality in which the world can be though as independent on who observes it, and the same can be said for statistical mechanics. Instead, quantum mechanics seems to suggest that physical objects do not exist `out there’ when someone is not observing them. In this framework, it is often suggested that any kind of causal explanation is impossible in the atomic and subatomic world, and therefore should be abandoned. This is why many think that it is in principle impossible for quantum theory to provide us with a coherent and comprehensive view of the world, in contrast with what happens with relativity and statistical mechanics. Is it really impossible to pursue Einstein’s ideal of physics also in the quantum framework? This book argues that this is not the case: the central idea is that Einstein’s vision of physics is still a live option, and indeed it is the one that best allows obtaining a unitary understanding of our physical theories. One can consider all the three theories mentioned above, suitably modified, as theories that are able to account and explain the world around us without too much departure from the classical framework. ---------------------------------------------------------------------------------------------------- -------------------------------------------------- -/- La teoria della relatività, la meccanica statistica e la meccanica quantistica hanno profondamente rivoluzionato il nostro modo di concepire spazio, tempo, materia, probabilità e causalità, nonché il rapporto tra universo fisico ed osservatore, nozioni che sono state al centro della discussione filosofica dal mondo greco fino ai nostri giorni. Questo volume, opera di Valia Allori, Mauro Dorato, Federico Laudisa e Nino Zanghì, non solo intende suggerire nuovi metodi di confronto tra fisica e filosofia, ma prova altresì a rendere espliciti i presupposti filosofici che sono presenti nell'interpretazione che i fisici stessi danno del formalismo matematico. (shrink)

The proceedings of a June 1995 conference in Luino, Italy. One poem and 16 papers explore various issues in the philosophy of science with an emphasis on the foundations of probability and statistics and quantum mechanics. The topics include subjective probability, Bayesian statistics, probability kinematics, causal decision making, and probability and realism in quantum mechanics. The problem of collecting new evidence and updating probability judgements are addressed in reference to different applications. No index. Reprinted from Erkenntnis vol. 45, nos. 2-3 (...) (1996). Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)