Incompleteness

A close reading of two paintings:

1. One poem draws on Escher’s Self Portrait lithograph by showing that the only way the  drawing avoids succumbing to infinite regress is by remaining incomplete.

2. The other poem responds to Magritte’s Key of Dreams: a surreal collection of object with mismatching nouns by teasing out relationships in a maneuver akin to dream interpretation.

International Gallerie Vol.13 No.2 2010 pg.52-55

In the recent literature we find various arguments against the possibility of absolutely general quantification. Far from being merely a technical question in the philosophy of logic, the impossibility of absolutely general quantification (if established) would have severe consequence for ontology, for it would imply the non-existence of the world as traditionally conceived. This paper will investigate these implications for ontology and consider some possible ways of addressing them.

On pense généralement que l'impossibilité, l'incomplétdulité, la paracohérence, l'indécidabilité, le hasard, la calcul, le paradoxe, l'incertitude et les limites de la raison sont des questions scientifiques physiques ou mathématiques disparates ayant peu ou rien dans terrain d'entente. Je suggère qu'ils sont en grande partie des problèmes philosophiques standard (c.-à-d., jeux de langue) qui ont été la plupart du temps résolus par Wittgenstein plus de 80 ans.
Je fournis un bref résumé de quelques-unes des principales conclusions de deux des plus éminents étudiants du comportement des temps modernes, Ludwig Wittgenstein et John Searle, sur la structure logique de l'intentionnalité (esprit, langue, comportement), en prenant comme point de départ La découverte fondamentale de Wittgenstein, à savoir que tous les problèmes véritablement « philosophiques » sont les mêmes, les confusions sur la façon d'utiliser la langue dans un contexte particulier, et donc toutes les solutions sont les mêmes— en regardant comment la langue peut être utilisée dans le contexte en cause afin que sa vérité (Conditions de satisfaction ou COS) sont claires. Le problème fondamental est que l'on peut dire n'importe quoi, mais on ne peut pas signifier (état clair COS pour) toute déclaration arbitraire et le sens n'est possible que dans un contexte très spécifique.
Je dissé que quelques écrits de quelques-uns des principaux commentateurs sur ces questions d'un point de vue wittgensteinien dans le cadre de la perspective moderne des deux systèmes de pensée (popularisé comme «penser vite, penser lentement»), en utilisant une nouvelle table de intentionnalité et la nomenclature de nouveaux systèmes doubles. Je montre qu'il s'agit d'un puissant heuristique pour décrire la vraie nature de ces questions scientifiques, physiques ou mathématiques putatives qui sont vraiment mieux abordés comme des problèmes philosophiques standard de la façon dont la langue doit être utilisée (jeux de langue dans Wittgenstein terminologie).

Em anterior volume (José Régio, il poeta di Dio e del Diavolo, Parma, MUP, 2003), Enrico Martines apresentara a edição crítico-genética de duas importante recolhas poéticas publicadas em vida pelo autor do "Cântico Negro" (Poemas de Deus e do Diabo, 1926, e Mas Deus é Grande, 1945), observando, através da análise dos respectivos materiais preparatórios, a aplicação dos processos de depuração estilística e conceptual dos poemas que, desde o primeiro rascunho, se desenvolveram com vistas à sua proposta ao público (reiterada, no caso da primeira recolha, em diversas edições revistas pelo autor). Com a presente edição, o estudioso italiano quer completar a sua incursão na oficina poética de José Régio através da proposta e do estudo do que ficou “dentro da gaveta do poeta”, por não satisfazer os seus severos critérios de exigência.
O material poético reunido e analisado tem natureza dúplice:
1) em primeiro lugar, são apresentados 121 poemas publicados de forma esparsa em revistas e jornais, mas nunca reunidos em livro por Régio, tendo ficado, portanto, fora do seu cânone; a sua leitura permite a análise dos critérios e dos motivos que levaram à sua exclusão, além de sugerir a sua possível aproximação às recolhas publicadas em que, por razões cronológicas, temáticas e formais, poderiam figurar;
2) secundariamente, o volume propõe 79 textos poéticos que o autor abandonou, não os considerando, por uma razão ou por outra, dignos de serem propostos ao público, nem mesmo merecedores de um labor de ulterior acabamento. Trata-se de material que apresenta diferentes níveis de elaboração, desde poemas formados e com título até fragmentos isolados, o que põe o estudioso perante o problema do inacabamento da escrita literária e sugere uma apreciação das considerações que levaram José Régio a abandonar a expressão daqueles motivos poéticos, possivelmente desenvolvidos em outras composições publicadas.
A edição é prefaciada por Ivo Castro.

What would be the consequences for Godel's incompleteness theorems if there were an error in the proofs? Elaborating on this question, an error posited in proposition V would lead in in proposition VI (first incompleteness theorem) to two contradictory implications. Moreover, it can be shown that these would lead to a paradoxical formula. While Godel theorised that the mathematical system is undecidable, the converse, the inconsistency of the mathematical system can be considered to be a corollary.

When the principle of explosion is applied to paradoxical premises any conclusion can be implied regarding consistency. Accordingly, proposition XI (second incompleteness theorem) implies a number of contradictory solutions for the status of the consistency of the mathematical system as described by classical logic, and also by U4. As a result, Godel " s incompleteness theorems cannot be viewed as proven.

This work presents some demonstrations of the consistency of classical arithmetic, proven by Gödel (1931), as being arithmetically unprovable. First, we demonstrate consistency based on a proof by Schütte (1951), a proof similar to Gentzen, which is built by transfinite induction and allows an infinitary rule of inference. We present new concepts, definitions and theorems. In the next part, we use reflection principles and the Paris-Harrington combinatorial principle to show that consistency can be obtained by recursive extensions. These are true extensions in the logical-mathematical sense, using methods beyond Peano axiomatic. Finally, we discuss problems and issues that still remain on the mathematical, logical and philosophical foundations of the addressed subjects. If we really prove the arithmetic´s consistency, upon which bases are we able to present it? Would we not be based on other assumptions, hidden or not, to achieve such results? Are all of these proofs still computable?

In questo saggio analizzo tre concetti di incompletezza in tre distinte prospettive: (i) incompletezza biologica (Antropologia culturale); (ii) incompletezza tecnica (Filosofia morale); (iii) incompletezza bioetica (Biodiritto). Nessuno dei tre concetti di incompletezza presi in esame attiene all’incompletezza normativa, la quale sussiste quando un sistema giuridico non comprende né la norma che proibisce un certo comportamento, né la norma che lo permette; cionondimeno, ciascun concetto di incompletezza considerato rivela una certa importanza per la Filosofia del diritto.

This commentary advances "incompleteness" as an explanatory category for infrastructure processes that do not yield or conform to standard ideals, and a corrective to interventions that regard everything that does not appear to yield or conform as failed. Incompleteness offers a useful lens for approaching infrastructures through situated, contingent, and embodied dimensions. It permits a proper reading of infrastructure as transient, and infrastructure development as a process that is affected not solely by neoliberal interventions but also sociomaterial practices and inscriptions. As such, incompleteness transcends conventional and completist frames, and complements theorizations of infrastructure since Graham and Marvin's Splintering Urbanism.

This paper claims that the use of the computer as generative methodological tool for designing urban and building scenarios (when perceived systematically) is a misnomer, because the typical approach does not account for the incompleteness of computational processes. We will argue that the computerisation of architectural and urban scenarios with autopoietic and/or artificial life simulations does not account for what Edsger W. Dijkstra called “radical novelty”; and Gilles Deleuze termed “line of flight”. Typical computational methods do not open up genuine alternatives that produce radical morphologies. Our argument is predicated on the dominant notion of computation as opposed to a critique of computation per se. A critical analysis of the perception of novelty is made to support our view, and its connection with the incompleteness of axiomatic systems is explored in relation to three phases of cybernetic enquiry. Our argument draws on the ontologies of Alfred North Whitehead and Gilles Deleuze, which we utilise to reorient computational design to emphasise the potential of generating radical novelty and identify the inherent locus therein a matter of nonhuman decision-making.

We briefly discuss ideas about computable economics, and comment on the contributions of A.A. Lewis and K.V. Velupillai.We then sketch the mathematical background for the Tsuji et al. (Tsuji, M., da Costa, N.C.A., Doria, F.A., 1998. The incompleteness of theories of games.
Journal of Philosophical Logic 27, 553–564) result on the undecidability and incompleteness of game theory and of the theory of competitive markets, using that result in the  concluding sections of the paper to examine the (possible) empirical interpretation of economic and
social systems as computing devices

This article offers a fundamental re-evaluation of Thomas Traherne's writing style through an examination of the typographic, calligraphic, and syntactic features of his texts as well as through a consideration of select topoi. In juxtaposing poems in Traherne's and his brother's hands, the article argues that Thomas' method of composition is founded on the centrifugal rather than centripetal forces of writing in order to produce generative texts which are manifested in the unfinished state of most of his works. This helps us to identify the genre of the non-finito as a genre which privileges the act of reading in rather than reading through as well as the practice of writing rather than the theory of writing. [ABSTRACT FROM AUTHOR]

Essentialism manifests itself in a diversity of forms and is used in multiple ways. Yet it is always potentially dangerous — even when it is mobilised strategically and in apparently worthy forms for purposes of overcoming oppressive structures. As the first in a collection of articles focused on various manifestations of essentialism, this article offers a brief historical outline of how social anthropology deployed essentialist thinking, even amongst its canonical exponents. It examines how Durkheimian theorisations and the structuralist traditions to which they gave rise — in particular assumptions of the singular and homogeneous symbolic classification of society — lent themselves to essentialism. It considers the example of South Africa where essentialist social theories contributed to inhumane political formations. Given that essentialism always carries a latency to be used for pernicious ends, the article concludes by considering social anthropological approaches that might permit an understanding of individuals and society in ways that neither lead to nor need essentialist thinking, and instead recognise the contradictoriness, flux and incompleteness inherent in social life.

unfinished (1400-1800)

What is a work unfinished? This panel seeks papers that critically probe this inquiry through early modern exempla of art, architecture, writing on art, and objects of visual culture considered unfinished. Small and multivalent case studies are equally invited, which investigate single objects, art projects, or entire oeuvres labelled not finished, here broadly conceived. Papers can also consider: is unfinished a formal, theoretical, symbolic, or contextual state of being? What or who decides on the criteria of the unfinished? Can an object go from being unfinished to finished? Does unfinishedness accrue value over time? And, finally, can any artistic product of the epoch be considered finished in the longue-durée of history? Proposals of up to 300 words should be sent using the UAAC " Call for Papers" form to Ivana Vranic by July 15.

Almost every Greek or Roman building, whose above-ground architecture is at least partially preserved, exhibits signs of incompleteness, mostly in form of undecorated mouldings or unfinished surfaces. Comprehensive studies devoted to this well-known phenomenon are still pending though. Hans Lauter’s article ‘Künstliche Unfertigkeit. Hellenistische Bossensäulen’ (1983) and Thanassis E. Kalpaxis’ monograph ‘Hemiteles. Akzidentelle Unfertigkeit und “Bossenstil” in der griechischen Baukunst’ (1986) were primarily focused on the definition of incompleteness and on the potential of unfinished stages for the development of accepted new architectural forms. Unfinished details are often discussed in publications concerning single buildings and in many cases the authors are proposing individual reasons which may indeed sometimes have played a role: the imminent visit of the Emperor, changing priorities for the use of available resources or death of the builder-owner, etc. Such reasons can however hardly explain the ubiquitous phenomenon of incompleteness, and therefore one should rather look for ‘system errors’ in all areas of ancient architectural construction.

Nahezu jedes griechische oder römische Gebäude, dessen aufgehende Architektur wenigstens ausschnittsweise erhalten ist, weist Unfertigkeiten auf. Diesem an sich wohlbekannten Phänomen sind bisher kaum umfassende Studien gewidmet worden. Auch Hans Lauters Aufsatz ,Künstliche Unfertigkeit. Hellenistischen Bossensäulenʻ von 1983 (JdI 98, 287–310) und Thanassis E. Kalpaxis’ Monographie ,Hemiteles. Akzidentelle Unfertigkeit und „Bossenstil“ in der griechischen Baukunstʻ von 1986 haben vor allem die Definition von Unfertigkeit und ihr Potential für das Entstehen akzeptierter neuer Architekturdetails im Blick. Die Unfertig-keiten einzelner Bauten werden zudem in zahlreichen Architekturpublikationen behandelt, und immer wieder wird nach individuellen Gründen, die es hier und da auch tatsächlich gege-ben haben wird, für die jeweilige Unfertigkeit gesucht: Ein Bauherr kann verstorben sein, ein Kaiserbesuch stand an, die Prioritäten für die Nutzung der vorhandenen Ressourcen änderten sich etc. Das Phänomen der Unfertigkeit tritt jedoch zu oft auf, als dass es insgesamt mit sol-chen Einzelbegründungen zu erklären wäre. Abgesehen davon, dass nach wie vor zu fragen ist, was zu welcher Zeit als unfertig galt oder als neue, aus Relikten des Werkprozesses hervorgegangene Form akzeptiert wurde, ist also ist also nach ,Systemfehlernʻ in allen Bereichen des antiken Bauwesens zu suchen.

यह आमतौर पर सोचा जाता है कि असंभवता, अपूर्णता, Paraconsistency, अनिर्णितता, Randomness, Computability, विरोधाभास, अनिश्चितता और कारण की सीमा अलग वैज्ञानिक शारीरिक या गणितीय मुद्दों में कम या कुछ भी नहीं कर रहे हैं आम. मेरा सुझाव है कि वे काफी हद तक मानक दार्शनिक समस्याओं (यानी, भाषा का खेल) जो ज्यादातर 80years पहले Wittgenstein द्वारा हल किए गए थे.

"क्या हम 'इस तरह के एक मामले में कहने के लिए' कर रहे हैं, ज़ाहिर है, दर्शन नहीं है, लेकिन यह अपने कच्चे माल है. इस प्रकार, उदाहरण के लिए, क्या एक गणितज्ञ वस्तुपरकता और गणितीय तथ्यों की वास्तविकता के बारे में कहने के लिए इच्छुक है, गणित का दर्शन नहीं है, लेकिन दार्शनिक उपचार के लिए कुछ है। विटगेनस्टीन पीआई 234

"Philosophers लगातार उनकी आँखों के सामने विज्ञान की विधि को देखने और irresistibly पूछने के लिए और जिस तरह से विज्ञान करता है में सवालों के जवाब परीक्षा कर रहे हैं. यह प्रवृत्ति तत्वमीमांसा का वास्तविक स्रोत है और दार्शनिक को पूर्ण अंधकार में ले जाती है।  विटगेनस्टाइन

मैं आधुनिक समय के व्यवहार के सबसे प्रतिष्ठित छात्रों में से दो के प्रमुख निष्कर्षों में से कुछ का एक संक्षिप्त सारांश प्रदान करते हैं, लुडविग Wittgenstein और जॉन Searle, जानबूझकर की तार्किक संरचना पर (मन, भाषा, व्यवहार), मेरे प्रारंभिक बिंदु के रूप में ले रही Wittgenstein की मौलिक खोज - कि सभी सही मायने में 'लोकप्रिय' समस्याओं को एक ही हैं एक विशेष संदर्भ में भाषा का उपयोग करने के बारे में भ्रम, और इसलिए सभी समाधान एक ही हैं-कैसे भाषा के संदर्भ में इस मुद्दे पर इस्तेमाल किया जा सकता है पर देख इतना है कि इसकी सच्चाई शर्तें (संतोष या COS की शर्तें) स्पष्ट हैं. मूल समस्या यह है कि एक कुछ भी कह सकते हैं, लेकिन एक मतलब नहीं कर सकते (राज्य स्पष्ट COS के लिए) किसी भी मनमाने ढंग से कथन और अर्थ केवल एक बहुत ही विशिष्ट संदर्भ में संभव है.

मैं सोचा की दो प्रणालियों के आधुनिक परिप्रेक्ष्य के ढांचे में एक Wittgensteinian दृष्टिकोण से इन मुद्दों पर प्रमुख टिप्पणीकारों में से कुछ के कुछ लेखन विच्छेदन (के रूप में लोकप्रिय 'तेजी से सोच, धीमी गति से सोच'), की एक नई मेज रोजगार जानबूझकर और नई दोहरी प्रणाली नामकरण.  मैं बताता हूँ कि यह इन putative वैज्ञानिक, शारीरिक या गणितीय मुद्दों जो वास्तव में सबसे अच्छा कैसे भाषा का इस्तेमाल किया जा रहा है के मानक दार्शनिक समस्याओं के रूप में संपर्क कर रहे हैं की सही प्रकृति का वर्णन करने के लिए एक शक्तिशाली heuristic है (Witgenstein में भाषा का खेल शब्दावली)

यह मेरा तर्क है कि जानबूझकर की मेज (तर्कसंगतता, मन, सोचा, भाषा, व्यक्तित्व आदि) है कि यहाँ प्रमुखता से सुविधाएँ अधिक या कम सही वर्णन करता है, या कम से कम के लिए एक heuristic के रूप में कार्य करता है, हम कैसे सोचते हैं और व्यवहार करते हैं, और इसलिए यह शामिल नहीं केवल दर्शन और मनोविज्ञान, लेकिन सब कुछ (इतिहास, साहित्य, गणित, राजनीति आदि). ध्यान दें कि विशेष रूप से जानबूझकर और तर्कसंगतता के रूप में मैं (Searle, Wittgenstein और अन्य लोगों के साथ) यह देखने के लिए, दोनों सचेत विचार विमर्श भाषाई प्रणाली 2 और बेहोश स्वचालित prelinguistic प्रणाली 1 कार्रवाई या सजगता भी शामिल है.

Riprendendo le riflessioni sulle differenti modalità con cui poesie di epoche diverse marcano la loro conclusione indagate da Barbara Herrnstein Smith in "Poetic Closure: A Study of How Poems End" (1968), sulla circolarità che il testo lirico innesca nell’atto di lettura proposta da Timothy Bahti in "Ends of the Lyric: Direction and Consequence in Western Poetry" (1996) e sul carattere queer che l’incompiutezza può assumere rivendicato in "Queer Lyrics: Difficulty and Closure in American Poetry" (2002) di John Emil Vincent, l’articolo  vuole indagare, attraverso  Wallace Stevens, Eugenio Montale, Louise Glück e John Ashbery, in che modo la poesia contemporanea si faccia carico dell’incompiutezza. L’ipotesi è che, se per secoli questa incompiutezza è stata anche un grande tema della poesia – si pensi soltanto all’incongruenza tra la chiusura formale del testo della poesia medievale e rinascimentale e la ribadita impossibilità di una perfetta rappresentazione dell’oggetto d’amore – dal Modernismo in poi la lirica non rinunci a intraprendere il suo percorso, ma assuma consapevolmente su di sé l’errore facendone il principio strutturante del proprio discorso. Il cerchio che non chiude diventa allora una forma specifica della temporalità per la lirica (e per il lettore) che non insegue il successo del percorso lineare, ma accoglie l’errore insito nel suo sforzo per accettare di praticare un’approssimazione infinita e per maturare coscienza della propria pratica. La non compiutezza della poesia, infine, potrebbe essere proprio quel che assicura la ripetibilità del testo. Partendo dal valore centrale che l’iteratività formale della lirica assume nel recente "Theory of the Lyric" (2015) di Jonathan Culler, nell’ultima parte l’articolo costruisce un’ipotesi sulle ragioni per cui proprio il fatto che la poesia, come artefatto, debba concludersi senza necessariamente compiersi interamente consente al testo lirico di presentarsi come performance ripetibile attraverso i secoli e rinnovabile a ogni atto di lettura.

I summarise a conception of morality as containing a set of rules which hold ceteris paribus and which impose pro-tanto obligations. I explain two ways in which moral rules are ceteris-paribus, according to whether an exception is duty-voiding or duty-overriding. I defend the claim that moral rules are ceteris-paribus against two qualms suggested by Luke Robinson’s discussion of moral rules and against the worry that such rules are uninformative. I show that Robinson’s argument that moral rules cannot ground pro-tanto obligations is unsound, because it confuses an absolute reason for an obligation with a reason for an absolute obligation, and because it overlooks the possibility that priority rules may be rules for ordering pro-tanto obligations rather than rules for eliminating contenders for the status of absolute obligation.

... Proposition 3.5 There is a noncooperative game View the MathML source with a finite number of players and a set of outcomes u 0 so that the sentence “ View the MathML source has u 0 as a Nash equilibrium” can neither be proved nor disproved from the axioms of S. ...

나는 컴퓨터로 계산과 우주의 한계에 대한 많은 최근의 토론을 읽었습니다, polymath 물리학자 및 결정 이론가 데이비드 울퍼트의 놀라운 작품에 대한 몇 가지 의견을 찾을 수 있기를 바라고 있지만 하나의 인용을 발견하지 않은 그래서 나는이 매우 간단한 요약을 제시. Wolpert는 계산을 수행하는 장치와 는 별개이며 물리학법칙과는 무관하므로 컴퓨터, 물리학 및 인간의 행동에 적용되므로 추론(계산)에 대한 제한에 대해 놀라운 불가능또는 불완전성 정리(1992년에서 2008년 참조 arxiv.org)를 입증했습니다. 그들은 캔터의 대각선화, 거짓말쟁이 역설 및 세계관을 사용하여 튜링 머신 이론의 궁극적 인 정리가 될 수있는 것을 제공하고, 겉보기에 불가능, 불완전성, 계산의 한계, 그리고 컴퓨터로서의 우주, 가능한 모든 우주와 모든 존재 또는 메커니즘에서, 생성, 비 양자 기계적 불확실성 및 증거. 차이틴, 솔로모노프, 코몰가로프, 비트겐슈타인의 고전 적 작품과 어떤 프로그램 (따라서 어떤 장치)이 소유보다 더 큰 복잡성시퀀스 (또는 장치)를 생성 할 수 없다는 개념에 명백한 연결이 있습니다. 이 작품의 몸은 물리적 우주보다 더 복잡한 어떤 실체가 있을 수 없고 비트겐슈타인의 관점에서 볼 때 '더 복잡한'은 의미가 없다고 말할 수 있습니다(즉, 진리를 제작자나 시험하는 조건은 없습니다). 심지어 '신'(즉, 무한한 시간과 에너지를 가진 '장치')은 주어진 '숫자'가 '무작위'인지 여부를 결정할 수없으며, 주어진 '수식', '정리' 또는 '문장' 또는 '장치'(이 모든 것이 복잡한 언어 게임)가 특정 '시스템'의 일부임을 보여줄 수 있는 특정 방법을 찾을 수 없습니다.
현대 의 두 systems보기에서인간의 행동에 대한 포괄적 인 최신 프레임 워크를 원하는 사람들은 내 책을 참조 할 수 있습니다'철학의 논리적 구조, 심리학, 민d와 루드비히 비트겐슈타인과 존 Searle의언어' 2nd ed (2019). 내 글의 더 많은 관심있는 사람들은 '이야기 원숭이를 볼 수 있습니다-철학, 심리학, 과학, 종교와 운명 행성에 정치 - 기사 및 리뷰 2006-2019 2nd 에드 (2019) 및 21st 세기 4번째 에드 (2019) 및 기타.

Two sonnets, two compliments, one man. Or, could he be one man and merit such divergent compliments? – Giovanni Battista Strozzi in his sonnet claimed that this 'man', alone, had vanquished all others, even Phidias, Apelles and their worthy followers: titans not painters. (" Tutti altri, e vince Fidia e vince Apelle,/ e tutto lor vittoriosi stuolo ") – Gian Piero Lomazzo, on the other hand, pitched on Protogenes, another mythical artist, suggesting that this 'man' was his equal: the equal of Protogenes, who mythically, never lifted his brush from his work. And this 'man' equaled him, says Lomazzo, by never finishing anything at all. (" Di cui opra non è finite pure ") Reflecting on Leonardo Da Vinci's work is like staring down a cul de sac, one where the wall is blind because it reflects the path that leads up to it. Leonardo's paintings are in many ways mirror-like and reflected Leonardo upon Leonardo. Perhaps that is why this raptness of Leonardo became an impasse that posterity has wrestled with. Giorgio Vasari, whose portrait of Leonardo Da Vinci in Lives of Artists is more in awe than critical of its subject, (an unusual thing in his work), stated, rather tamely, that it was because of his profound knowledge of painting that Leonardo started so many things without finishing them. Vasari explained that Leonardo was convinced that his hands, for all their skill, could never perfectly express the subtle and wonderful ideas of his imagination. All this ebb and flow of conviction was slow work indeed. — In the Convent of Santa Maria delle Grazie in Milan, Matteo Bandelli a contemporary and a fabulist, who was a young monk at the time, reported that Leonardo, while painting the Last Supper, used to climb up the scaffolding early in the morning and remain there till twilight contemplating the incomplete painting below. This would continue for days. Coupled with this notorious slowness was the tendency, at the peak of his powers, to stop painting altogether in favour of whimsical though compelling scientific forays. Leonardo's withdrawal from his art was accounted for by Sigmund Freud in his intriguing thesis, Leonardo da Vinci: A Memoir of His Childhood, as being the result of acute sexual repression, by which he implied that a conversion of physical instinctual force into various forms of activity can perhaps no more be achieved without loss than a conversion of physical forces. Freud's view culminated in his assertion that Leonardo da Vinci had not embraced a woman with passion in his life, unlike his great rival Michelangelo Buonarotti, who, as Freud suggested, always 'had' Vittoria Colonna. In fact, he further suggested that Leonardo's scientific heading was necessitated by his desire to escape his childhood memories: a time fraught with uncertainty and pain. Scientific researches were seen, thus, as a way of dodging one's self, (that painting made one confront), a way that precluded any personal reminiscence and reference.

Desde hace algunos años los estudios sobre juventud refieren a la categoría de jóvenes en plural para dar cuenta de la diversificación de maneras de vivir y sentir esa etapa y las muy diferentes representaciones que sobre ella se generan en la sociedad. Si bien, desde la perspectiva de estos estudios es clara la existencia de una gran variedad de situaciones personales y colectivas que haría imposible ubicar a una franja generacional bajo una misma identificación, observamos que desde la perspectiva de las instituciones sociales, y en particular de las instituciones educativas, se impone con frecuencia una mirada ligada a cierta lógica deficitaria, que en pos de capturar su especificidad homogeneiza a este grupo etario bajo el signo de la incompletud.En este sentido, en los ámbitos educativos coexisten distintas tendencias. En una, se intenta construir o definir al joven como un sujeto con características relativamente fijas o esenciales, modelo que se utiliza como anticipación de l...

The work of Ilya Prigogine and Isabelle Stengers exposes a radical asymmetry at the heart of physics: different mathematical formulations of the same problem produce equally valid yet not equivalent representations of matter and the universe.  This chapter examines how this onto-epistemological bifurcation marks thought with the impossibility to reach past the contingency of present knowledge and yet enables a rigorous logic.
When trying to account for the coherence of sense, contemporary philosophy seems unable to let go of the habit of purging thought of all that is historical and contingent, as nothing more than noise that clouds the voice of the ontological ultimate. Prigogine’s asymmetry disrupts this reductionist paradigm. Departing from the absolutist interpretations of contingency proposed by Object Oriented Ontology as well as from Latour’s neo empiricist methodology, this chapter develops Prigogine’s asymmetry to its most extreme consequences.  It explains how a rigorous system of knowledge can function thanks to rather than despite of the contingent complexity of the present. The argument will revisit the thought of Descartes, Husserl, Rorty, Popper, Gödel, Deleuze, and Golding, to propose a daring reorganisation of the logic of sense that takes decidability beyond the true-false dichotomy and introduces a positive interpretation of incompleteness, by retaining rather than cleansing the contingent and entropic roughness of the present as the very condition of knowledge and the possibility of making sense. 
As will be seen, this reversal of the hierarchy between the simplicity of the ultimate and the complexity of the present shows that the patterns of possibility and impossibility encountered in knowledge systems distribute and orientate thought as dimensions logically rigorous and yet radically material. While this newly discovered materiality of knowledge is nothing new for the artist, it blows asunder the ontological edifice that keeps identity and predicate rigorously apart in the subject-object distribution of epistemology.

Il est loin d’être inhabituel, dans le domaine de la bande dessinée, que des séries soient vouées à demeurer inachevées, au gré des aléas éditoriaux. Il est plus rare, en revanche, qu’une œuvre en un seul tome soit livrée au lecteur sans conclusion définitive ; c’est pourtant le cas de deux livres de Lewis Trondheim, Lapinot et les carottes de Patagonie (1995) et Capharnaüm (2015), le premier ayant propulsé l’auteur sur le devant de la scène, le second ayant connu plusieurs incarnations avant sa forme publiée définitive.
L’étude de ces deux volumes est révélatrice à bien des égards. Elle témoigne, d’abord, d’une évolution graphique du dessinateur, au sein d’un même tome mais également entre les deux ouvrages. Elle montre ensuite l’éventail scénaristique que Trondheim est apte à déployer, et les thèmes et motifs narratifs récurrents qui surviennent tout au long de sa longue bibliographie. Enfin, elle dévoile son aptitude à l’improvisation, aucun des deux tomes n’ayant été totalement planifié au cours de son élaboration.
En plus de ces questions touchant spécifiquement à l’œuvre de Trondheim, je souhaite également par cet article aborder la réception de telles œuvres, toutes deux sans conclusion mais avec des développements relativement différents (un récit quasiment complet avec les Carottes, une sorte de longue première partie pour Capharnaüm). Leur inachèvement, exhibé au lecteur dès le titre ou la préface de l’œuvre, devient presque leur motif articulatoire principal et empêche d’aborder leur lecture comme on le ferait pour toute autre bande dessinée. D’autre part, il convient d’interroger la façon dont elles sont rythmiquement construites, Trondheim ayant ainsi indiqué à de nombreuses reprises avoir profité de la longueur projetée (ou fantasmée) de ces œuvres pour s’autoriser des étirements graphique et narratifs à plusieurs reprises. Enfin, on peut se demander si les Carottes et Capharnäum peuvent être satisfaisantes dans leur « clôture », pour reprendre le terme de Jane Yellowlees Douglas, c’est-à-dire dans la façon que peut avoir le lecteur de faire sens de sa lecture une fois le volume terminé. Reprenant sur ce point des réflexions d’abord élaborées dans mon article « Quand le feuilleton s’enraye : intégrales tronquées et séries interrompues » paru dans l’ouvrage Imaginaire sériel, je compte en poursuivre ici la portée en me demandant comment le lecteur d’une œuvre inachevée peut réconcilier les ambitions de l’auteur, la fin inexistante du récit et ses propres projections narratives.

We show that without assuming completeness or continuity, a strongly independent preorder on a possibly infinite dimensional convex set can always be given a vector-valued representation that naturally generalizes the standard expected utility representation. More precisely, it can be represented by a mixture-preserving function to a product of lexicographic function spaces.