Quantum Mechanical Unbounded Operators and Constructive Mathematics – a Rejoinder to Bridges

As argued in Hellman (1993), the theorem of Pour-El and Richards (1983) can be seen by the classicist as limiting constructivist efforts to recover the mathematics for quantum mechanics. Although Bridges (1995) may be right that the constructivist would work with a different definition of closed operator, this does not affect my point that neither the classical unbounded operators standardly recognized in quantum mechanics nor their restrictions to constructive arguments are recognizable as objects by the constructivist. Constructive substitutes that may still be possible necessarily involve additional incompleteness in the mathematical representation of quantum phenomena. Concerning a second line of reasoning in Hellman (1993), its import is that constructivist practice is consistent with a liberal stance but not with a radical, verificationist philosophical position. Whether such a position is actually espoused by certain leading constructivists, they are invited to clarify.     

The relationship between perceived surface-lightness and perceived illumination

Summary An attempt was made to specify the relationship between perceived surface lightness and perceived illumination under the stimulus conditions where different combinations of albedo and illuminance gave 10 approximately equal-luminance levels of a test field (TF) on three different (black-, gray- and white-appearing) backgrounds. Two types of category judgments for TF-lightness and overall illumination were made on the total of 94 TFs by 5 Ss. The results indicated that under the condition where achromatic surface colors appear, the perceptual scission which produces two different perceptual dimensions (lightness and perceived illumination) from one sort of stimulation (luminance) was clearly observed. The relation between the two judgments was consistent with the lightness-illumination invariance hypothesis: As lightness judgments (A) changed from darker to lighter, illumination judgments (I) shifted form brighter to dimmer, the sum of A and I being kept nearly invariant for a given luminance of the TF; the psychological relationship between lightness and illumination, A+I, changed as a linear function of the photometric combination of albedo and illuminance, log A+log I. It was also found that the albedo of the background was an important factor determining the extent of perceptual scission between lightness and illumination.     

Trying to Resolve the Two-Envelope Problem

After explaining the well-known two-envelope paradox by indicating the fallacy involved, we consider the two-envelope problem of evaluating the factual information provided to us in the form of the value contained by the envelope chosen first. We try to provide a synthesis of contributions from economy, psychology, logic, probability theory (in the form of Bayesian statistics), mathematical statistics (in the form of a decision-theoretic approach) and game theory. We conclude that the two-envelope problem does not allow a satisfactory solution. An interpretation is made for statistical science at large.     

Promoting perspective coordination by dilemma discussion. The effectiveness of classroom group discussion on interpersonal negotiation strategies of 12-year-old students

Promoting social competence and social cognition is an important aim of education and socialization. According to theories of social cognitive and moral development, social cognition may be promoted by adolescent peer interaction. In this study, social cognition is theoretically conceptualized by the interpersonal negotiation strategies model of Selman which distinguishes levels of perspective coordination and steps of information processing (identification of a problem, generating negotiation strategies, selection of a strategy, evaluation). In a pre-post control group design this study investigated whether dilemma discussions among peers lead to higher individual levels of perspective coordination compared to an individualistic condition. Members of the discussion-condition exhibited higher gain scores in perspective coordination compared to the control group regarding the information processing steps generating strategies and strategy selection. In order to analyze verbal interaction in the discussion groups, an integrative coding schedule was developed. In addition, trait-like argumentative motives of the participants were assessed. The results of multilevel analyses suggest that progress in posttest-perspective coordination is mediated by the groups consensual solution of the dilemma as well as by an explanation-oriented discussion style, but only if the latter is accompanied by a trait-like subject- and consensus-oriented argumentative motive. Theoretical and practical conclusions are drawn.     

Some notes on the nature of methodological indeterminacy

This paper is an attempt to extend the meaning of the concept of indeterminacy for the human sciences. The authors do this by coining the term methodological indeterminacy and arguing that indeterminacy is better understood when linked to specific methodological techniques. Paradoxically, while specific research techniques demonstrate that the issue of indeterminacy is complex, yielding the possibility of types and degrees, it does not eliminate the problem of translation first raised by Quine. However, the authors go on to argue that, from a research perspective, indeterminacy can and must be approached in such a way that it is possible to reduce cases of it, even though never completely eliminating it in the human sciences.     

Commensurability, incommensurability, and cumulativity in scientific knowledge

Until the middle of the present century it was a commonly accepted opinion that theory change in science was the expression of cumulative progress consisting in the acquisition of new truths and the elimination of old errors. Logical empiricists developed this idea through a deductive model, saying that a theory T superseding a theory T must be able logically to explain whatever T explained and something more as well. Popper too shared this model, but stressed that T explains the old known facts in its own new way. The further pursual of this line quickly led to the thesis of the non-comparability or incommensurability of theories: if T and T are different, then the very concepts which have the same denomination in both actually have different meanings; in such a way any sentence whatever has different meanings in T and in T and cannot serve to compare them. owing to this, the deductive model was abandoned as a tool for understanding theory change and scientific progress, and other models were proposed by people such as Lakatos, Kuhn, Feyerabend, Sneed and Stegmüller. The common feature of all these new positions may be seen in the claim that no possibility exists of interpreting theory change in terms of the cumulative acquisition of truth. It seems to us that the older and the newer positions are one-sided, and, in order to eliminate their respective shortcomings, we propose to interpret theory change in a new way.The starting point consists in recognizing that every scientific discipline singles out its specific domain of objects by selecting a few specific predicates for its discourse. Some of these predicates must be operational (that is, directly bound to testing operations) and they determine the objects of the theory concerned. In the case of a transition from T to T, we must consider whether or not the operational predicates remain unchanged, in the sense of being still related to the same operations. If they do not change in their relation to operations, then T and T are comparable (and may sometimes appear as compatible, sometimes as incompatible). If the operational predicates are not all identical in T and T, the two theories show a rather high degree of incommensurability, and this happens because they do not refer to the same objects. Theory change means in this case change of objects. But now we can see that even incommensurability is compatible with progress conceived as the accumulation of truth. Indeed, T and T remain true about their respective objects (T does not disprove T), and the global amount of truth acquired is increased.In other words, scientific progress does not consist in a purely logical relationship between theories, and moreover it is not linear. Yet it exists and may even be interpreted as an accumulation of truth, provided we do not forget that every scientific theory is true only about its own specific objects.It may be pointed out that the solution advocated here relies upon a limitation of the theory-ladeness of scientific concepts, which involves a reconsideration of their semantic status and a new approach to the question of theoretical concepts. First of all, the feature of being theoretical is attributed to a concept not absolutely, but relatively, yet in a sense different from Sneeds's: indeed every theory is basically characterized by its operational concepts, and the non-operational are said to be theoretical, this distinction clearly depending on every particular theory. For the operational concepts it happens that their mean-     

The Definition of Moral Dilemmas: A Logical Problem

This paper concerns one of the undecided disputes of modern moral philosophy: the possibility of moral dilemmas. Whereas proponents of the possibility of moral dilemmas often appeal to moral experience, many opponents refer to ethical theory and deontic logic. My aim in this paper is to clarify some of the tension between moral experience and ethical theory with respect to moral dilemmas. In Part One I try to show that a number of logical arguments against the possibility of moral dilemmas, though apparently very different, turn out to be basically the same, as they are all based on the following concept of ought: if A ought to be done, doing B is impermissible and doing A itself is permissible. In Part Two I present an overview of several definitions of moral dilemmas that have been given by proponents of moral dilemmas: definitions that define moral dilemmas in terms of oughts and definitions that define them in terms of reasons. I conclude that, while reason is to weak, ought is too strong a concept to define moral dilemmas with. In this way, the arguments from Part One create a logical problem for proponents of the possibility of moral dilemmas to define moral dilemmas.     

Once More into the Breach of Self-Ownership: Reply to Narveson and Brenkert

In reply to Narveson, I distinguish his no-proviso argument from his liberty argument, and I show that both fail. I also argue that interference lacks the strategic status he assigns to it, because it cannot be appropriately distinguished, conceptually and morally, from prevention; that natural resources do enjoy the importance he denies they have; that laissez-faire economies lack the superiority he attributes to them; that ownership can indeed be a reflexive relation; that anti-paternalism does not entail libertarianism; and that he misrepresents the doctrines of a number of philosophers, including John Locke, Ronald Dworkin, and myself. In reply to Brenkert, I show that he seriously misconstrues my view of the nature of freedom, and of its relationship to self-ownership. I then refute his criticisms of my treatment of the contrasts between self-ownership, on the one hand, and autonomy and non-slavery, on the other. I also show that his attempt to exorcize the demon of self-ownership is multiply flawed.     

Early Adversity and the Prospective Prediction of Depressive and Anxiety Disorders in Adolescents

The current study was a prospective exploration of the specificity of early childhood adversities as predictors of anxiety and depressive disorders in adolescents. Participants were 816 adolescents (414~males, 402 females) with diagnostic information collected at age 15; information on early adversities had been collected from the mothers during pregnancy, at birth, age 6 months, and age 5~years for a related study. Adolescents with pure anxiety disorders were compared with adolescents with pure depressive disorders (major depressive disorder, dysthymia), and these groups were compared to never-ill controls. Analyses controlled for gender and maternal depression and anxiety disorders. Results indicated that adolescents with anxiety disorders were more likely than depressed youth to have been exposed to various early stressors, such as maternal prenatal stress, multiple maternal partner changes, and more total adversities, whereas few early childhood variables predicted depressive disorders. Even when current family stressors at age 15 were controlled, early adversity variables again significantly predicted anxiety disorders. Results suggest that anxiety disorders may be more strongly related to early stress exposure, while depressive disorders may be related to more proximal stressors or to early stressors not assessed in the current study.     

Relationship between psychological stress and lymphocytic 5′-ectonucleotidase

The relationship between psychological stress and lymphocytic 5-ectonucleotidase, an enzyme marker for lymphocyte differentiation, was studied. Lymphocytic 5-ectonucleotidase was decreased significantly by about twofold in persons experiencing psychological stress, with a corresponding change in Total Mood Disturbance scores of the Profile of Mood States. Enzyme values were reversible in that they returned to normal once the stress had been reduced. Administration of high doses of ascorbate to severely depressed patients also normalized 5-ectonucleotidase activities, and implied that low enzyme values in stressed persons may be mediated by oxygen radical damage. This finding was consistent with previous reports of heightened inflammatory responses occurring in depressed patients. The primary cause of lowered 5-ectonucleotidase during stress may be the breakdown in the homeostatic mechanisms of the hypothalamic-pituitary-adrenal axis and immune system resulting in lymphoid tissue resistance to corticosteroids. It is suggested that this lowering of lymphocyte 5-ectonucleotidase may contribute to stress-mediated immune suppression by inhibiting lymphocyte maturation.     

The relevance of Habermas' communicative turn

This paper points out the way in which educational and communicative action (Habermas) are to be related. It is shown that earlier attempts to put Habermas ideas to use have led to a dead end because they do not realize clearly that the new basic notion introduced by Habermas, namely communicative action, is the expression of a communicative turn. It is argued that Habermas' concept expresses a radical new attempt to grasp the intersubjective character of social action. Next implications of this communicative turn for the concept of education as a social praxis are indicated. Education can be conceived of as a praxis responding to the vulnerability of a communicative self.     

Power,Freedom, and Individuality: Foucault and Sexual Difference

This paper offers a detailed account of Foucaults ethical and political notion of individuality as presented in his late work, and discusses its relationship to the feminist project of the theory of sexual difference. I argue that Foucaults elaboration of the classical ethos of care for the self opens the way for regarding the I-woman as an ethical, political and aesthetic self-creation. However, it has significant limitations that cannot be ignored. I elaborate on two aspects of Foucaults avoidance of sexual difference as a relevant category for an account of political and ethical individuality, which thus implicitly associates individual agency with men. I argue that Foucault implicitly assumes the existence of an ontological desire to become engaged in political self-creation. However, the ethical position of self-knowledge and desire should be understood as a contingent option that depends on material and historical conditions for its realization. Hence, I argue that a feminist reworking of Foucaults notion of political individuality should add a substantial ethical condition to the imperative of self-knowledge and self-creation – making possible the desiring woman subject.     

Mathematics of Totalities: an alternative to mathematics of sets

I dare say, a set is contranatural if some pair of its elements has a nonempty intersection. So, we consider only collections of disjoint nonempty elements and call them totalities. We propose the propositional logicTT, where a proposition letters some totality. The proposition is true if it letters the greatest totality. There are five connectives inTT: , , , , # and the last is called plexus. The truth of # means that any element of the totality has a nonempty intersection with any element of the totality . An imbeddingG of the classical predicate logicCPL inTT is defined. A formulaf ofCPL is a classical tautology if and only ifG(f) is always true inTT. So, mathematics may be expounded inTT, without quantifiers.     

Valuational semantics of rule derivability

If a certain semantic relation (which we call local consequence) is allowed to guide expectations about which rules are derivable from other rules, these expectations will not always be fulfilled, as we illustrate. An alternative semantic criterion (based on a relation we call global consequence), suggested by work of J.W. Garson, turns out to provide a much better — indeed a perfectly accurate — guide to derivability.     

The Dancing Philosopher

This excerpt from Kenneth Kings essay, The Dancing Philosopher, traces its genesis from Nietzsches Thus Spoke Zarathustra (a work that greatly impacted Isadora Duncans founding of modern dance) that, in tandem with the emerging technology of the writing machine (typewriter), camera and kinetoscope (cinematography), conjoined the kinetropic and lexigraphemic to inaugurate the kinetic cogito. Maurice Merleau-Pontys phenomenological exposition of corporeality further amplified the reflexive potential of movement and the philosophical understanding of kinesthesia, and King cites as well the technosophic synergy of John Cages and Merce Cunninghams long artistic collaboration that furthered the frontier of a mind-body epistemic.     

Metaphysics and the interpretation of persons: Davidson on thinking and Conceptual Schemes

Certain metaphysical and epistemological presuppositions are shown to play a role in the defense of Davidson's claims that an empirically constructed theory of truth provides an adequate theory of meaning for any natural language. Dadivson puts forward demonstrative arguments in favor of these presuppositions in On the Very Idea of a Conceptual Scheme, Thought and Talk, and The Method of Truth in Metaphysics. These arguments are examined and found to include controversial and dubitable assumptions as premises. It is then suggested that both these controversial assumptions and Davidson's metaphysical and epistemological presuppositions can be partially defended, however, by dialectical, interpretive, and historical arguments that elucidate the nature of persons.     

Логистическая система, исходными связками которой являются эквивалентность и дизъюнкция

- Allatum est die 5 Martii 1970     

Mathematical modeling of the effects of ‘capability’ and ‘intent’ on the stability of a competitive international system

In international relations theory, there is a long history of Richardson-like modeling of the evolution of military capability. Usually, such models are deterministic and predictive and do not allow for the representation of the transition from competitive peace to shooting war. More recently, models have been developed which attempt to represent the evolution of relationship between nations. The relationship between nations, varying from friendship to hostility, is taken to be synonymous with the intent of nations towards each other, varying from good will to malice. Generally, these relationship models do not include capability though common sense would indicate that capability and mutual intent should profoundly influence each other. A model is presented here which combines these two fundamental attributes of international relations and attempts to represent the outbreak of war in the world system by the onset of deterministic chaos in the extended model.On leave 1994–95 at U.S. Arms Control and Disarmament Agency, Washington, D.C. 20451, U.S.A.     

Stuffed Cabbage in the Old New School Cafeteria

The purpose of this lecture is to celebrate the memory of Aron Gurwitsch by examining and enlarging the domain of phenomenological clarification of some elements of what Gurwitsch called the logic of reality. Chief among those elements are the nature of the taken-for-grantedness of our existential belief, the difference between presentive and non-presentive indices of reality and the ground for the self-illumination of the world of working.     

A generalization of the theory of subjective probability and expected utility

A generalization of the usual approach to the expected utility theory is given, with the aim of representing the state of belief of an agent who may decline on grounds of ignorance to express a preference between a given pair of acts and would, therefore, be considered irrational from a Bayesian point of view. Taking state, act, and outcome as primitive concepts, a utility function on the outcomes is constructed in the usual way. Each act is represented by a utility-valued function on the states — but not all such functions are taken to represent acts. A weaker than usual set of axioms on preferences between acts is now postulated. It is shown that any agent can be represented by a risk function that assigns to each (mixed) state a number that gives the maximum loss (in utility) the agent might expect should be the actual state of the world. The form of the risk function is determined, both in general and in important particular cases. The results show that any rational agent behaves as though he were acting under the guidance of a set of Bayesian (or, more generally, pseudo-Bayesian) advisors.