This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The Kolmogorov complexity of a finite binary string is the length of the shortest description of the string. This gives rise to some ‘standard’ lowness notions for reals: A isK-trivial if its initial segments have the lowest possible complexity and A is low forKif using A as an oracle does not decrease the complexity of strings by more than a constant factor. We weaken these notions by requiring the defining inequalities to hold only up to all${\rm{\Delta }}_2^0$orders, and call the (...) new notions${\rm{\Delta }}_2^0$-bounded K-trivialand${\rm{\Delta }}_2^0$-bounded low for K. Several of the ‘nice’ properties ofK-triviality are lost with this weakening. For instance, the new weaker definitions both give uncountable set of reals. In this paper we show that the weaker definitions are no longer equivalent, and that the${\rm{\Delta }}_2^0$-boundedK-trivials are cofinal in the Turing degrees. We then compare them to other previously studied weakenings, namelyinfinitely-often K-trivialityandweak lowness for K. We show that${\rm{\Delta }}_2^0$-boundedK-trivial implies infinitely-oftenK-trivial, but no implication holds between${\rm{\Delta }}_2^0$-bounded low forKand weakly low forK. (shrink)

I was led to philosophy by politics. There can be no foundation for political action except in ethics; and there can be no foundation for ethics except in some form of metaphysics, whether religious or other. And one cannot travel very far along the philosophic road— particularly if one has in mind the need of arriving at some definite destination—without finding as an obstacle the perennial problem of Free Will. It is an obstacle which has somehow to be crossed. It (...) cannot be evaded or ignored. The man who is dealing with public affairs—with the principles of Criminal Law, for example, or with the factors that make for peace or war, and indeed with any of the major questions that confront our society—if he tries to think things out, is faced constantly by the problem of individual human responsibility; just as the man of religion is faced by it constantly. (shrink)

§ . As a corollary to the proposition that all institutions must be subordinated to the law of equal freedom, we cannot choose but admit the right of the citizen to adopt a condition of voluntary outlawry. If every man has freedom to do all that he wills, provided he infringes not the equal freedom of any other man, then he is free to drop connection with the state - to relinquish its protection and to refuse paying toward its support. (...) It is self evident that in so behaving he in no way trenches upon the liberty of others, for his position is a passive one, and while passive he cannot become an aggressor. It is equally self evident that he cannot be compelled to continue one of a political corporation without a breach of the moral law, seeing that citizenship involves payment of taxes; and the taking away of a man's property against his will is an infringement of his rights. Government being simply an agent employed in common by a number of individuals to secure to them certain advantages, the very nature of the connection implies that it is for each to say whether he will employ such an agent or not. If anyone of them determines to ignore this mutual safety confederation, nothing can be said except that he loses all claim to its good offices and exposes himself to the danger of maltreatment - a thing he is quite at liberty to do if he likes. He cannot be coerced into political combination without a breach of the law of equal freedom; he can withdraw from it without committing any such breach, and he has therefore a right so to withdraw. (shrink)

Motivated by results on interactive proof systems we investigate an ∃-∀hierarchy over P using word quantifiers as well as two types of set quantifiers. This hierarchy, which extends the polynomial-time hierarchy, is called the analytic polynomial-time hierarchy. It is shown that every class of this hierarchy coincides with one of the following Classes: ∑math image, Πmath image , PSPACE, ∑math image or Πmath image . This improves previous results by Orponen [6] and allows interesting comparisons with the above mentioned results (...) on inter-active proof systems. (shrink)

A convenient and practical method is presented for the generation of unbiased random sequences. The method is based on combining discrete outputs and does not require either precisely specified and unbiased input or complex procedures and equipment.

Review of N. Immler: Das Familiengedächtnis der Wittgensteins (2011).