Operators in the paradox of the knower

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense.I am deeply indebted to Robert F. Barnes and Evan W. Conyers, without whom these ideas might not have germinated and certainly would not have grown. Many of the results offered here evolved in the course of mutual discussion and correspondence. I am also grateful to an anonymous reviewer forSynthese for many very helpful suggestions.The current paper contains the technical results promised in Footnote 25 of Grim (1988) and Footnote 26, Chapter 3, of Grim (1991).     

A coding of the countable linear orderings

Associate to any linear ordering on the integers the mapping whose value on n is the cardinality of {k<n; kn}: a purely combinatorial characterization for the mappings associated to the well-orderings is established.This work was partially supported by a CNRS grant PRC mathématiques and informatique.     

The role of compliance in hypnotic and nonhypnotic analgesia

We modified the standard procedure for administering finger pressure pain in order to assess the extent to which subjects biased their reports of pain reduction when exposed to compliance-inducing instructions. Experiment 1 used only highly hypnotizable subjects and found that compliance-induced reductions in reported pain were about half as large as the reported reductions produced by hypnotic analgesia suggestions. Experiment 2 used low as well as high hypnotizables and administered hypnotic or nonhypnotic analgesia instructions and compliance instructions to the same subjects on separate pain trials. Reported pain reductions produced by hypnotic and nonhypnotic analgesia suggestions and those produced by compliance instructions were substantially and significantly correlated. Furthermore, hypnotizability correlated with compliance-induced reported pain reductions as highly as it correlated with the reported reductions produced by hypnotic analgesia suggestions. Among high hypnotizables (but not low hypnotizables) compliant responding was predicted by social desirability. The findings of both studies indicate that compliance strongly influences the reports of hypnotic and nonhypnotic analgesia proffered by high hypnotizables. The role of compliance in the pain reductions reported by low hypnotizables is less clear-cut.     

Psychosocial predictors of stress associated with the male midlife transition

This study was designed to examine the correlates of developmental psychological stress for 36 middle-aged professional men. Based on sex role convergence and role adjustment theories, two sets of predictor variables were hierarchically entered into a multiple regression equation with a third set of variables entered to control for individual stressors. Controlling for individual stressors, midlife stress outcome was found to be influenced only by role adjustment (R²=.3593). The sex role convergence cluster did not account for a significant increase in variance. Controlling for individual stressors, the best univariate predictors of stress outcome associated with the midlife transition were (a) the quality of the parent-adolescent relationship and (b) marital satisfaction.     

Ratings of Emotional Response to Pictorial Stimuli: Positive and Negative Affect Dimensions

The purpose of this study was to investigate the structure of emotional responses to pictorial stimuli within the affective space defined by orthogonal dimensions of positive affect (PA) and negative affect (NA). College student participants (N = 151) viewed 60 color photographic slides from the International Affective Picture System (Lang, Bradley, & Cuthbert, 1995) and rated their emotional responses to each slide using the Positive and Negative Affect Schedule (Watson, Clark, & Tellegen, 1988). Consistent with prediction, affective reactions to pleasant slides were characterized as high in PA, and low in NA. Unpleasant slides produced elevations on the NA scale, but contrary to expectation, also produced elevated ratings of PA, with the magnitude of PA scale scores increasing systematically with NA scale scores. The results suggest an interesting divergence between the structure of pictorially elicited affective reactions and that of ad hoc mood states. Directions for future research are discussed in relation to the unique properties of the slide viewing paradigm.     

Fractal Images of Formal Systems

Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex value spaces, with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic.\looseness=-1     

Positive and Negative Hypothesis Testing by Cooperative Groups

In a rule induction problem positive hypothesis tests select evidence that the tester expects to be an example of the correct rule if the hypothesis is correct, whereas negative hypothesis tests select evidence that the tester expects to be a nonexample if the hypothesis is correct. Previous research indicates the general effectiveness of a positive test strategy for individuals, but there has been very little research with cooperative groups. We extend the analysis of Klayman and Ha (Psychological Review, 1987) of ambiguous verification or conclusive falsification of five possible types of hypotheses by positive and negative tests by emphasizing the importance of further examples following hypothesis tests. In two experiments four-person cooperative groups solved rule induction problems by proposing a hypothesis and selecting evidence to test the hypothesis on each of four arrays on each trial. In different conditions the groups were instructed to use different combinations of positive and negative tests on the four arrays. Positive tests were more likely to lead to further examples than negative tests, and the proportion of correct hypotheses corresponded to the proportion of positive tests, in both experiments. We suggest that positive tests are more effective than negative hypothesis tests in generating further evidence, and thus in inducing the correct rule, in experimental rule induction tasks with a criterion of certainty imposed by the researcher.     

SEEING TWO AS ONE:

Abstract -Object tokens are episodic visual representations that mediate the ability to track visual events as they move about and change over time. Multiple tokens also allow the viewer to individuate multiple instances of a single type of object. In the present study, we established a functional link for object tokens in two seemingly disparate visual phenomena: apparent motion and repetition blindness [RB]. In RB, repeated items are more difficult to perceive than unre-peated items. Using displays in which two sets of alphanumeric characters streamed in opposite directions across a computer screen in apparent motion, we found increased RB for targets appearing within a single apparent motion stream, relative to targets in different apparent motion streams. The results are inconsistent with refractory period or memory retrieval accounts of RB and support the role of object tokens in both apparent motion and RB.     

“mother is not holding competely respect”: Making social sense of schizophrenic writing

This paper provides a phenomenological account of the writing of a young woman diagnosed with schizophrenia. The method of interpretation is to put ourselves in the place of the author drawing upon a combination of sympathy, reason, common-sense, experience, and “an intersubjective world, common to us all” (Schutz, 1945: 536). The result is the recognition of the person as also capable of putting herself in the place of others so as to understand their behavior. This “role-taking success” identifies the limits of the current sociological understanding of insanity's significance in social interaction as an instance of “role-taking failure” (Rosenberg, 1992). The very appearance of a piece of writing often permits one to recognize the presence of schizophrenia. The use of space may be quite bizarre. The varying margins betray the writer's changing mood. The letter may start at the bottom or side of the paper or very close to the top .... Capital letters and all letters are employed without any apparent rules, the former even in the middle of a word. (Bleuler, 1950: 159) What we want to understand is not something hidden behind the text, but something disclosed in front of it. (Ricoeur, 1971: 557) Why do we need an art of guessing? Why do we have to “construe” the meaning? Not only — as I tried to say a few years ago — because language is metaphorical and because the double meaning of metaphorical language requires an art of deciphering which tends to unfold the several layers of meaning.... [But also] because [a text] is not a mere sequence of sentences, all on an equal footing and separately understandable. A text is a whole, a totality. (Ricoeur, 1971: 548)