We show that one can solve Post's Problem by constructing generic sets in the usual set theoretic framework applied to tiny universes. This method leads to a new class of recursively enumerable sets: r.e. generic sets. All r.e. generic sets are low and simple and therefore of Turing degree strictly between 0 and 0'. Further they supply the first example of a class of low recursively enumerable sets which are automorphic in the lattice E of recursively enumerable sets with inclusion. (...) We introduce the notion of a promptly simple set. This describes the essential feature of r.e. generic sets with respect to automorphism constructions. (shrink)

We prove optimal lower bounds on the computation time for several well-known test problems on a quite realistic computational model: the random access machine. These lower bound arguments may be of special interest for logicians because they rely on finitary analogues of two important concepts from mathematical logic: inaccessible numbers and order indiscernibles.

This paper contributes to the question of under which conditions recursively enumerable sets with isomorphic lattices of recursively enumerable supersets are automorphic in the lattice of all recursively enumerable sets. We show that hyperhypersimple sets (i.e. sets where the recursively enumerable supersets form a Boolean algebra) are automorphic if there is a Σ 0 3 -definable isomorphism between their lattices of supersets. Lerman, Shore and Soare have shown that this is not true if one replaces Σ 0 3 by Σ (...) 0 4. (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

This paper is the most complete presentation of my views on deterministic causation. It develops the deterministic theory in perfect parallel to my theory of probabilistic causation and thus unites the two aspects. It also argues that the theory presented is superior to all regularity and all counterfactual theories of causation.

This paper discusses the nature of consciousness’ intrinsic intentionality from a transcendental-phenomenological viewpoint. In recent philosophy of mind the essentially intentional character of consciousness has become obscured because the latter is predominantly understood in terms of “qualia” or the “what-it-is-like-ness” of mental states and it is hard to see why such subjective “feels”, of all things, could bestow states with objective reference. As the paper attempts to demonstrate, this is an inadequate understanding of consciousness, which should instead be defined in (...) terms of presence. Consciousness essentially takes place as presence-of, i.e., consists in something coming to appearance. This presence-of is not only a fundamental, irreducible phenomenon, but also in a radical sense un-naturalisable. Naturalism only knows “nature”, as the world of objects, and the question of intentionality then seems to be how certain inner-worldly objects can be “representations” of other inner-worldly objects. In fact, no object is ever intrinsically “about” anything. This is exclusively the nature of subjectivity qua consciousness, which is not an object alongside other objects but rather exists as the manifestation of objects. (shrink)