We consider the question of randomness of the probability ΩU[X] that an optimal Turing machine U halts and outputs a string in a fixed set X. The main results are as follows: ΩU[X] is random whenever X is $\Sigma _{n}^{0}$-complete or $\Pi _{n}^{0}$-complete for some n ≥ 2. However, for n ≥ 2, ΩU[X] is not n-random when X is $\Sigma _{n}^{0}$ or $\Pi _{n}^{0}$ Nevertheless, there exists $\Delta _{n+1}^{0}$ sets such that ΩU[X] is n-random. There are $\Delta _{2}^{0}$ sets (...) X such that ΩU[X] is rational. Also, for every n ≥ 1, there exists a set X which is $\Delta _{n+1}^{0}$ and $\Sigma _{n}^{0}$-hard such that ΩU[X] is not random. We also look at the range of ΩU as an operator. We prove that the set {ΩU[X]: X ⊆ 2<ω} is a finite union of closed intervals. It follows that for any optimal machine U and any sufficiently small real r, there is a set X ⊆ 2<ω recursive in ∅′ ⊕ r, such that ΩU[X] = r. The same questions are also considered in the context of infinite computations, and lead to similar results. (shrink)

We define a program size complexity function $H^\infty$ as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in ${\{0,1\}}^\omega$ relative to the $H^\infty$ complexity. We prove that the classes of Martin-Löf random sequences and $H^\infty$-random sequences coincide and that the $H^\infty$-trivial sequences are exactly the recursive ones. We also study some properties of $H^\infty$ and compare it with other complexity functions. In particular, $H^\infty$ (...) is different from $H^A$, the prefix-free complexity of monotone machines with oracle A. (shrink)

Using possibly infinite computations on universal monotone Turing machines, we prove Martin-Löf randomness in ∅' of the probability that the output be in some set.

In this paper we study the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest input that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if the machine is allowed to overwrite its output, this complexity coincides with the classical Kolmogorov complexity for halting computations relative to the first (...) jump of the halting problem. However, on machines that cannot erase their output –called monotone machines–, we prove that our complexity for non effective computations and the classical Kolmogorov complexity separate as much as we want. We also consider the prefix-free complexity for possibly infinite computations. We study several properties of the graph of these complexity functions and specially their oscillations with respect to the complexities for effective computations. (shrink)

El objetivo de este artículo es comentar las prácticas que lleva a cabo el equipo docente de la asignatura Epistemología y Metodología de la Investigación en Ciencias Jurídicas (FCEJS-UNSL) –cuya actividad inició en 2012– respecto de la enseñanza del derecho desde una perspectiva compleja. Concebir lo jurídico desde tal enfoque implica considerar la diversidad de las realidades actuales. Asimismo, si se asume que los entornos son múltiples, heterogéneos, no es posible estudiarlos desde un único campo de conocimiento. Adoptar tales miradas (...) epistemológicas necesita de una actitud pedagógica que se adapte al cambio. Por ende, este texto evidenciará las formas en que una asignatura de grado afronta desafíos cotidianos para plantear estrategias que pongan en cuestión el sentido jurídico dominante y, a partir de ello, trascender el positivismo. Por otra parte, a toda la humanidad sorprendió la situación suscitada a partir de la pandemia por COVID-19, que mostró la importancia de asumir una didáctica dinámica. Por ello, también se dará cuenta de las adaptaciones realizadas por el equipo docente para atender a ese nuevo contexto. (shrink)

"Die folgenden Untersuchungen zielen unmittelbar auf eine Einteilung der Realwissenschaften ab, und zwar auf die adäquate, dem Ganzen dieser Wissenschaften angemessene Einteilung. Soll dies Ziel erreicht werden, so sind die Realwissenschaften nach allen Seiten hin eindringender wissenschaftstheoretischer Betrachtung zu unterziehen. So hat dies Buch eine vergleichende Wissenschaftslehre (Gegenstandslehre, Logik und Erkenntnistheorie) sozusagen eine vergleichende Anatomie der Wissenschaften, insbesondere der Realwissenschaften, anzustreben. In dieser Aufgabe liegt die eigentliche Absicht, während das Einteilungsproblem mehr das äussere, unmittelbare Ziel abgibt." (Erich Becher,Vorwort) Erich (...) Becher ( 1882 - 1929 ) war ein deutscher Philosoph und Psychologe. Er studierte an der Universität Bonn Naturwissenschaften, Mathematik, Sozialwissenschaften und Philosophie, u.a. bei Benno Erdmann, und schloss das Studium mit der Promotion zum Dr. phil. sowie dem Staatsexamen für das höhere Lehramt ab. Seine Habilitationsschrift trägt den Titel "Philosophische Voraussetzungen der exakten Naturwissenschaften". Nach einigen Jahren als Privatdozent an der Universität Bonn wurde er 1909 an die Universität Münster berufen, bevor er 1916 auf den Lehrstuhl für Philosophie und Psychologie an der Universität München wechselte. Zudem war er seit 1924 ordentliches Mitglied der Bayerischen Akademie der Wissenschaften. Sorgfältig überarbeiteter Nachdruck des Originals von 1921. (shrink)

In the course of the 11th century, the economic and demographic growth within the Italian cities and its consequential social problems led to an increasing tension between the aristocratic vassal milieu comprising the bishop on one side and the urban elites on the other. Amongst others, one consequence was the takeover of domination by communal institutions resulting in an independent political participation of the citizens. However, these new communes suffered from a lack of legitimacy. The contemporaries were well aware of (...) the contingency of the communes. The communal discourse as taught in the rhetoric system of the ars dictaminis reveals how domination was conceptualized in the 12th century. (shrink)

We obtain a large class of significant examples of n-random reals (i.e., Martin-Löf random in oracle $\varphi ^{(n - 1)} $ ) à la Chaitin. Any such real is defined as the probability that a universal monotone Turing machine performing possibly infinite computations on infinite (resp. finite large enough, resp. finite self-delimited) inputs produces an output in a given set O ⊆(ℕ). In particular, we develop methods to transfer $\Sigma _n^0 $ or $\Pi _n^0 $ or many-one completeness results of (...) index sets to n-randomness of associated probabilities. (shrink)

Anna Vaninskaya's Fantasies of Time and Death: Dunsany, Eddison, Tolkien brings together three major writers of fantasy and studies their treatment of temporality and mortality. This book is about our ongoing conversation regarding time and death and the unique ability for fantasy to tackle these biggest of subjects. If writers have long envisioned time as a river and death as the sea, for instance, what Vaninskaya's new book discusses is how fantasy allows us, through the use of impossible creations and (...) new metaphors, to imagine new ways of understanding our ontological trap. The genre attempts to try to see the world as one of the gods creating it, or to understand time as the eternal burden of the elves; we may... (shrink)

Mark Doyle's Utopian and Dystopian Themes in Tolkien's Legendarium reads Tolkien's work through the history of utopian and dystopian thought. The aim of this new study is not to prove that Tolkien set out to write dystopian fiction or create a blueprint for a utopian society, but that utopian and dystopian societies and settings crucially inform his legendarium. By placing his study outside of its usual fantasy context, Doyle gives us a valuable societally focused and historicized contribution to both Tolkien (...) and utopian studies respectively, yet one occasionally marred by the author's own unexamined value judgments.The book examines several aspects of Tolkien's legendarium, from its utopian and dystopian literary... (shrink)

Ocherk 1. Voprosy ontologii -- Ocherk 2. Voprosy ėtiki i ėstetiki -- Ocherk 3. Voprosy gnoseologii i aksiologii.

many symbols. We define o, as the probability that an arbitrary machine be circular and we prove that o, is a random number that goes beyond..