Continuing his exploration of the organization of complexity and the science of design, this new edition of Herbert Simon's classic work on artificial ...

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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)

I am pleased to receive the reigns of Metaphor and Symbol from Ray Gibbs, who has served as Editor for no less than 19 years. Ray has guided the journal successfully over this time, an era of great...

This outline of the transformations of the concept of reason is based on the idea that this can be presented/illustrated by means of a historical sketch of the criticism of reason, because all essential differentiations in that concept can be understood as consequences of critical arguments. In Kant's work, the Critique of Speculative Reason reaches its first conclusion; it was followed by a Critique of Critical Reason by Hegel and his followers, and Schopenhauer established a new type of critical argument: (...) the Critique of Functional Reason which dominates the radical criticism of reason in our time. This radical criticism is the great challenge for the philosophy of reason today. (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)