We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage’s sure-thing principle, known (...) as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested. (shrink)

В сборнике представлены очерки, герои которых - художники, философы, священнослужители, ученые, император Индии, французская крестьянка, Учитель Гималайского Братства и другие - сыграли немаловажную роль в земном творчестве Космической эволюции. Для широкого круга читателей.

The idea of the common good has been a signature feature of Catholic social teaching and so of modern Catholic engagement in public affairs. It has recently been suggested that the notion is now obsolete due to changes in the culture and politics of the West. In keeping with this suggestion, some argue that Catholics should abandon it in favor of an appeal based on lower intermediate goods in a manner more related to Augustine’s engagement with the largely pagan culture (...) of his time than to Aquinas’s categories tailored to an integrally Christian society. I argue that such a solution misreads aspects of the tradition and of the present political and cultural situation and I suggest some alternative grounds on which Catholic engagement with contemporary public life should proceed and that thinking again about the common good is a necessary part of such engagement. (shrink)

The development of the social sciences needs to rely on precise methods. The nomological model of explanation adopted in the natural sciences is ill-suited for the social sciences. An algorithmic model of society can be a promising solution to existing problems. In its most general form, an algorithm is a generally understood prescription for what actions to perform and in what order to achieve the desired result. Any algorithm can be represented as a set of rules of the form «If (...) A, do D to get P». People are the bearers of this kind of rules that apply in different areas of their activities. The rules are subject to change based on personal and collective experience. There is a special mathematical discipline that studies the laws of evolution of such rules. This discipline is called genetic programming. Contrary to the threatening name, the algorithmic model does not imply the deprivation of a person’s right to free choice, but it needs this right as a necessary condition for the evolution of social algorithms. These algorithms allow us to give a non-causal, but law-like explanation of many well-known social phenomena, as well as to effectively model the future, which is critically important today. A retrospective look at the evolution of social algorithms shows that the current global crisis of human society is associated with the approach to the point of singularity in their evolution. This is due to the fact that there is no need for direct human participation in the implementation of social algorithms, which is reflected in a fundamental change in the sphere of employment and less need for further development of the sciences. (shrink)

A compact edition of Mr. Beck's excellent translation of the second Critique, slightly revised, together with a helpful short introduction and a bibliography.--V. C. C.

The process of turning a myth into a fairy tale, its internal and external causes, patterns, consequences... It may be difficult to find a more traditional way of exploring a fairy tale than this one. We will not avoid it either, because whatever aspect of the fairy tale analysis we choose, it is impossible to bypass this side of its genesis. And the choice of the method of explication of this problem largely predetermines both the angle of her vision and (...) the means of solution. The same traditions have already been given peculiar power lines that urge more and more researchers to move in the area of ​​these lines and to cover more and more varieties of the same dimensions of the object: demythologization and desacralization of the hero, his actions, his environment; giving the myth an exoteric character, with the elements of fiction and irony that are inconceivable as a result; the shrinking of the scale of the hero's actions, and hence the replacement of the mystery of myth with mysteriousness, intrigue in the fairy tale, the decline of the mythological worldview. The topics of branching of the subjects through the myth to the fairy tale, finding and researching common for both phenomena of binary oppositions, etc., are densely addressed. (shrink)

This work is devoted to the relations between Lambek’s Syntactic Calculus and noncommutative variants of Girard’s Linear Logic; in particular the paper will consider: the geometrical representation of the laws of LC by means of proof-nets; the discovery - due to such a geometrical representation - of some laws of LC not yet considered; the discussion of possible linguistic uses of these new laws.

Hilbert's conference lectures during the year 1922, Neuebegründung der Mathematik. Erste Mitteilung and Die logischen Grundlagen der Mathematik (both are published in (Hilbert [1935] 1965) pp. 157-195), contain his first public presentation of an axiom system for propositional logic, or at least for a fragment of propositional logic, which is largely influenced by the study on logical woks of Frege and Russell during the previous years.The year 1922 is at the beginning of Hilbert's foundational program in its definitive form. The (...) final public presentation by Hilbert of an axiom system for propositional logic is contained in the 1934 book Grundlagen der Mathematik, I (Hilbert and Bernays [1934] 1968). Sequent .. (shrink)

Some questions connected with the carry over of fundamental group theory to constructive mathematics, and with the relationship between classical and constructive group theories are considered herein. All the considerations are carried out within the scope of constructive mathematics.