We define $\Psi $ -autoreducible sets given an autoreduction procedure $\Psi $. Then, we show that for any $\Psi $, a measurable class of $\Psi $ -autoreducible sets has measure zero. Using this, we show that classes of cototal, uniformly introenumerable, introenumerable, and hyper-cototal enumeration degrees all have measure zero. By analyzing the arithmetical complexity of the classes of cototal sets and cototal enumeration degrees, we show that weakly 2-random sets cannot be cototal and weakly 3-random sets cannot be of (...) cototal enumeration degree. Then, we see that this result is optimal by showing that there exists a 1-random cototal set and a 2-random set of cototal enumeration degree. For uniformly introenumerable degrees and introenumerable degrees, we utilize $\Psi $ -autoreducibility again to show the optimal result that no weakly 3-random sets can have introenumerable enumeration degree. We also show that no 1-random set can be introenumerable. (shrink)

En publiant en 1965 Le Péché et la durée de l’ange, le P. Guérard des Lauriers, o. p. (1898-1989) offrait une contribution majeure à un débat qui divisait les thomistes. En 1946 en effet, la parution de Surnaturel du P. de Lubac avait remis en cause, textes de Thomas d’Aquin à l’appui, la thèse de l’impeccabilité naturelle de l’ange, jusqu’alors (presque) unanimement reçue dans l’École thomiste. Deux interprétations de Thomas d’Aquin polarisèrent alors le débat : la raison de la peccabilité (...) de l’ange est à rechercher ou bien dans son élévation à l’ordre surnaturel ( De malo, q. 16, a. 4), ou bien dans la structure même de la créature angélique ( Summa theologiae I a Pars, q. 63, a. 1). Servi par une herméneutique renouvelée des textes de Thomas sur la peccabilité de l’ange, et fort d’un redéploiement d’une doctrine thomiste de la liberté, articulée dans sa double dimension de spécification et d’exercice, Guérard établit que le fondement de la liberté des créatures spirituelles – et donc leur peccabilité – se situe au cœur de leur constitution métaphysique, dans la distinction réelle entre nature et personne, sans qu’intervienne nécessairement la distinction des ordres naturel et surnaturel. Son analyse pénétrante et novatrice le conduit à mettre au jour une structure du libre arbitre, laquelle intègre et unit sans confusion les deux ordres de réalité engagés dans l’acte libre : le métaphysique et le moral. Il offre ainsi une contribution de premier plan à l’élaboration d’une philosophie contemporaine de la liberté, attestant par-là la fécondité de la tradition thomiste. (shrink)

Evaluative studies of inductive inferences have been pursued extensively with mathematical rigor in many disciplines, such as statistics, econometrics, computer science, and formal epistemology. Attempts have been made in those disciplines to justify many different kinds of inductive inferences, to varying extents. But somehow those disciplines have said almost nothing to justify a most familiar kind of induction, an example of which is this: “We’ve seen this many ravens and they all are black, so all ravens are black.” This is (...) enumerative induction in itsfullstrength. For it does not settle with a weaker conclusion (such as “the ravens observed in the future will all be black”); nor does it proceed with any additional premise (such as the statistical IID assumption). The goal of this paper is to take some initial steps toward a justification for the full version of enumerative induction, against counterinduction, and against the skeptical policy. The idea is to explore various epistemic ideals, mathematically defined as different modes of convergence to the truth, and look for one that is weak enough to be achievable and strong enough to justify a norm that governs both the long run and the short run. So the proposal is learning-theoretic in essence, but a Bayesian version is developed as well. (shrink)

1. Ikkŭnŭn mal -- 2. Han nara ŭi yet kŭlssi ro tora kaja : K'ang Yuwei, sŏye wa mihakchŏk chŏnhwan -- 3. Chosŏn ŭi yesul ŭn illyu ŭi pigŭk ŭl tamnŭnda : Yanagi Muneyosi, minye uĭ palgyŏn -- 4. Nŏhŭi nŭn T'ap ŭi himch'am ŭl poannŭn'ga : Ko Yu-sŏp, Han'guk hyŏndae mihak ŭi t'ansaeng -- 5. Naganŭn mal.

The article analyzes the theoretical foundations of the modern project of rational ethics, in which the ethics of discourse is interpreted as a critical theory of society and a critic of modern morality. I. Kant was one of the first to offer the possibility of generalizing the norms of morality and perception of ethics as a transcendental critique of morality. Neo-Kantianism develops ethics as the most important part of the philosophical system and fixes its scope by the idealistic theory of (...) morality. In Russian philosophy, modern ethics is perceived as a normative theory that has to do with issues of self-determination, moral regulation, and freedom of choice. The origins of discourse ethics in the philosophy of the 20th century go back to the “pragmatic turn” and to vigorous discussions about hermeneutics of language and its a priori status in German philosophy, and in analytical philosophy regarding the understanding of metaetics. The modern program of ethics of discourse receives meaningful justification as the logic of moral argumentation in the social philosophy of J. Habermas and in the transcendental pragmatics K.-O. Apel. The ethics of discourse is born from the real need to justify moral requirements and norms. Ethics as a critique of moral argument is associated with the pre-reflexive horizon of the life world, why it is a deontological, formalistic and universal ethics. Two significant projects of discourse ethics, presented in the article as an analysis, should be defined as “weak and strong” variants of philosophical transcendental idealism in modern science. (shrink)

The article examines the controversy between the “orthodox” Indian philosophical school Vaiśeṣika and one of the greatest Buddhist philosophers - Vasubandhu on the existence of subject as a reality. The discussion is investigated on the example of the text “Pudgalaviniścaya”. PV of Vasubandhu - literally “Study on the Self”, or “pudgala” - is traditionally considered the 9th chapter of “Abhidharmakośabhaṣya” of the same author and is one of the most important polemical treatises on the self, or ātman, in Buddhist philosophy. (...) Among the issues discussed are the famous “epistemological argument”, the ability of recall and perception, how a difference between moments of consciousness is possible, whether the substrate for consciousness is necessary. One of the strategies of Vasubandhu is that he tries to find internal contradictions in the arguments of opponents. We can say that the main argument of Vasubandhu is aimed at justifying the mechanism of the cause-and-effect occurrence of all phenomena. If the Vaiśeṣikas proceed from their logic about the need for a substance for qualities, then Vasubandhu tries to persuade them to his side and offer a fundamentally new explanatory model, according to which there are only sequence-like moments-phenomena that flow from each other according to the law of cause and effect. (shrink)