A note on russell's paradox in locally cartesian closed categories

Working in the fragment of Martin-Löfs extensional type theory [12] which has products (but not sums) of dependent types, we consider two additional assumptions: firstly, that there are (strong) equality types; and secondly, that there is a type which is universal in the sense that terms of that type name all types, up to isomorphism. For such a type theory, we give a version of Russell's paradox showing that each type possesses a closed term and (hence) that all terms of each type are provably equal. We consider the kind of category theoretic structure which corresponds to this kind of type theory and obtain a categorical version of the paradox. A special case of this result is the degeneracy of a locally cartesian closed category with a morphism which is generic in the sense that every other morphism in the category can be obtained from it via pullback.The financial support of the Royal Society in London is gratefully acknowledged.     

Coherence and transituational generality in coping: the unity and the diversity

We investigated the transituational coherence of coping strategy use by collecting coping data on multiple occasions, and assessing the effects of aggregation over varying numbers of occasions. Study 1 examined the effects of aggregating daily coping reports over three- and six-day periods. Study 2 extended the results of Study 1 by assessing the extent to which aggregation increased the correlation between a dispositional coping measure and daily coping reports. Both studies strongly supported the hypothesis that aggregation would enhance the consistency of coping preferences, suggesting some degree of coherence within the domain of coping strategy used. Aggregated coping reports correlated with each other at significantly higher levels (ranging from 0.46 to 0.77 in Study 1 and from 0.65 to 0.95 in Study 2), than unaggregated coping reports (ranging from -0.12 to 0.30 in Study 1 and from 0.12 to 0.53 in Study 2). Study 2 also showed that aggregated daily reports were better predictors of subsequent coping than scores derived from a standard dispositional coping survey.     

Manufacturing a cartesian closed category with exactly two objects out of a C-monoid

A construction is described of a cartesian closed category A with exactly two elements out of a C-monoid such that can be recovered from A without reference to the construction.The first author was partially supported by the Dutch government through the SPIN project PRISMA; the second author was partially supported by the EEC through Esprit project 415.     

Epistemic luck and the generality problem

Epistemic luck has been the focus of much discussion recently. Perhaps the most general knowledge-precluding type is veritic luck, where a belief is true but might easily have been false. Veritic luck has two sources, and so eliminating it requires two distinct conditions for a theory of knowledge. I argue that, when one sets out those conditions properly, a solution to the generality problem for reliabilism emerges.

Synonym comprehension and the generality of categorization models

Memory & Cognition - When subjects classify a two-word display as representing the “same” category or two “different” categories, semantic similarity between the words...     

The specificity of the generality problem

In “Why the generality problem is everybody’s problem,” Michael Bishop argues that every theory of justification needs a solution to the generality problem. He contends that a solution is needed in order for any theory to be used in giving an acceptable account of the justificatory status of beliefs in certain examples. In response, first I will describe the generality problem that is specific to process reliabilism and two other sorts of problems that are essentially the same. Then I will argue that the examples that Bishop presents pose no such problem for some theories. I will illustrate the exempt theories by describing how an evidentialist view can account for the justification in the examples without having any similar problem. It will be clear that other views about justification are likewise unaffected by anything like the generality problem.     

The generality of learned helplessness in the rat

Two experiments were simultaneously conducted in which two different groups of 40 rats each were exposed to one of two different stressors. In both experiments half the subjects were pretreated with shock, half with underwater exposure. For each pretreatment stressor, half the subjects were allowed to escape, the other half were not. The experiments differed in the test task used. Approximately 24 hr after pretreatment, one-half the subjects from each pretreatment group received 20 water-escape trials in an underwater maze, the other half received 20 shock-escape trials in a two-way shuttle box. The subjects in each of the inescapable pretreatment conditions were slower to escape in the subsequent shock-escape and water-escape tasks when compared with subjects in the corresponding escapable pretreatment condition. The “learned helplessness” effect appeared to be no smaller when aversive stimuli were changed between pretreatment and test than when they remained the same.     

Attributional style and the generality of learned helplessness

According to the logic of the attribution reformulation of learned helplessness, the interaction of two factors influences whether helplessness experienced in one situation will transfer to a new situation. The model predicts that people who exhibit a style of attributing negative outcomes to global factors will show helplessness deficits in new situations that are either similar or dissimilar to the original situation in which they were helpless. In contrast, people who exhibit a style of attributing negative outcomes to only specific factors will show helplessness deficits in situations that are similar, but not dissimilar, to the original situation in which they were helpless. To test these predictions, we conducted two studies in which undergraduates with either a global or specific attributional style for negative outcomes were given one of three pretreatments in the typical helplessness triadic design: controllable bursts of noise, uncontrollable bursts of noise, or no noise. In Experiment 1, students were tested for helplessness deficits in a test situation similar to the pretreatment setting, whereas in Experiment 2, they were tested in a test situation dissimilar to the pretreatment setting. The findings were consistent with predictions of the reformulated helplessness theory.     

The issue of generality in ethics

Conclusion Does ethics have adequate general theories? Our analysis shows that this question does not have a straightforward answer since the key terms are ambiguous. So we should not concentrate on the answer but on the question itself. Ethics stands for many things, but we let that pass. Adequate may refer to varied arrays of methodological principles which are seldom fully articulated in ethics. General is a notion with at least three meanings. Different kinds of generality may be at cross-purposes, so we must not expect theories to be general in sundry senses. Theory, for that matter, is itself ambiguous. Some thinkers say that ethics cannot have theories, while others deny it. We doubt whether opposing parties are talking about the same things.No wonder, then, that controversies in ethics are long-lasting and unproductive. We hope that the methodology we have presented will alleviate some of them. The examples we chose show that this is feasible. Views such as Hare's and Jonsen and Toulmin's which are seemingly wide apart, show convergence if we put them in a methodological perspective.Our analysis also suggests that many alleged differences between science and ethics could fade away if methodology is brought to bear on them. Specifically, the idea that ethics compares poorly with science in view of limited generality, or poor means of justification, is unfounded. Those who defend this view over-rate the powers of science.     

On the generality and limits of abstraction in rats and humans

In this review, we address the question, central to cognition, of whether nonhuman animals such as rats are capable of extracting and extending information from a given learning situation to a new learning situation without generalizing through a physical dimension of the stimuli. This capacity underlies abstraction, which is a hallmark of human cognition and necessary for complex information processing such as language acquisition. We selectively review recent experiments with rats in which systematic changes in information processing of new stimuli are observed after training with different stimuli. These results strongly suggest that this capacity is present in rats. We also review two articles in which clear limitations to this capacity are detected. We conclude that, within specified limits, rats are capable of using prior experience when faced with a learning situation that involves new stimuli. We interpret this ability as a rudimentary form of abstraction. In the face of these provocative results, new theories of learning should be designed to account for these findings.     

Geometry and generality in Frege's philosophy of arithmetic

This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege'sGrundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes ofGrundlagen are developed: the relationship Frege envisions between arithmetic and geometry and the way in which the study of reasoning is to illuminate this. In the final section, it is argued that the sorts of issues Frege attempted to address concerning the character of mathematical reasoning are still in need of a satisfying answer.I am indebted to many people for helpful conversations and comments on this paper, notably Stephen Glaister, Phil Kremer, Madeline Larson, John McDowell, Jim Conant, Charles Chihara, William Craig, Jan Alnes, Joan Weiner, Leon Henkin, Paul Benacerraf, Juliet Floyd, Bill Demopoulos, Jose Ferreiros, Tom Hawkins, Gideon Rosen. Two superb papers on Frege — Bill Demopoulos' (1994) and Mark Wilson (1992) played a significant role in the early stages of composition. Special thanks are due to Hans Sluga, Mark Wilson, Bob Brandom, and Ken Manders for comments, encouragement, information and advice.     

The four-card problem and the generality of formal reasoning

Three experiments were designed to investigate the failure of intelligent adults to solve an apparently simple problem of formal reasoning devised by Wason. Both the mode of presentation and the type of material reduced the difficulty of the problem, while retaining its essential form. However, success on the original problem remained at a low level, even when subjects had attempted an easier version and had been given an explanation.

These results enable one to reject a “strong” formulation of Piaget's theory of formal reasoning. A “weaker” formulation is suggested as a basis for further research.     

On the generality of some memory laws

Several memory laws have been established for the free recall of word lists. The generality of some of these laws were tested, using tasks which the subjects performed (SPTs) as to-be-recalled list items. SPT recall obeyed one law of word recall in showing a strong positive recency effect in immediate free recall, which appeared to be due to these events being in a temporary state of high accessibility. Differences between word and SPT recall were: 1) The reliable primacy effect associated with word recall did not appear in SPT recall; 2) Subjects reported using active memorisation strategies for word lists, but not for SPT lists; 3) Unlike word recall, diverting the subject's attention to so-called deep or shallow features of the SPTs during presentation did not affect the level of their recall. These results considered together with Cohen & Stewart's (1981) finding that SPT recall was not age-sensitive were taken to indicate that SPTs should be regarded as a different class of memory event than words, and that memory models dealing with SPT recall should de-emphasize the importance of encoding, stressing instead retention, and retrieval operations.