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)

This article presents a process account of some typicality effects and related similarity-dependent accuracy and response time phenomena that arise in the context of supervised concept acquisition. We describe Symbolic Concept Acquisition (SCA), a computational system that acquires and activates category prediction rules. In contrast to gradient representations, SCA performs by probing for prediction rules in a series of discrete steps. For learning new rules, it acquires general rules but then incrementally learns more specific ones. In describing SCA, we emphasize (...) its functionality in terms of accuracy and efficiency and motivate its design within the set of symbolic mechanisms and memory structures defined by the Soar architecture (Laird, Newell & Rosenbloom, 1987). For replicating human behavior, we first show how SCA exhibits some typicality effects in the course of learning responding faster and more accurately to more typical test examples. Then, using data from human experiments, we evaluate SCA's qualitative predictions on accuracy and response time on individual dataset instances. We show how SCA's predictions correlate with human data across three experimental conditions concerning the effect of instruction on learning strategy. (shrink)

This article seeks to introduce the topics of green schools and sustainability education to the reader as the first article in a series of pieces on such subject matters. With respect to the first essay, the modern historical development of sustainability related education is assessed through the lens of its roots in both the U.S. educational system and the environmental movement. Furthermore, many of the purported benefits of green school construction practices are examined subsequently given their relative importance and popularity (...) with respect to the topic. Finally, a brief but important examination is proffered per several of the philosophical ramifications of these efforts in an effort to further develop the understanding and discussion of such topics and the related series of articles. (shrink)

We call A weakly low for K if there is a c such that $K^A(\sigma)\geq K(\sigma)-c$ for infinitely many σ; in other words, there are infinitely many strings that A does not help compress. We prove that A is weakly low for K if and only if Chaitin's Ω is A-random. This has consequences in the K-degrees and the low for K (i.e., low for random) degrees. Furthermore, we prove that the initial segment prefix-free complexity of 2-random reals is infinitely (...) often maximal. This had previously been proved for plain Kolmogorov complexity. (shrink)

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call 1/2-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the K-trivial sets. We characterize 1/2-bases as the sets computable from both halves of Chaitin’s Ω, and as the sets that obey the cost function c(x,s)=Ωs−Ωx−−−−−−−√. Generalizing these results yields a dense hierarchy of (...) subideals in the K-trivial degrees: For k<n, let Bk/n be the collection of sets that are below any k out of n columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be Ω. Furthermore, the corresponding cost function characterization reveals that Bk/n is independent of the particular representation of the rational k/n, and that Bp is properly contained in Bq for rational numbers p<q. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the K-trivial sets; we can calculate from the family which Bp it characterizes. We finish by studying the union of Bp for p<1; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic81(3) (2016) 1028–1046], who showed that it is a proper subclass of the K-trivial sets. We prove that all such sets are robustly computable from Ω, and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a Σ03 subideal of the K-trivial sets. (shrink)

We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is -random, then A is K-trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of K-triviality and answering a question of Yu. We also prove that if A is K-trivial, then for all Y such that Ω is Y-random, ≡LRY. This answers a question of Merkle and Yu. The other direction is immediate, so (...) we have the second characterization of K-triviality.The proof of the first characterization uses a new cupping result. We prove that if A≰LRB, then for every set X there is a B-random set Y such that X is computable from Y⊕A. (shrink)

The tower number ${\mathfrak t}$ and the ultrafilter number $\mathfrak {u}$ are cardinal characteristics from set theory. They are based on combinatorial properties of classes of subsets of $\omega $ and the almost inclusion relation $\subseteq ^*$ between such subsets. We consider analogs of these cardinal characteristics in computability theory.We say that a sequence $(G_n)_{n \in {\mathbb N}}$ of computable sets is a tower if $G_0 = {\mathbb N}$, $G_{n+1} \subseteq ^* G_n$, and $G_n\smallsetminus G_{n+1}$ is infinite for each n. (...) A tower is maximal if there is no infinite computable set contained in all $G_n$. A tower ${\left \langle {G_n}\right \rangle }_{n\in \omega }$ is an ultrafilter base if for each computable R, there is n such that $G_n \subseteq ^* R$ or $G_n \subseteq ^* \overline R$ ; this property implies maximality of the tower. A sequence $(G_n)_{n \in {\mathbb N}}$ of sets can be encoded as the “columns” of a set $G\subseteq \mathbb N$. Our analogs of ${\mathfrak t}$ and ${\mathfrak u}$ are the mass problems of sets encoding maximal towers, and of sets encoding towers that are ultrafilter bases, respectively. The relative position of a cardinal characteristic broadly corresponds to the relative computational complexity of the mass problem. We use Medvedev reducibility to formalize relative computational complexity, and thus to compare such mass problems to known ones.We show that the mass problem of ultrafilter bases is equivalent to the mass problem of computing a function that dominates all computable functions, and hence, by Martin’s characterization, it captures highness. On the other hand, the mass problem for maximal towers is below the mass problem of computing a non-low set. We also show that some, but not all, noncomputable low sets compute maximal towers: Every noncomputable (low) c.e. set computes a maximal tower but no 1-generic $\Delta ^0_2$ -set does so.We finally consider the mass problems of maximal almost disjoint, and of maximal independent families. We show that they are Medvedev equivalent to maximal towers, and to ultrafilter bases, respectively. (shrink)

We study reals with infinitely many incompressible prefixes. Call $A \in 2^{\omega}$ Kolmogorot random if $(\exists^{\infty}n) C(A \upharpoonright n) \textgreater n - \mathcal{O}(1)$ , where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by $Martin-L\ddot{0}f$ , Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random. Together with the converse-proved by Nies. Stephan and Terwijn [11]-this provides a natural characterization of 2-randomness in terms of plain complexity. We finish with a related characterization of 2-randomness.

The Securities and Exchange Commission requires publicly held US corporations to disclose all information, whether it is positive or negative, that might be relevant to an investor's decision to buy, sell, or hold a company's securities. The decisions made by corporate managers to disclose such information can significantly affect the judgments and decisions of investors. This paper examines academic accounting research on corporate managers' voluntary disclosures of earnings forecasts and non-GAAP earnings measures. Much of the evidence from this research indicates (...) that some managers engage in opportunistic disclosure behavior that often benefits one group (managers and shareholders) at the expense of other groups (often other investors). The paper concludes by discussing the ethical implications of this behavior. (shrink)

We examine the Dual Ramsey Theorem and two related combinatorial principles VW(k,l) and OVW(k,l) from the perspectives of reverse mathematics and effective mathematics. We give a statement of the Dual Ramsey Theorem for open colorings in second order arithmetic and formalize work of Carlson and Simpson [1] to show that this statement implies ACA 0 over RCA 0 . We show that neither VW(2,2) nor OVW(2,2) is provable in WKL 0 . These results give partial answers to questions posed by (...) Friedman and Simpson [3]. (shrink)

The West has lost its traditional spiritual anchors following the rise of science and the social revolution of the sixties. Healing and wholeness begins with reclaiming the spiritual forms that gave rise to Western culture to provide grounding to meet the challenges of meaning in the era global cultural interchange.

We consider effective versions of two classical theorems, the Lebesgue density theorem and the Denjoy–Young–Saks theorem. For the first, we show that a Martin-Löf random real z ∈ [0, 1] is Turing incomplete if and only if every effectively closed class.

'Miller's writing style makes the book easy to pick up and difficult to put down. Written at a level appropriate for advanced undergraduates, it is an important and valuable acquisition for academic libraries.' |s CHOICE.

EveryK-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem.

Are free will and determinism compatible? Philosophical focus on this deceptively simple `compatibility question' has historically been so pervasive that the entire free will debate is now standardly framed in its terms - that is, as a dispute between compatibilists, who answer the question affirmatively, and incompatibilists, who respond in the negative. This dissertation, in contrast, adopts a position that I call `descriptive variantism,' according to which prevailing notions of free will exhibit significant aspects of both compatibilism and incompatibilism. My (...) formulation and defense of this position provides a framework for considering several important issues that cannot be adequately addressed on the traditional conception of the free will debate. The theoretical advantages of descriptive variantism become apparent, I argue, only after adopting needed refinements to the compatibility question itself. As it stands, this question conflates at least two distinct issues: whether free will, as ordinarily understood, does in fact conflict with determinism, and whether free will should be taken to involve such a conflict. The vast majority of work in this area, I maintain, implies that (a) the shared notion of free will exemplified in everyday usage conforms exclusively to either compatibilism or incompatibilism, and (b) the (singular) position suggested by this shared notion constitutes the most adequate response to the compatibility question. This is a mistake: it ignores several other possibilities, among them the prospect that multiple `shared notions' are implicated in the complex network of judgments, attitudes, and social practices related to free will. Having reformulated various aspects of the free will debate in ways that address these issues, I go on to argue that no single account of free will can underwrite the broad range of phenomena associated with this notion. Most importantly, I maintain that contextual features, especially those related to abstraction and concreteness, engender significantly different notions of free will: abstract contexts tend to elicit judgments and other behaviors conducive to incompatibilism, while concreteness often promotes tendencies best captured by compatibilist theories. I support these empirical claims primarily by drawing out the conceptual implications of recent experimental work on these topics in a variety of disciplines, including philosophy, psychology, and neuroscience, and defend my interpretation against alternative accounts that purport to `explain away' the contextual differences exhibited in the experimental data. If these claims are correct, then the fundamental conflicts inherent in prevailing notions of free will have the potential to manifest themselves in some highly problematic ways. For example, criminal laws enacted in abstract contexts may presuppose constraints on free agency deeply at odds with those implicitly adopted by jurors evaluating concrete violations of these laws. I attempt to make some preliminary progress on these vexing, but vital, issues by suggesting that revision towards compatibilism represents an initially appealing method of resolving some of these practical difficulties. Importantly, though, this suggestion is tentative, particularly insofar as the extent to which such revision is ultimately desirable, feasible, or even psychologically possible remains unclear. Further consideration of these issues thus constitutes an important avenue for future research. (shrink)

This paper reviews the experience of an integrated approach to CSR in the U.S. electric utility sector. The authors report on the results of Southern Company’s historical definition of CSR as a dynamic model, balancing stakeholder needs through shifting pressures to assure long-term shareholder value, superior customer, price performance, and sustainable economic development. Using financial and utility sector measures, the paper assesses the company’s “balancing” approach to addressing CSR, which weights corporate, environmental, community, and economic factors in driving successful and (...) sustained financial, social, and environmental performance. The paper concludes by suggesting that CSR success in this sector requires, first, that the global warming issue be governed by the same balancing considerations to which all stakeholders and their legitimate interests are subject, and second, an energy policy that embraces both atechnology policy and appropriate regulatory incentives. (shrink)

This paper reviews the experience of an integrated approach to CSR in the U.S. electric utility sector. The authors report on the results of Southern Company’s historical definition of CSR as a dynamic model, balancing stakeholder needs through shifting pressures to assure long-term shareholder value, superior customer, price performance, and sustainable economic development. Using financial and utility sector measures, the paper assesses the company’s “balancing” approach to addressing CSR, which weights corporate, environmental, community, and economic factors in driving successful and (...) sustained financial, social, and environmental performance. The paper concludes by suggesting that CSR success in this sector requires, first, that the global warming issue be governed by the same balancing considerations to which all stakeholders and their legitimate interests are subject, and second, an energy policy that embraces both atechnology policy and appropriate regulatory incentives. (shrink)