Interval representations for interval orders and semiorders

This paper discusses two types of real interval representations for interval orders and semiorders ? on a set X of arbitrary cardinality. In each type, each x in X is mapped into a real interval F(x). The first model is: x ? y iff a < b for all a in F(x) and all b in F(y). The second is: x ? y iff sup F(x) < infF(y). Necessary and sufficient countability conditions are presented for the second model for interval orders and for semiorders; simpler sets of these conditions are shown to be sufficient for the first model. Some special properties for the representations are noted, including two monotonicity properties for the semiorder representation.     

Continuous representability of semiorders

In the framework of the analysis of orderings whose associated indifference relation is not transitive, we study the structure of a semiorder, paying attention to the problem of its continuous representability through a real-valued function and a positive threshold. For the case of connected topological spaces, we obtain a full characterization of the continuous representability of semiorders without extremal elements.     

Lexicographic aggregation of semiorders

It is well known that the lexicographic aggregation of complete preorders gives a complete preorder. Unfortunately, this property is no longer true when the lexicographic rule is applied to semiorders. In this paper we study some ways of defining a lexicographic aggregation of semiorders and the properties of the resulting structures.     

On jnd representations of semiorders

This paper determines automorphisms and endomorphisms associated with constant jnd (just noticeable difference) semiorder representations. Building on the constant jnd case, a novel representation theorem is given for countable semiorders which provides insight into the role of more complex jnd functions. The significance of the representation problem for countable structures is clarified by discussion of relations among observations, representations, and theories. The stress is on motivation, and on general methods applicable to many measurement models.     

The Scott-Suppes theorem on semiorders

Luce introduced semiorders as a natural generalization of weak orders. The basic representation theorem for semiorders was established in 1958 by Scott and Suppes. In this note this theorem is given a simple contructive proof.     

Some problems for Gibbard's norm-expressivism

Conclusion I conclude that Gibbard fails to solve several of the traditional problems for expressivism. He solves some of these problems, but his solutions to them in effect give up expressivism. Of course, one might respond that it does not really matter whether his theory is expressivist. In some ways, I agree. Gibbard says many fascinating things about morality which have at most indirect connections to his expressivist analysis. I am thinking especially of his later discussions of hyperscepticism (180), parochialism (203 ff.), and indirect pragmatism (224). These views could still be developed even if he gave up expressivism. All I have tried to show here is that he does need to give up expressivism unless he can solve the problems that I have raised.     

Some big ideas for some big problems

Although most psychologists do not see sustainability as a psychological problem, our environmental predicament is caused largely by human behaviors, accompanied by relevant thoughts, feelings, attitudes, and values. The huge task of building sustainable cultures will require a great many psychologists from a variety of backgrounds. In an effort to stimulate the imaginations of a wide spectrum of psychologists to take on the crucial problem of sustainability, this article discusses 4 psychological approaches (neo-analytic, behavioral, social, and cognitive) and outlines some of their insights into environmentally relevant behavior. These models are useful for illuminating ways to increase environmentally responsible behaviors of clients, communities, and professional associations.     

Ethnoracial political representation in Toronto: Patterns and problems

This paper examines both the statistical and substantive dimensions of ethnoracial electoral representation in Toronto. We compare politician profiles across the municipal, provincial and federal arenas of politics and conclude there is a dual “representation gap’ in Toronto’s electoral politics. First, minority communities—especially visible minorities—are numerically badly underrepresented in Toronto across all levels of government. Second, the record of minority-identity politicians on municipal council suggests they do not necessarily serve minority community interests well. The paper analyzes these patterns and problems, concluding that solutions likely lie beyond the parameters of liberal democratic norms of political representation.     

Some technical problems of countertransference

There are several aspects of the psychoanalytic interaction that foster the emergence of countertransference. First is a persistent identification with the patient, based primarily on the sharing of unconscious fantasies. Then there is the evocative power the patient's material may have upon latent unresolved conflicts in the analyst. Finally, the analytic setting itself may evoke a broad range of countertransference responses. Particular attention must be paid to those interventions of the analyst which represent attempts to divert his own and the patient's attention from emerging derivatives of the conflicts. There are many clues that should alert the analyst to the possibility of interfering countertransference.     

Some problems facing intuitionist meta-methodologies

Intuitionistic meta-methodologies, which abound in recent philosophy of science, take the criterion of success for theories of scientific rationality to be whether those theories adequately explicate our intuitive judgments of rationality in exemplary cases. Garber's (1985) critique of Laudan's (1977) intuitionistic meta-methodology, correct as far as it goes, does not go far enough. Indeed, Garber himself advocates a form of intuitionistic meta-methodology; he merely denies any special role for historical (as opposed to contemporary or imaginary) test cases. What all such positions lack is a base from which to inform, criticize, or restructure our core methodological intuitions. To acquiesce in this is to deny that exemplary cases can serve the sort of warranting role required for intuitionism. This point is reinforced by a series of reasons for denying the warranting role of pre-analytic judgments of rationality. These reasons point the way toward an improved approach to meta-methodology.     

Some problems in forensic assessment

The establishing of facts in criminal cases calls for the marshalling of evidence, from every angle and without bias, in strict compliance with the law. The findings of the court in respect of criminal accountability must likewise be established beyond doubt; probability is inadequate as a basis for conviction. The highest degree is inadequate as a basis for conviction. The highest degree of forensic competence in matters psychiatric and psychological must be assured. Expert opinion must proceed from an evaluation of the accused person's capacity to distinguish between right and wrong, taking account of the nature of the offense. Part of this evaluation consists in the determination of the combined effect of the principal determining factors. Greater depth of knowledge is required respecting the part played by alcohol in the capacity to distinguish right from wrong compared with impulse, mental deficiency, grave abnormal development, etc. In the interests of securing a sound judgment of criminal accountability, further research is desirable into the complexus of determining factors, for example, into the multifunctional contribution of deranged physiological structures and processes which take a mental and/or psychopathological course.     

Some problems of Wilson's disease

The Leipzig Center for Wilson's Disease in the GDR is charged with the registration and diagnosis of all homozygous Wilson gene carriers, the clarification of all suspected cases, including the heterozygote test, and the co-ordination of long-term treatment. At present, there are 78 recorded Wilson gene carriers living. On the basis of our own comprehensive observations and investigations over prolonged periods of time, questions concerning pathogenesis, genetics, diagnosis and therapeutic measures, including their side-effects, are dealt with.