When I was Dickinson Miller's assistant from 1940 to 1942, I soon realized that I had encountered an unusually powerful, acute, and original mind and a writer whose clear but vivid style matched the high quality of his intelligence. These traits were apparent in his comments about eminent philosophers with whom he had associated - particularly William James but also Santayana, Dewey, Husserl, and Wittgenstein - and in the mutual criticism he demanded of his writing and my first efforts. (...) I was pleased and felt immensely privileged to share in his planning of a book devoted to "analysis, the method of philosophy at work" as in his articles on the knowledge-problem, induction, and free will. In view of the penetration of his articles, such a book seemed long overdue as James had insisted even in 1905. When Miller's projected book on "analysis at work" did not appear by 1956, I consulted him about putting together a collection of his published essays. Such a collection seemed but slight homage to one who had made such a striking contribution to American philosophy in rela tion to James and one from whom I had learned so much. He felt, however, that such a collection would be inappropriate and preferred to concentrate on a book, never finished, on "the principles of practical intelligence", the application of intelligence in a "morality of results" for human welfare. (shrink)

We show that the Turing degrees are not sufficient to measure the complexity of continuous functions on [0, 1]. Computability of continuous real functions is a standard notion from computable analysis. However, no satisfactory theory of degrees of continuous functions exists. We introduce the continuous degrees and prove that they are a proper extension of the Turing degrees and a proper substructure of the enumeration degrees. Call continuous degrees which are not Turing degrees non-total. Several fundamental results are proved: a (...) continuous function with non-total degree has no least degree representation, settling a question asked by Pour-El and Lempp; every non-computable f $\epsilon \mathcal{C}[0, 1]$ computes a non-computable subset of $\mathbb{N}$ ; there is a non-total degree between Turing degrees $a _\eqslantless_{\tau}$ b iff b is a PA degree relative to a; $\mathcal{S} \subseteq 2^{\mathbb{N}}$ is a Scott set iff it is the collection of f-computable subsets of $\mathbb{N}$ for some f $\epsilon \mathcal{C}[O, 1]$ of non-total degree; and there are computably incomparable f, g $\epsilon \mathcal{C}[0, 1]$ which compute exactly the same subsets of $\mathbb{N}$ . Proofs draw from classical analysis and constructive analysis as well as from computability theory. (shrink)

We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, or Schnorr random reals. (...) We show that Low(ML, Kurtz) coincides with the non-DNR degrees, while both Low(CR, Kurtz) and Low(Schnorr, Kurtz) are exactly the non-high, non-DNR degrees. (shrink)

Relational dimensions of ethical decision making are a potentially interesting focus to enrich our understanding of decision-making processes. This study examines decision preferences and reactions to decisions in a situation of possible harm. Two ethical value orientations, just value orientation and relational value orientation , are introduced. Participants chose relational cooperation, instrumental cooperation, or independence in dealing with an uncertain situation of possible harm. JVO contributes to a decision of relational cooperation. Only RVO was related to expected mutual benefit and (...) relational connection. Overall, this study supports our central thesis that a relational dimension of ethical decisions provides interesting insights into behavioral ethics in organizations and could expand the scope of ethical decision research. (shrink)

An important disagreement in contemporary debates about free will hinges on whether an agent must have alternative possibilities to be morally responsible. Many assume that notions of alternative possibilities are ubiquitous and reflected in everyday intuitions about moral responsibility: if one lacks alternatives, then one cannot be morally responsible. We explore this issue empirically. In two studies, we find evidence that folk judgments about moral responsibility call into question two popular principles that require some form of alternative possibilities for moral (...) responsibility. Survey participants given scenarios involving agents that fail to satisfy these principles nonetheless found these agents to be morally responsible, blameworthy, deserving of blame, and at fault for morally bad actions and consequences. We defend our interpretation of this evidence against objections and explore some implications of these findings for the free will debate. (shrink)

In dynamic epistemic logic and other fields, it is natural to consider relativization as an operator taking sentences to sentences. When using the ideas and methods of dynamic logic, one would like to iterate operators. This leads to iterated relativization. We are also concerned with the transitive closure operation, due to its connection to common knowledge. We show that for three fragments of the logic of iterated relativization and transitive closure, the satisfiability problems are fi1 11–complete. Two of these fragments (...) do not include transitive closure. We also show that the question of whether a sentence in these fragments has a finite (tree) model is fi0 01–complete. These results go via reduction to problems concerning domino systems. (shrink)

It is time for a new paper about open questions in the currently very active area of randomness and computability. Ambos-Spies and Kučera presented such a paper in 1999 [1]. All the question in it have been solved, except for one: is KL-randomness different from Martin-Löf randomness? This question is discussed in Section 6.Not all the questions are necessarily hard—some simply have not been tried seriously. When we think a question is a major one, and therefore likely to be hard, (...) we indicate this by the symbol ▶, the criterion being that it is of considerable interest and has been tried by a number of researchers. Some questions are close contenders here; these are marked by ▷. With few exceptions, the questions are precise. They mostly have a yes/no answer. However, there are often more general questions of an intuitive or even philosophical nature behind. We give an outline, indicating the more general questions.All sets will be sets of natural numbers, unless otherwise stated. These sets are identified with infinite strings over {0, 1}. Other terms used in the literature are sequence and real. (shrink)

We examine the sequences A that are low for dimension, i.e. those for which the effective dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness. By considering analogues of characterizations of lowness for randomness, we show that lowness for dimension can be characterized in several ways. It is equivalent to lowishness for randomness, namely, that every Martin-Löf random sequence has effective dimension (...) 1 relative to A, and lowishness for K, namely, that the limit of KA/K is 1. We show that there is a perfect [Formula: see text]-class of low for dimension sequences. Since there are only countably many low for random sequences, many more sequences are low for dimension. Finally, we prove that every low for dimension is jump-traceable in order nε, for any ε > 0. (shrink)

Nuclear intermolecular duplexes appear to be a general feature of nucleated cells. Most of these duplexes are formed between large RNA as well as between large and small RNA molecules. A significant portion of the large molecules belong to a special class of RNA that is restricted to the nucleus and, therefore, not designated for export. These molecules are assembled with proteins and form a structure of a higher order. The possibility that these molecules and a set of small nuclear (...) RNAs are components of a complex machine, “the transportosome”, which functions in nucleocytoplasmic traffic, is discussed. (shrink)