Mathematical quantum theory I: Random ultrafilters as hidden variables

The basic purpose of this essay, the first of an intended pair, is to interpret standard von Neumann quantum theory in a framework of iterated measure algebraic truth for mathematical (and thus mathematical-physical) assertions — a framework, that is, in which the truth-values for such assertions are elements of iterated boolean measure-algebras (cf. Sections 2.2.9, 5.2.1–5.2.6 and 5.3 below).The essay itself employs constructions of Takeuti's boolean-valued analysis (whose origins lay in work of Scott, Solovay, Krauss and others) to provide a metamathematical interpretation of ideas sometimes considered disparate, heuristic, or simply ill-defined: the collapse of the wave function, for example; Everett's many worlds'-construal of quantum measurement; and a natural product space of contextual (nonlocal) hidden variables.More precisely, these constructions permit us to write down a category-theoretically natural correlation between ideal outcomes of quantum measurements u of a universal wave function, and possible worlds of an Everett-Wheeler-like many-worlds-theory.The universal wave function, first, is simply a pure state of the Hilbert space (L ₂([0, 1]) ^M in a model M an appropriate mathematical-physical theory T, where T includes enough set-theory to derive all the analysis needed for von Neumann-algebraic formulations of quantum theory.The worlds of this framework can then be given a genuine model-theoretic construal: they are random models M(u) determined by M-random elements u of the unit interval [0, 1], where M is again a fixed model of T.Each choice of a fixed basis for a Hilbert space H in a model of M of T then assigns ideal spectral values for observables A on H (random ultrafilters on the range of A regarded as a projection-valued measure) to such M-random reals u. If is the universal Lebesgue measure-algebra on [0, 1], these assignments are interrelated by the spectral functional calculus with value 1 in the boolean extension (V( )) ^M , and therefore in each M(u).Finally, each such M-random u also generates a corresponding extension M(u) of M, in which ideal outcomes of measurements of all observables A in states are determined by the assignments just mentioned from the random spectral values u for the universal position-observable on L ₂([0, 1]) in M.At the suggestion of the essay's referee, I plan to draw on its ideas in the projected sequel to examine more recent modal and decoherence-interpretations of quantum theory, as well as Schrödinger's traditional construal of time-evolution. A preliminary account of the latter — an obvious prerequisite for any serious many-worlds-theory, given that Everett's original intention was to integrate time-evolution and wave-function collapse — is sketched briefly in Section 5.3. The basic idea is to apply results from the theory of iterated measure-algebras to reinterpret time-ordered processes of measurements (determined, for example, by a given Hamiltonian observable H in M) as individual measurements in somewhat more complexly defined extensions M(u) of M.In plainer English: if one takes a little care to distinguish boolean- from measure-algebraic tensor-products of the universal measure-algebra L, one can reinterpret formal time-evolution so that it becomes internal to the universal random models M(u).     

Liberalism, entitlement, and verdict exclusion

In a series of recent papers, Crispin Wright has developed and defended an epistemic account of borderline cases which he calls ‘Liberalism’. If Verdict Exclusion is the claim that no polar verdict on borderline cases is knowledgeable, then Liberalism implies the view that Verdict Exclusion is itself nothing we are in a position to know. It is a matter of ongoing discussion what more Liberalism implies. In any case, Wright argues that Liberalism affords the means to account for the intuition that polar verdicts on borderline cases are equally permissible. Here I argue that Liberalism fails to deliver and that an account of borderline cases based on Verdict Exclusion fares much better when it comes to showing that our ordinary practice of reaching verdicts on borderline cases is fully legitimate: all it needs is a reassessment of the nature of the claims such verdicts express.     

The premack principle, response deprivation, and establishing operations

This paper describes response deprivation as an establishing operation. In this context, we review the concept of establishing operation, in particular, its reinforcer-establishing and evocative effects; we place response deprivation in the literature on the reinforcing effects of behavioral activity, wherein response deprivation subsumes the Premack principle; we describe the reinforcer-altering and evocative effects of response deprivation; and we address a methodological concern about the evocative effect. In closing, we discuss some conceptual and empirical implications of the foregoing analyses.     

The sure thing principle,dilations, and objective probabilities

The common theme that unites the four sections is STP, the sure thing principle. But the paper can be divided neatly into two parts. The first, consisting of the first two sections, contains an analysis of STP as it figures in Savage?s system and proposals of changes to that system. Also possibilities for partially ordered acts are considered. The second, consisting of the last two sections, is about imprecise probabilities, dilations and objective probabilities. Variants of STP are considered but this part is self-contained and can be read separately. The main claim there is that dilations, which can have extremely counterintuitive consequences, can be eliminated by a more careful analysis of the phenomenon. It outlines a proposal of how to do it. Here the concept of objective probabilities plays a crucial role.     

The reality principle, tragic knots, and the analytic process

Civilization and Its Discontents is shown to occupy a special place in Freud's development of psychoanalytic theory and technique. Especially emphasized is its implications for an inclusive understanding of the reality principle. The concept tragic knots is then defined and used to emphasize Freud's readiness to include tragic elements in that principle. An extended section then illustrates the spread of tragic knots into several diverse aspects of human existence: victimization, intimacy, and maintaining privacy. Finally, implications are drawn for the clinical assessment of working through unconscious conflicts.     

Demographic variables, smoking variables, and outcome across five studies.

OBJECTIVE: Intervention effectiveness can potentially be affected by membership in different demographic subgroups (race, ethnicity, gender, age, and education level) or smoking behavior variables (time to first cigarette, longest previous quit attempt, number of attempts in the past year, number of cigarettes, and stage of change). Previous research on these 2 sets of variables has produced mixed results. DESIGN: This secondary data analysis combined data from 5 effectiveness trials (a random-digit-dial sample [N=1,358], members of an HMO [N=207], parents of students recruited for a school-based study [N=347], patients from an insurance provider list [N=535], and employees [N=175]) in which smokers were all proactively recruited from a defined population and all received the same expert system intervention. The intervention produced a consistent 22% to 26% point prevalence cessation rate across the 5 studies. MAIN OUTCOME MEASURES: The main outcome measures were 24-hr point prevalence, 7-day point prevalence, 30-day prolonged abstinence, and 6-month prolonged abstinence. RESULTS: There were no significant differences in outcome across gender, race, and ethnicity subgroups. There were significant differences and small effect sizes for age and education subgroups. There were significant differences and large effect sizes for all 5 smoking behavior variables. DISCUSSION: Demographic variables are static variables, whereas the smoking variables are more dynamic, that is, open to change. Given the dynamic nature of the smoking variables and the large effect sizes, interventions tailored on the smoking variables should be more successful.     

Relations among cognitive,semantic, and syntactic variables in children's comprehension of the minimum distance principle: A 2-year developmental study

Theoretical issues regarding cognitive aspects of the semantic interpretation of two syntactic structures were examined. A 2-year study was conducted investigating possible developmental trends in children's sentence-processing strategies. Experimental materials incorporated two levels of role expectations and two levels of syntactic complexity. Subjects were initially 6–10 years old; 12 original subjects from each age group were retested a year later. Exceptional and typical syntactic structures were not of significantly different difficulty either year. Semantic and cognitive complexity, as reflected in the two levels of expectation, was significant both years (p<0.001). Performance improved, over the 12-month period, in all but the 7- to 8-year-old group (p<0.005). Results are discussed with reference to cognitive strategies in sentence processing.This article is based on research reported at the annual meeting of the Northeastern Educational Research Association, Ellenville, New York, October 29–31, 1975.     

潜在思想论略

本文厘定了潜在思想,深入分析了其产生的原因,并做了类型划分,指出了把握潜在思想的重要意义。     

潜在思想再论

思想是行为的先导,行为反映思想。然而实然思想与外显行为不匹配、不一致的现象却时有发生,究其缘由乃潜在思想使然。因此,从潜在的层面把握思想,进而分析思想与行为的辨证统一关系不失为一个好的路径选择。     

The hidden grief of abortion

This article explores the possibility of dealing with grief reaction when counseling a woman who has undergone an abortion. It first defines what is meant by a grief reaction in this context, then proposes a model for understanding various degrees of grief reaction, and finally examines some of the factors which determine the severity of a grief reaction in the case of abortion.     

The minimum principle and the perception of absolute,common, and relative motions

Wheel-generated motions have served as a touchstone for discussion of the perception of wholes and parts since the beginning of Gestalt psychology. The reason is that perceived common motions of the whole and the perceived relative motions of the parts are not obviously found in the absolute motion paths of points on a rolling wheel. In general, two types of theories have been proposed as to how common and relative motions are derived from absolute motions: one is that the common motions are extracted from the display first, leaving relative motions as the residual; the other is that relative motions are extracted first leaving common motions as the residual. A minimum principle can be used to defend both positions, but application of the principle seems contingent on the particular class of stimuli chosen. We propose a third view. It seems that there are at least two simultaneous processes—one for common motions and one for relative motions—involved in the perception of these and other stimuli and that a minimum principle is involved in both. However, for stimuli in many domains the minimization of relative motion dominates the perception. In general, we propose that any given stimulus can be organized to minimize the complexity of either its common motions or its relative motions; that which component is minimized depends on which of two processes reaches completion first (that for common or that for relative motions); and that the similarity of any two displays depends on whether common or relative motions are minimized.     

The exclusion of the other2

The author begins by noting that the subject of obsessions and obsessional neurosis seems to have fallen out of favour with the analytic community in spite of the important part it played in the formation of Freud's theories, and notwithstanding the significance of its mechanisms in the maturation of the ego. He then discusses some theoretical considerations regarding the development of the taboo on touching and, by extension, contact. Attention is drawn to the parallels with autistic functioning emphasised by other authors. Particular importance is attached to the distinction between internal and external reality that arises during the anal‐sadistic phase and that leads to polarisation and splitting in obsessional neurosis. Following a discussion of the transference' countertransference situation with obsessional patients and of their concretistic experience in the treatment situation, as also featured in the literature, an extensive case history exemplifies the author's contentions and shows how the patient concerned developed during the course of his analysis. After pointing out the importance of the avoidance of identifications as a mechanism of obsessional defence, the author concludes the paper with a brief comparison of obsessional and hysteriform functioning and a characterisation of the obsessional defence as the excessive recourse to perverted thought functions so as to ward off paranoid anxieties.     

Chaos,quantization, and the correspondence principle

Work on this paper was supported by the National Science Foundation under grant No. DIR-9012010.