scholarly journals Constructive Dimension and Turing Degrees

2009 ◽  
Vol 45 (4) ◽  
pp. 740-755 ◽  
Author(s):  
Laurent Bienvenu ◽  
David Doty ◽  
Frank Stephan
Author(s):  
Marc Rölli

Husserls Analyse der Wahrnehmung und Heideggers Zeittheorie sind beide in ihrem Theorieaufbau auf die Gegenständlichkeit der Gegenstände – oder auf den Gegenstandsbezug der Erfahrung und seine wesensmäßige Konstitution – fixiert. Hierin spiegelt sich, bei Heidegger explizit, Kantisches Erbe. Diese phänomenologische, transzendentalphilosophische Relevanz des Gegenstands verweist im Kern auf Intentionalität – und damit auf eine objektbezogene Selbstüberschreitungsfigur der Subjektivität. Ganz anders bestimmt Latour den Stellenwert der Dinge im Kollektiv, wenn er ihnen eine Handlungsmacht zuschreibt, die den traditionellen Gegensatz zwischen Handlungssubjekten und Objektbehandlung einklammert. Der folgende Beitrag kreist den kritischen Punkt ein, der in der Theoriebildung zur Verzweigung phänomenologischer und ANTistischer Ansätze führt. Während sich die Phänomenologie im Zuge einer begrifflichen Rekonstruktion der Erfahrung von Gegenständen konsolidiert, ist die ANT auf die Beschreibung von Handlungsstrukturen ausgerichtet, die sich aus Aktanten aller Art zusammensetzen. Abschließend stellt sich die Frage, ob nicht die kollektivistische Soziologie Latours von dem methodischen Solipsismus der Phänomenologie lernen kann, dass es eine konstruktive Dimension und Machtfülle der deskriptiven Arbeit gibt, die nicht einfach den Akteuren überhaupt, sondern vor allem der Analytikerin überlassen ist? </br></br>Husserl's analysis of perception and Heidegger's theory of time are both fixated on the objectivity of objects - or the objectrelation of experience and its essential constitution. This reflects - and in the case of Heidegger quite explicitly - Kantian heritage. This phenomenological, transcendental relevance of the object essentially refers to intentionality - and thus an object-related figure of self-transcending subjectivity. Quite differently, Latour determines the status of things in the collective, ascribing to them an agency that brackets the traditional opposition between acting subjects and passive objects. The contribution encircles precisely that critical point which leads to the separation of phenomenological and ANTistical approaches. While phenomenology grounds itself by reconstructing the experience of objects, ANT focuses on the description of the structures of action, which are composed of actants of all kinds. Finally, the question arises whether Latour's collectivist sociology can learn from phenomenology's methodological solipsism that there is a constructive dimension and plenitude of power in the work of description that is not just left to actors in general, but above all to the analyst herself?


2012 ◽  
Vol 12 (01) ◽  
pp. 1250005 ◽  
Author(s):  
MINGZHONG CAI ◽  
RICHARD A. SHORE ◽  
THEODORE A. SLAMAN

We study the global properties of [Formula: see text], the Turing degrees of the n-r.e. sets. In Theorem 1.5, we show that the first order of [Formula: see text] is not decidable. In Theorem 1.6, we show that for any two n and m with n < m, [Formula: see text] is not a Σ1-substructure of [Formula: see text].


2018 ◽  
Vol 24 (2) ◽  
pp. 165-174
Author(s):  
BJØRN KJOS-HANSSEN

AbstractIs there a nontrivial automorphism of the Turing degrees? It is a major open problem of computability theory. Past results have limited how nontrivial automorphisms could possibly be. Here we consider instead how an automorphism might be induced by a function on reals, or even by a function on integers. We show that a permutation of ω cannot induce any nontrivial automorphism of the Turing degrees of members of 2ω, and in fact any permutation that induces the trivial automorphism must be computable.A main idea of the proof is to consider the members of 2ω to be probabilities, and use statistics: from random outcomes from a distribution we can compute that distribution, but not much more.


2000 ◽  
Vol 65 (3) ◽  
pp. 1193-1203 ◽  
Author(s):  
P.D. Welch

AbstractWe characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down ζ, the least ordinal not the length of any eventual output of an Infinite Time Turing machine (halting or otherwise); using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated with the jump operator satisfy a Spector criterion, and correspond to the Lζ-stables. It also implies that the machines devised are “Σ2 Complete” amongst all such other possible machines. It is shown that least upper bounds of an “eventual jump” hierarchy exist on an initial segment.


Author(s):  
Mayra Rivera

Sylvia Wynter’s work seeks to expose Man as an arbitrary conception inherently linked to racism and too often mistaken for the human as such. She also offers a more capacious model for being human—one that is culturally specific, relational and dynamic. This constructive dimension of her work is especially evident in her novel, The Hills of Hebron, for the literary genre is consonant with her argument that communities invent genres of being human from their local histories, the specificities of landscape, religious visions, and creative practices. This essay examines the contribution of the novel to Wynter’s broader project of deconstructing the doctrine of Man.


Author(s):  
Harold Hodes

A reducibility is a relation of comparative computational complexity (which can be made precise in various non-equivalent ways) between mathematical objects of appropriate sorts. Much of recursion theory concerns such relations, initially between sets of natural numbers (in so-called classical recursion theory), but later between sets of other sorts (in so-called generalized recursion theory). This article considers only the classical setting. Also Turing first defined such a relation, now called Turing- (or just T-) reducibility; probably most logicians regard it as the most important such relation. Turing- (or T-) degrees are the units of computational complexity when comparative complexity is taken to be T-reducibility.


Computability ◽  
2014 ◽  
Vol 3 (2) ◽  
pp. 105-134
Author(s):  
Wesley Calvert ◽  
Valentina Harizanov ◽  
Alexandra Shlapentokh

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