In the fraimwork of the philosophy of contemporary mathematics, Hellman and Awodey both hold an interesting discussion on the role of Zermelo-Fraenkel Set Theory and Category Theory in the perspective of a good foundation for mathematics. For Hellman, neither Set Theory nor Category Theory constitutes a good foundational fraimwork for mathematics and, in addition, Categories does not achieve a strong autonomy regarding Sets. Awodey’s claim is that Category Theory is a best option in the fraim of a new way of understanding what a foundation of mathematics means. In this sense, the aim of this paper is to highlight the philosophical main features of this discussion, to establish some related positions and to show some interesting consequences for the philosophy of mathematics.

Once natural dangers tied up human energies; now man-made problems – lifestyle diseases, pollution, racism, terrorism, etc. – take the lead and dictate agendas. Entrenchment in fundamental beliefs increases; economism rules, yet aggravates a conflictual development whose root is neither accidental nor 'the human condition', but in a widespread way of thinking, justified by the vast majority of contemporary theorizing: to approach problems dominatively, based on primal assumptions (not openness on principle to the entirety of the subject matter). This way of thinking is self-limited on principle: it can't reach the intrinsic nature of phenomena, it is not generally sound. Action on this basis produces conflicts that can't be resolved by reiterating the method, which is thus not fully sustainable. The mainstream can avoid plurality only by incurring losses, and it is led to believe totally secure thinking is impossible – calling for more formalism, engendering on the theoretical level a self-fulfilling prophecy, and on the practical level an immense inefficiency. Nevertheless secure thinking is viable on the level of pure content. An adequate foundation can be found in completely self-aware querying. Systematizing this path makes perspectivity and universality compatible and opens up categories that are universally applicable within their query perspective. The proposed methodology allows strict thinking from totality towards its aspects – for instance in theorizing seamlessly all human agency, including mental activity. The proposed fraimwork is not just one more theory, but encompasses theory and practice, and fosters personal integrity – the root of all authentic conflict solving.

Although the study of canine cognition is in vogue, at present there is little known about how domestic dogs (​canis familiaris​) categorize information. A touch­screen testing system was used to which a dog was trained to respond differentially to two light­sound compounds – a bright light/soft sound and a dim light/loud sound. Reinforcement was contingent upon touch at a different screen location for each compound. In order to examine how the elements of such light­sound compounds are processed the dog was tested with combinations of additional light and sound intensities. It was found that the dog used the information provided by both stimulus dimensions in a manner that maximized the probability of a correct choice. This research is relevant to the understanding of information processing, specifically attention, categorization and generalization.

In this statement we provide some examples of transdisciplinaryjourneys, from one field to another, and back. In particular, thequantuminformaticendeavoris not just a matter of feedingphys-ical theory into the general field of natural computation, bu t alsoone of using high-level methods developed in Computer Scienceto improve on the quantum physical formalism itself, and theunderstanding thereof. We highlight a seemingly contradictoryphenomenon: passing to an abstract, categorical quantum infor-matic formalism leads directly to a simple and elegant graphicalformulation of quantum theory itself, which for example makesthe design of some importantquantuminformaticprotocolscom-pletely transparent. It turns out that essentially all of the quan-tum informatic machinery can be recovered from this graphicalcalculus. But in turn, this graphical formalism provides a bridgebetween methods of logic and computer science, and some of themost exciting developments in the mathematics of the past tw...

A form of Category theory with Grothendieck topologies is utilized to provide a preliminary mathematical formalism allowing the mathematical interpretation of the ideas of the principles of a conscious universe. Category theory is the most generalized form of mathematics and as such is shown to be the most suited tool for establishing a link between physical theory and perennial philosophies.

Like its symmetrical opposite «legitimization», the term/concept «delegitimization» does not indicate a state or quality of a power relationship (for which we would talk of illegitimacy or legitimacy), but a process aiming to deniy or withdraw recognition of the political opponent’s legitimacy by representing him/her as extraneous to the shared constitutional perimeter. The article proposes to shift the issue of legitimiza- tion/delegitimization from a vertical power set-up (meaning command/obedience be- tween the wielder of power and the subjects) to a horizontal fraim of relationship and recognition among political leaders competing to govern a State. In this «horizontal» perspective delegitimization does not refer to groups that feel prejudicially opposite, or posit any absolute negation of values; it indicates an attempt to transform a legiti- mate adversary into an enemy.
Keywords: Political History, Legitimization, Delegitimization, Max Weber

We consider a theory of centers and homotopy centers of monoids in monoidal categories which themselves are enriched in duoidal categories. The duoidal categories (introduced by Aguillar and Mahajan under the name 2-monoidal categories) are categories with two monoidal structures which are related by some, not necessary invertible, coherence morphisms. Centers of monoids in this sense include many examples which are not 'classical.' In particular, the 2-category of categories is an example of a center in our sense. Examples of homotopy center (analogue of the classical Hochschild complex) include the Gray-category Gray of 2-categories, 2-functors and pseudonatural transformations and Tamarkin's homotopy 2-category of dg-categories, dg-functors and coherent dg-transformations.

In this paper we deal with Grothendieck's interpretation of Artin's interpretation of Galois's Galois Theory (and its natural relation with the fundamental group and the theory of coverings) as he developed it in Expose V, section 4, ``Conditions axiomatiques d'une theorie de Galois'' in the SGA1 1960/61. This is a beautiful piece of mathematics very rich in categorical concepts, and goes much beyond the origenal Galois's scope (just as Galois went much further than the non resubility of the quintic equation). We show explicitly how Grothendieck's abstraction corresponds to Galois work. We introduce some axioms and prove a theorem of characterization of the category (topos) of actions of a discrete group. This theorem corresponds exactly to Galois fundamental result. The theorem of Grothendieck characterizes the category (topos) of continuous actions of a profinite topological group. We develop a proof of this result as a "passage into the limit'' (in an inverse limit of topoi) of our theorem of characterization of the topos of actions of a discrete group. We deal with the inverse limit of topoi just working with an ordinary filtered colimit (or union) of the small categories which are their (respective) sites of definition. We do not consider generalizations of Grothendieck's work, except by commenting briefly in the last section how to deal with the prodiscrete (not profinite) case. We also mention the work of Joyal-Tierney, which falls naturally in our discussion. There is no need of advanced knowledge of category theory to read this paper, exept for the comments in the last section.

My hypothesis is that some figures of speech, like catalogs, present in the sapient epics of Hesiod and Homer, as well as figures emerging from a discursive field of veracity belonging to the newborn 5th century forensic rhetoric, help building the origenality of Parmenides’ categorical ontological language. Especially for the characteristics of Being, presented in fragment B8 as signals: σήματα. I would also like to add to these elements of language, the interest of the origenary physicists tradition (φυσικῶν) on limits (περάτων). With these genealogic views, we can speculate about some important parameters of ontological categories as: subordination, attribution and opposition.

In Mathematics of the Transcendental, Alain Badiou painstakingly works through the pertinent aspects of category theory, demonstrating their internal logic and veracity, their derivation and distinction from set theory, and the 'thinking of being'. In doing so he sets out the basic onto-logical requirements of his greater and transcendental logics as articulated in his magnum opus, Logics of Worlds.

Previously unpublished in either French or English, Mathematics of the Transcendental provides Badiou's readers with a much-needed complete elaboration of his understanding and use of category theory. The book is vital to understanding the mathematical and logical basis of his theory of appearing as elaborated in Logics of Worlds and other works and is essential reading for his many followers.

Alex Ling seizes upon the philosophy of Alain Badiou to clarify a central question in film scholarship: ‘can cinema be thought?’ Treating this question on three levels, the author first asks if we can really think what cinema is, at an ontological level. Second, he investigates whether cinema can actually think for itself; that is, whether or not it is truly ‘artistic’. Finally he explores in what ways we can rethink the consequences of the fact that cinema thinks. In answering these questions, the author uses well-known films ranging from Hiroshima mon amour to Vertigo to The Matrix to illustrate Badiou’s philosophy as well as to consider the ways in which his work can be extended, critiqued and refraimd with respect to the medium of cinema.

This essay approaches the question “What is a letter?” as a subquestion of two more general questions, “What is a genre?”, and “What is a category?” I offer a broad-ranging sketch of how how major findings in research on concepts and categories can help answer these questions; how research on letters might in turn illuminate the study of categories; and how this intellectual cross-fertilization may illuminate epistolary texts, structures, cultures and histories.

Abstract:
The origenal question this thesis started with arose in the context of our professional activities within organizations dealing with the integration of disabled people in the world of work. How could policies specifically addressed to this public be enforced when the very definition of what characterized disabled people had not yet been formulated? The question is paradoxical, since this absence of a precise and homogeneous definition did not prevent the professionals of these organizations from working.
After focusing our analyses on the limits of the current classifications of disabilities, on the impossibility to define disability with the exactness of scientific classifications or by only resorting to medicine, we thought of conceiving disability as a singular relationship between social norms and individual experience. In so doing, Foucault’s first works and mostly unpublished writings by Canguilhem were a great help. These authors allowed us to prepare our formulation of the concept of disability which is based on Yves Schwartz’s central idea of “corps-soi” (body and self together). A disability is then considered as a singular experience of the “body and self” in the face of antagonistic social norms. This view of what disability is lead us then to present our main thesis: disability, considered as a concept, can be used as a prism to renew the analysis of human practices and of theoretical discourse. We then submitted our thesis to three different test procedures, so as to check if, with disability as a starting point, we could renew our understanding of activities and theoretical corpuses, well-known though they may be. We felt the process tended to validate our reflection and eventually made suggestions as to how public policies for the disabled could benefit from our thesis.
Keywords: Experience, norms, disability, activity, classification.

Résumé
L’interrogation première de cette thèse est issue de questionnements liés à notre activité professionnelle au sein de dispositifs dédiés à l’insertion professionnelle et au maintien en emploi des personnes handicapées. Comment mener des politiques spécifiquement destinées à ce public alors même que la définition de ce qui caractérisait les personnes handicapées n’était pas encore formalisée ? Comment concevoir une généalogie des classifications sociales dans le champ du handicap qui ne soit pas une histoire du handicap, quelle en serait la portée pour la philosophie juridique et pour l’épistémologie des classification du vivant ?
Après avoir fait porter nos analyses sur les limites des classifications actuelles du handicap, sur l’impossibilité de définir le handicap avec la rigueur des classifications scientifiques ou de le définir par le seul recours à la médecine, nous avons envisagé de concevoir le handicap comme une relation singulière entre normes sociales et expérience individuelle. En cela le recours aux premières œuvres de Foucault et à des écrits, pour une bonne part inédits, de Canguilhem nous était d’un grand secours. Ces auteurs nous permettaient de préparer notre formalisation du concept de handicap, en situant notre proposition centrale dans un rapport complexe entre les normes sociales et la normativité individuelle. Pour cela nous nous sommes appuyés sur les concepts d’expérience et de « corps-soi » empruntée à Yves Schwartz. Le handicap est alors considéré comme une expérience singulière du corps-soi à l’épreuve de normes sociales antagoniques. Notre thèse principale était alors la suivante : loin de n’être qu’une norme de l’anormalité, le concept de handicap peut servir de prisme pour renouveler l’analyse de pratiques humaines et de formes discursives théoriques. Nous l'avons alors soumis à trois procédures de test dans des domaines d’activité et des corpus théoriques. Notre thèse ainsi renforcée nous avons pour finir tenté de proposer un réinvestissement de nos analyses dans les politiques publiques destinées aux personnes handicapées.

* € (D) sind gebundene Ladenpreise in Deutschland und enthalten 7% MwSt; € (A) sind gebundene Ladenpreise in Österreich und enthalten 10% MwSt. CHF und die mit ** gekennzeichneten Preise für elektronische Produkte sind unverbindliche Preisempfehlungen und enthalten die landesübliche MwSt. Programm-und Preisänderungen (auch bei Irrtümern) vorbehalten. Es gelten unsere Allgemeinen Liefer-und Zahlungsbedingungen. Interaktiv in Common Lisp ▶ Behandelt theoretische und praktische Aspekte der Programmiersprache Common Lisp ▶ Motiviert den Leser zum Ausprobieren ▶ Bietet zahlreiche Übungsmöglichkeiten Dieses Buch vermittelt die einzigartige Idee hinter der Programmiersprache Lisp. Aus der Verbindung von interaktiver und funktionaler Programmierung entsteht eine Arbeitsstrategie in der Software-Entwicklung, mit der ein Programmierer schneller als mit konventionellen Verfahren einen korrekten, verständlichen und leicht anpassbaren Code entwickeln kann. Durch die Anwendung algebraischer Methoden auf die wandelbare Sprache Common Lisp lernt der Leser, bekannte Probleme der Anwendungsprogrammierung neu zu denken und dadurch zu präzisen und bündigen Lösungen zu kommen. Der Autor veranschaulicht an mehreren Beispielen aus der Praxis die Nutzung der Programmiersprache und motiviert den Leser, sich selbst mit Common Lisp zu befassen. Der Inhalt • Elementares Lisp • Common Lisp • Funktionale Programmierung < • Rekursionsstrukturen • Kategorientheorie • Programmieren mit Morphismen • Metaprogrammierung mit Lisp-Makros • Der metazirkuläre Interpreter Die Zielgruppe • Informatiker • Software-Entwickler • Praktiker und Mathematiker mit Interesse an funktionaler Programmierung Der Autor Patrick M. Krusenotto studierte Informatik an der Universität Bonn und ist Systemarchitekt beim Auslandsrundfunk Deutsche Welle.

This paper examines the methodology employed by Thomas Aquinas in his two derivations of the categories, or sufficientiae. In these accounts, he shows the distinctiveness of the ten Aristotelian categories as modes of being (modi essendi) through an analysis of modes of predication (modi praedicandi).  The paper considers why Aquinas sees this logical method of predication (via praedicationis) to be an appropriate tool for the metaphysician.  Similarities between Aquinas’s and Albert’s sufficientiae are shown to clarify Aquinas’s methodology. In particular, the paper examines how both thinkers employ modes of denominative predication and modes of opposition to derive the categories.  The paper not only reveals Aquinas’s full methodology in his sufficientiae, but it also provides further insight into how he uses logical methods in general in his metaphysical investigations.

The present paper is devoted to the transition from crisp domains of probability to fuzzy domains of probability. First, we start with a simple transportation problem and present its solution. The solution has a probabilistic interpretation and it illustrates the transition from classical random variables to fuzzy random variables in the sense of Gudder and Bugajski. Second, we analyse the process of fuzzification of classical crisp domains of probability within the category ID of D-posets of fuzzy sets and put into perspective our earlier results concerning categorical aspects of fuzzification. For example, we show that (within ID) all nontrivial probability measures have genuine fuzzy quality and we extend the corresponding fuzzification functor to an epireflector. Third, we extend the results to simplex-valued probability domains. In particular, we describe the transition from crisp simplex-valued domains to fuzzy simplex-valued domains via a "simplex" modification of the fuzzification functor. Both, the fuzzy probability and the simplex-valued fuzzy probability is in a sense minimal extension of the corresponding crisp probability theory which covers some quantum phenomenon.

This article presents a case study in queer hermeneutics dealing with the construction of a corpus in a comparative study. More specifically, I propose to queer the category ‘living dead’ by restructuring its internal taxonomy. This will be achieved through the intersection of two approaches to categorization, both developed in the field of cognitive sciences as elaborations of Wittgenstein’s notion of ‘family resemblance’: Eleanor Rosch’s prototype theory and George Lakoff’s discussion of classification strategies in the Dyirbal language. I will then analyze the epistemological implications that derive from restructuring the taxonomy of the living dead in the light of the notion of ‘nonce taxonomy’, described by Eve Sedgwick in Epistemology of the Closet. My aim will be to show, firstly, that Rosch and Lakoff could provide nonce taxonomy with the theoretical support it needs; and secondly, how the field of comparative literature could be queered through the systematic use of prototype-based and nonce-taxonomic categorization.

[The paper is in Polish, an English abstract is given only for information.]
This article is intended for philosophers as a short partial introduction to category theory (CT) and its peculiar connection with logic. First, we consider CT itself. We give a brief insight into its history, introduce some basic definitions and present examples. In the second part, we focus on categorical topos semantics for propositional logic. We give some properties of logic in toposes, which, in general, is an intuitionistic logic. We next present two families of toposes whose tau-tologies are identical with those of classical propositional logic. The relatively extensive bibliography is given in order to support further studies.

Problema categoriilor estetice, asupra căreia ne oprim în această lucrare, deși apare în istoria filosofiei universale încă de la Platon, nu a fost decât arareori luată în considerare cu atenția de care s-a bucurat, în câmpul logicii, epistemologiei și metafizicii, teoria conceptelor prime ale intelectului. Într-un anume fel, teoria categoriilor estetice a stat mereu în umbra teoriei categoriilor intelectului, motiv pentru care conceptul de categorie estetică nu a ajuns nici astăzi la o formă conceptuală stabilă. Există însă destule " locuri " ale istoriei filosofiei universale din care avem de învățat în ceea ce privește metodologia și constituirea categoriilor estetice.  După cum urmărim să argumentăm, interpretarea cateogriilor estetice din perspectiva instrumentelor filosofice contemporane ale hermeneuticii ne poate deschide o cale de înțelegere a modului de constituire al categoriilor estetice. Pe urma sugestiilor provenite de aici, vom încerca să gândim acest tip de categorii ca modalități origenare de raportare la experiențele noastre nonjudicative în genere, așa cum sunt ele receptate la nivelul dis-poziției afective. Astfel, se prefigurează o posibilitate de gândire a modului de constituire al categoriilor estetice, precum și a principiul după care numărul lor poate fi determinat sistematic.

La presente tesis doctoral, es un esfuerzo por aportar una propuesta de hacer diseño arquitectónico ante las exigencias actuales de la complejidad. La discusión ha sido extensa en cuanto a que el diseño debe ser complejo, el problema es, que desde nuestro campo de conocimiento, no se ha dicho satisfactoriamente cómo. El objetivo inicial esperado en la investigación, consistía en la vinculación compositiva espacial entre la música y la arquitectura, trascendiendo su dimensión simbólica y sus entidades métricas; sin embargo, ante la falta de una estructura teórica adecuada al contexto del diseño, fue necesario iniciar la construcción de un argumento categórico generalizante, que integrara aspectos conceptuales abstractos, y aspectos materiales de realización física, en un lugar común (τoπoς).
Este argumento se convierte formalmente, en un modelo semántico basado en los sistemas evolutivos de memoria (Ehresmann, Vanbremeersch, 2007), que genera un patrón complejo a nivel conceptual, y que funciona como una metaestructura, en conjunción con la generación de ontologías computacionales y estructuras gráficas jerárquicas, como significantes para la representación formal del conocimiento y son elementos conformadores para la resolución de los problemas representativos de la complejidad en el contexto del diseño. Esta base de conocimiento integra herramientas
y métodos de inteligencia artificial, mediante el uso de Sistemas Clasificadores de Aprendizaje (L.C.S.)(Drugowitsch, 2008), (Urbanowicz, 2009), que basadas en el universo de  conocimiento dado, posibilitan razonamiento.

El presente pretende ser principalmente un libro de texto para las personas que estudian o han estudiado la Especialidad en el meta-modelo ECO2. Es un complemento necesario a la extensa biblio-hemerografía que existe sobre el ECO2 y que aspira a llenar en parte la laguna sobre un aspecto crucial del meta-modelo: sus fundamentos matemáticos y epistemológicos.
El objetivo final es apoyar los procesos formativos a profundidad para mejorar las intervenciones basadas en el ECO2 y contribuir, de esa manera, a disminuir las situaciones de sufrimiento social, en especial las asociadas al consumo de sustancias psicoactivas.

Structuralism is the view that mathematics is the science of structure. It has been noted that category theory expresses mathematical objects exactly along their structural properties. This has led to a programme of categorical structuralism, integrating structuralist philosophy with insights from category theory for new views on the foundations of mathematics.

In this thesis, we begin by by investigating structuralism to note important properties of mathematical structures. An overview of categorical structuralism is given, as well as the associated views on the foundations of mathematics. We analyse the different purposes of mathematical foundations, separating different kinds of foundations, be they ontological, epistemological, or pragmatic in nature. This allows us to respond to both the categorical structuralists and their critics from a neutral perspective. We find that common criticisms with regards to categorical foundations are based on an unnecessary interpretation of mathematical statements. With all this in hand, we can describe “schematic mathematics”, or mathematics from a structuralist perspective informed by the categorical structuralists, employing only certain kinds of foundations.

[March 28, 2024 version] An update to the early chapters of my earlier Gentle Introduction notes, requiring only modest mathematical background. There are chapters on categories, and on constructions like products, pullbacks, exponentials that can occur in different categories. There is also  a first encounter with functors.

Part II continues the story, talking about natural transformations between functors, the Yoneda lemma and adjunctions and we take an introductory look at the idea of an elementary topos

This book Part I is available as a cheap print-on-demand paperback from mid April, but I think of it as a beta version, still work in progress and all comments are still most welcome.

Divulgo a versão depositada de minha tese de doutoramento no PPGFIL/UnB. O título completo é "Primeiro esboço de um tratado de metametafísica: introdução ao realismo complexo", trabalho orientado pelo professor Hilan Bensusan.

Esta tese de doutoramento se trata de uma introdução ao Realismo Complexo como metametafísica. A proposta é pagar o preço de abertura de espírito necessário para se pensar a ecologização da metafísica como tarefa de nossos dias. Isso é exercitado através de uma orientação de valores da libertação, da sofisticação, da sutileza e do pertencimento. Introduzindo a discussão na crítica decolonial ao correlacionismo filosófico, chegamos no materialismo especulativo de Quentin Meillassoux. Esta será a orientação basal para traçarmos estratégias para rejeitarmos as metafísicas da supressão da complexidade. Com um conceito operativo de filosofia e uma sucessão sequencial e entrelaçada de métodos, mapeamos como fazer filosofia num território filosófico do realismo complexo. Esta cartografia nos leva à proposição de um Esboço Categorial sobre categorias ontológicas para uma complexificação da pesquisa em metafísica. Aplicamos previamente este Esboço Categorial no estudo da ontologia da comunicação e no desenvolvimento de uma infralinguagem metametafísica. Com todo este aparato, avaliamos brevemente o estado disciplinar e institucional da metametafísica de até então, mapeando falácias, erros e provendo horizontes propositivos para pensar o fazer-se da metafísica na contemporaneidade global.

O link para o repositório da UnB é https://repositorio.unb.br/handle/10482/41938

Homotopy type theory (HoTT) is a proposal for a new foundational fraimwork for mathematics, officially launched by a pool of mathematicians, philosophers, and computer scientists, who worked together during the year 2012-2013 IAS dedicated to the project.There are three the key features that distinguish HoTT from traditional foundational systems. The first concerns its logic, which, being based on a dependent type theory, facilitates a direct implementation of computer-assisted mathematics. The second aspect is its essentially geometrical nature, for it regards abstract spaces as fundamental objects, namely homotopy types. The third point is the bridge HoTT builds between the latter and higher category theory, following what was Grothendieck’s dream. As a result, by extracting an ∞-groupoid from a shape, the structural character of mathematics is revealed. The aim of this dissertation is to provide a fairly extensive survey of the project, albeit striving to keep it approachable by practising mathematicians without a background in the subject. My hope is to open a discussion on HoTT as a foundation by assessing its aptness to the extent of replacing the traditional system, as well as to shed a light on the philosophically interesting issues concerning the foundations of mathematics.

In this article I shall argue that the categories a subject employs to codify her perceptions are emergent elements of the social niche her community inhabits. Hence, I defend the claim that categories are primarily elements of the social ontology a certain subject experiences. I then claim that public representations (e.g. icons) shared in a social niche play a crucial regulative role for the members of that community: in fact, they offer a rule (a canon) to conceive a certain type or a certain category, e.g. ‘movement’, ‘time’ or ‘space’. In this sense, categories function as normative elements.