A solution to the many attitudes problem

Philosophical Studies - According to noncognitivism, normative beliefs are just desire-like attitudes. While noncognitivists have devoted great effort to explaining the nature of normative belief,...     

A general solution to Mosier's oblique procrustes problem

Browne provided a method for finding a solution to the normal equations derived by Mosier for rotating a factor matrix to a best least squares fit with a specified structure. Cramer showed that Browne's solution is not always valid, and proposed a modified algorithm. Both Browne and Cramer assumed the factor matrix to be of full rank. In this paper a general solution is derived, which takes care of rank deficient factor matrices as well. A new algorithm is offered.     

A modest solution to the problem of religious disagreement

Many assume that the best, and perhaps only, way to address the so-called Problem of Evil (PoE) is to claim that God does not do evil, but that God merely allows evil. This assumption depends on two claims: (i) the doing-allowing distinction exists and (ii) the doing-allowing distinction is morally significant. In this paper I try to undermine both of these claims. Against (i) I argue that some of the most influential analyses of the doing-allowing distinction face grave difficulties and that these difficulties are only exacerbated when applied to God. Against (ii) I argue that broadly Kantian considerations give a better explanation of the moral differences in paradigm cases than the doing-allowing distinction and, when applied to God, effectively dissolve the moral significance of the doing-allowing distinction. The upshot of this is that those who claim God does evil are no worse off than those who claim God allows evil regarding the PoE.     

Illusory contours as the solution to a problem

The perception of certain figures with illusory contours entails a reversal of figure and ground. It is hypothesized that this process occurs in two stages. First, some factor must suggest or cue the reversal. Experiments are described that isolate three such factors, namely, alignment of physically present contours, recognized incompletion of parts of the stimulus array, and set. Once cued, however, other experiments indicate that in a further stage of processing the solution is examined with respect to its compatibility with the stimulus display or with other preceptual properties to which the display gives rise. Only if such compatibility is present will the perception of a figure with illusory contours be maintained.     

A solution to a problem raised in Luce and Marley (2005)

Luce and Marley [2005. Ranked additive utility representations of gambles: Old and new axiomatizations. Journal of Risk and Uncertainty, 30, 21-62] examined various relations between mathematical forms for the utility of joint receipt ⊕ of gambles and for the utility of uncertain gambles. Their assumptions lead to a bisymmetry functional equation which, when the gambles are ranked, is defined on a restricted domain. Maksa [1999. Solution of generalized bisymmetry type equations without surjectivity. Aequationes Mathematicae, 57, 50-74] solved the general case and Kocsis [2007. A bisymmetry equation on restricted domain. Aequationes Mathematicae, 73, 280-284] presents the solution for the ranked case. The latter solution allows us to solve open problem 5 in Luce and Marley (2005) by showing that the assumptions of their Theorem 19 for an order-preserving ranked additive utility (RAU) representation U imply that U is a ranked weighted utility (RWU) representation that is additive over ⊕.     

Moorean pluralism as a solution to the incommensurability problem

Several prominent ethical philosophers have attempted to demonstrate that there exist instances or types of value that are of crucial moral significance but which cannot legitimately be compared with one another. Bernard Williams and Michael Stocker, for example, argue that it can sometimes be rational to regret having chosen the all-things-considered better of two alternatives, and that this sense of regret entails that the goodness of the worse option is not made up for by and is therefore incommensurable with that of the better. Joseph Raz and others have made similar points. In this paper, I propose a theory of value that is monistic in that it countenances just one sort of morally crucial value, but pluralistic in that several distinct properties bearer this value. I then explain how this view avoids incommensurable values without doing violence to the core intuitions that seemed to necessitate them, and how it fits into a larger conception of morality, right conduct, and moral psychology.     

Skinner and a solution to the problem of inner events

Skinner's treatment of inner states has been criticized not only by cognitivists but also by people who are close to behaviorist views. In particular, critics have argued that because of the limited conceptual resources of his scientific framework, Skinner cannot account for "mental" phenomena such as the qualitative character of feelings, conscious contents, or states of awareness. The present paper claims that these criticisms are mistaken. By paying careful attention to Skinner's strict physicalist position and by employing a consistent physicalist terminology, it can be shown that Skinner is able to account for the phenomena in question.     

A general first-order solution to the ramification problem with cycles

We provide a solution to the ramification problem that integrates findings of different axiomatic approaches to ramification from the last ten to fifteen years. For the first time, we present a solution that: (1) is independent of a particular time structure, (2) is formulated in classical first-order logic, (3) treats cycles – a notoriously difficult aspect – properly, and (4) is assessed against a state-transition semantics via a formal correctness proof.This is achieved as follows: We introduce indirect effect laws that enable us to specify ramifications that are triggered by activation of a formula rather than just an atomic effect. We characterise the intended models of these indirect effect laws by a state-transition semantics. Afterwards, we show how to compile a class of indirect effect laws into first-order effect axioms that then solve the ramification and frame problems. We finally prove the resulting effect axioms sound and complete with respect to the semantics defined earlier.     

Tooley's solution to the inference problem

Conclusion Tooley's speculative theory, I have tried to show, is beset with difficulties. I warned that this theory threatens to fail in its goal of illuminating the possible nature of a necessitation relation if it employs radical principles about parts and wholes and universals. Secondly, I argued that regardless of how we interpret the crucial phrase existing only as a part of, the speculative theory cannot solve the inference problem without appealing to such radical principles. Finally, I considered and rejected a version of Tooley's speculative theory that attempts to solve the inference problem using the Indiscernibility of Identicals.I conclude that the speculative theory fails. Tooley must fall back to the stipulative theory and live with the lack of an illuminating solution to the inference problem. But this is not to admit defeat. While it would be nice to have a more complete account of its workings, we may view the introduction of the necessitation relation as a theoretical posit, analogous to the positing of subatomic particles in physics to account for various data.I would like to thank Phillip Bricker for his persistent help with this paper. I would also like to thank David Lewis and an anonymous referee for Philosophical Studies for their comments.     

A minimum-cost network-flow solution to the case V thurstone scaling problem

This paper presents an approach for determining unidimensional scale estimates that are relatively insensitive to limited inconsistencies in paired comparisons data. The solution procedure, shown to be a minimum-cost network-flow problem, is presented in conjunction with a sensitivity diagnostic that assesses the influence of a single pairwise comparison on traditional Thurstone (ordinary least squares) scale estimates. When the diagnostic indicates some source of distortion in the data, the network technique appears to be more successful than Thurstone scaling in preserving the interval scale properties of the estimates.My special thanks go to Alvin Silk, Thomas Magnanti, and Roy Welsch for their support and advice throughout the formative stages of this paper, and to V. Srinivasan for his helpful comments on a later draft of this paper. I also wish to thank the Editor, Associate Editor, and two reviewers for their constructive suggestions.James M. Lattin is Associate Professor of Marketing and Management Science and the James and Doris McNamara Faculty Fellow for 1988-1989.     

A generalized solution of the orthogonal procrustes problem

A solutionT of the least-squares problemAT=B +E, givenA andB so that trace (EE)= minimum andTT=I is presented. It is compared with a less general solution of the same problem which was given by Green [5]. The present solution, in contrast to Green's, is applicable to matricesA andB which are of less than full column rank. Some technical suggestions for the numerical computation ofT and an illustrative example are given.This paper is based on parts of a thesis submitted to the Graduate College of the University of Illinois in partial fulfillment of the requirements for a Ph.D. degree in Psychology.The work reported here was carried out while the author was employed by the Statistical Service Unit Research, U. of Illinois. It is a pleasure to express my appreciation to Prof. K. W. Dickman, director of this unit, for his continuous support and encouragement in this and other work. I also gratefully acknowledge my debt to Prof. L. Humphreys for suggesting the problem and to Prof. L. R. Tucker, who derived (1.7) and (1.8) in summation notation, suggested an iterative solution (not reported here) and who provided generous help and direction at all stages of the project.     

The elegant solution to the problem of impotence

Although most therapists are committed to debunking the dual myths that sex requires an erection and that sex equals intercourse, sex researchers continue to use successful intercourse as a primary dependent variable. It is here asserted that RET therapists would do well to approach the problem of erectile dysfunction from a more elegant philosophical perspective. The treatment approach outlined here is aimed at reducing client disturbance as well as increasing sexual satisfaction rather than at simply helping the client to regain his potency.     

Children's capacity to remember a novel problem and to secure its future solution

Much of humans’ success rests on foresight, the ability to predict what will happen or what is needed in the future. Surprisingly little is known about how this faculty develops. In three experiments (N = 170), 3‐ and 4‐year‐old children were presented with simple puzzles. Fifteen minutes later in a different room they were given the opportunity to secure a solution to take back to the puzzle. Only the older children performed above chance, whereas both age groups could solve the task in an instant condition. The same pattern of results emerged for another task involving selection of something to ‘feed ’ a puppet whose favorite food was initially unavailable. Control conditions suggest that temporal rather than spatial displacement influenced performance. Verbal reports substantiated the conclusion that by age 4 some children can remember a novel problem sufficiently enough to recognize a solution and select that solution in anticipation of applying it to the problem in the future.     

A new solution to the additive constant problem in metric multidimensional scaling

A new solution to the additive constant problem in metric multidimensional scaling is developed. This solution determines, for a given dimensionality, the additive constant and the resulting stimulus projections on the dimensions of a Euclidean space which minimize the sum of squares of discrepancies between the formal model for metric multidimensional scaling and the original data. A modification of Fletcher-Powell style functional iteration is used to compute solutions. A scale free index of the goodness of fit is developed to aid in selecting solutions of adequate dimensionality from multiple candidates.This research is based in part on the author's Ph.D. dissertation at the University of Illinois at Urbana-Champaign. Computer time was provided by the Campus Computing Network of the University of California, Los Angeles.