An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by \. It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued Łukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued (...) Łukasiewicz predicate calculus corresponding to the dual of the alternative existential quantifier is proven. (shrink)

An extension of the hypothetical experiment of Szilard, which involved the action of a one-molecule gas in an isolated isothermal system, is developed to illustrate how irreversibility may arise out of Brownian motion. As this development requires a consideration of nonmolecular components such as wheels and pistons, the thought-experiment is remodeled in molecular terms and appears to function as a perpetuum mobile.

A particle of molecular dimensions which can exist in two states is associated with a membrane pore through which molecules of a gas can pass. The gas molecules from two identical phases on either side of the membrane may pass only when the particle is in one particular state. If certain restrictions are imposed on the system, then the particle appears to act like a Maxwell's Demon(1) which “handles” the gas molecules during their passage through the pore.

Abstract Islam displaces the ancient idea of time as an implacable enemy with the scriptural image of time as the stage of judgment, a narrow bridge of accountability stretched between creation and eternity. The stark contrast of temporal evanescence with all the immutability of eternity challenges Muslim theologians and philosophers of the classic age. The dialectical theologians of the kalam describe time and change atomisti?cally and even occasionalistically, seeking to preserve the absoluteness of the contrast and to avoid compromising the (...) purity of God's creative act and the sheer facticity of its temporal effect. The falasifa, philosophers in the Greek tradition, use Platonic, Aristotelian, and Neoplatonic arguments to reconcile temporality with eternity. Stripped of argument, their emanative and archetypal schemes join the core symbolisms of Islam, but only when accommodated to the Qur'anic ideas of judgment and creation. (shrink)

THE first-century Skeptic philosopher Agrippa was said by Sextus Empiricus to have based his attack against the possibility of philosophical understanding on five "tropes" or ploys--for sophisticated Skeptics did not refer to their considerations as arguments, lest that imply the concession that there is a recognized and recognizable criterion of truth. Rather they appealed only to the plausibility of their tropes, as a means of suggesting that philosophical questions are best left unasked, since they appear to be in principle unanswerable. (...) Agrippa's tropes rested on the following considerations. (shrink)

Familiar proof theoretical and especially automated deduction methods sometimes accept infinity where, in fact, it can be omitted. Our first example deals with the infinite supply of individual variables admitted in 1-order deductions, the second one deals with infinite-branching rules in sequent calculi with number-theoretical induction. The contents of Section 1 summarize and extend basic ideas and results published elsewhere, whereas basic ideas and results of Section 2 are exposed for the first time in the present paper. We consider classical (...) formalisms only, to which constructive formalisms can be reduced by Shanin-style interpretations. (shrink)

When people speak of the precipice on which we are sitting, they often appeal to some particular features of Russian culture, the Russian people, etc. I will not be discussing this point. I do not want to do so mainly because such discourses very often amount to no more than a peculiar type of racism.

The very title of our conference, "Violence in Post-Totalitarian Society," implies the existence of certain expectations. We have always assumed that the communist regime would never fall without violence; an outburst of violence seemed a natural reaction to the demise or weakening of the system. It is extremely difficult to assess today the extent to which these fears have been borne out. Statistics are unreliable at present, and in the past they did not exist for many parameters. Hence it is (...) not always possible to compare current and previous levels of violence on the basis of statistical data. As for the widespread opinion that crime is unlimited, it is determined, like any other social attitude, by a mass of factors among which the real state of affairs does not necessarily head the list. As for the violence originating with the state, although the present regime clearly does not shrink from violence, so far the general level of coercion and cruelty is infinitely distant from that perpetrated for decades under the previous system. (shrink)