Falsificationism and Statistical Learning Theory: Comparing the Popper and Vapnik-Chervonenkis Dimensions

We compare Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory. Popper’s notion of the dimension of a theory is contrasted with the apparently very similar VC-dimension. Having located some divergences, we discuss how best to view Popper’s work from the perspective of statistical learning theory, either as a precursor or as aiming to capture a different learning activity.     

Flexible cue use in food-caching birds

An animal’s memory may be limited in capacity, which may result in competition among available memory cues. If such competition exists, natural selection may favor prioritization of different memory cues based on cue reliability and on associated differences in the environment and life history. Food-caching birds store numerous food items and appear to rely on memory to retrieve caches. Previous studies suggested that caching species should always prioritize spatial cues over non-spatial cues when both are available, because non-spatial cues may be unreliable in a changing environment; however, it remains unclear whether non-spatial cues should always be ignored when spatial cues are available. We tested whether mountain chickadees (Poecile gambeli), a food-caching species, prioritize memory for spatial cues over color cues when relocating previously found food in an associative learning task. In training trials, birds were exposed to food in a feeder where both spatial location and color were associated. During subsequent unrewarded test trials, color was dissociated from spatial location. Chickadees showed a significant pattern of inspecting feeders associated with correct color first, prior to visiting correct spatial locations. Our findings argue against the hypothesis that the memory of spatial cues should always take priority over any non-spatial cues, including color cues, in food-caching species, because in our experiment mountain chickadees chose color over spatial cues. Our results thus suggest that caching species may be more flexible in cue use than previously thought, possibly dependent upon the environment and complexity of available cues.     

Internal approach to external sets and universes

In this article we show how the universe of HST, Hrbaek set theory (a nonstandard set theory of external type, which includes, in particular, the ZFC Replacement and Separation schemata for all formulas in the language containing the membership and standardness predicates, and Saturation for standard size families of internal sets, but does not include the Power set axiom) admits a system of subuniverses which keep the Replacement, model Power set and Choice (in fact all of ZFC, with the exception of the Regularity axiom, which indeed is replaced by the Regularity over the internal subuniverse), and also keep as much of Saturation as it is necessary.This gives sufficient tools to develop the most complicated topics in nonstandard analysis, such as Loeb measures.Partially supported by AMS grants in 1993 – 1995 and DFG grants in 1994 – 1995. Robert Goldblatt     

The justification of political conformism: The mythology of Soviet intellectuals

Only during a brief period in the aftermath of the revolution was a portion of the Soviet intelligentsia eager sincerely to cooperate with the Soviet system. Soon, with Stalin's repressions, the intelligentsia, and especially its elite — the intellectuals, or those involved in creative activities such as science, literature and the arts, became locked in permanent conflict with the government.Once mass terror disappeared after Stalin's death in 1953, intellectuals faced the possibility of confronting the regime without fear of instant arrest and eventual death in the Gulag.Moral choices became a serious problem, especially during the period of political reaction under Brezhnev in the 1970's, when the regime resorted to repressions (albeit in milder form than during Stalin's times) and corruption in order to prevent the oppositional activity of intellectuals. Brezhnev's regime was rather successful in this endeavor, an issue which was hotly debated by Russian intellectuals in the period ofglasnost' when soul-searching and recanting about their behavior of the 1970's.The political conformism of intellectuals bore an interesting product, namely, a special mythology which had to exculpate passive intellectuals as well as those who corroborated with the authorities and betrayed their colleagues.The goal of this paper is to analyze this mythology. The author makes a distinction between two kinds of mythology used by the intellectuals to justify their conformity — a current mythology, which is employed for the vindication of contemporary deeds and a retrospective mythology, the purpose of which is to acquit one of past actions. The importance of the mythology employed by the intellectuals goes beyond the Soviet experience and reminds one of the developments in the American intellectual community during the McCarthy era, as well as in German and French communities during the Second World War. As a theoretical basis for this paper, the author uses the concept of a two-level mentality which helps explain how people can easily separate their behavior from their system of values.     

Clustering with relational constraint

The paper deals with clustering problems where grouping is constrained by a symmetric and reflexive relation. For solving clustering problems with relational constraints two methods are adapted: the standard hierarchical clustering procedure based on the Lance and Williams formula, and local optimization procedure, CLUDIA. To illustrate these procedures, clusterings of the European countries are given based on the developmental indicators where the relation is determined by the geographical neighbourhoods of countries.Extended version of the paper presented at the European meeting of the Psychometric Society, Groningen, June, 19–21, 1980.This work was supported in part by the Boris Kidri Fund, Yugoslavia.     

The golden section and an algebraic model of ethical cognition

In experimental investigations related to Kelly's theory of constructs (1955. The psychology of personal constructs. New York: Norton) a special constant was discovered. It was found that subjects on the average choose a positive over a negative pole with the probability 0.62. (Adams-Webber and Benjafield 1973. Canadian Journal of Behavioral Science5, 234–241). The same constant was also found in other experiments related to the choice of elements marked “good” and “bad.” Benjafield and Adams-Webber (1976. British Journal of Psychology67, 11–15) hypothesized that the precise value of this constant coincides with “golden section” ≈0.6180. In this paper it is shown that if we suppose that the subjects actualize mechanisms of choice described by the algebraic model of ethical cognition (which was constructed without any relation to the constant 0.62), then the existence of this constant is mathematically explained. Under very broad assumptions its value is 0.625, and under more constrained conditions it is equal to the golden section ratio precisely.     

Scientific problems and questions from a logical point of view

Scientific knowledge systems function as effective and specialized apparatus for formulating, analyzing and solving scientific problems. In science, problems become internal parts of the knowledge systems; thus they acquire new forms and properties in comparison with common-sense problems. Definite theoretical structures connected with problems and questions appear in the theory. Among them are erotetic expressions and languages, calculi and algebras of problems. On the basis of the structure-nominative reconstruction of a theory, the unified treatment of these structures is given. Methods of the theory of named sets are used in the logical analysis of problems and their systems. As a consequence a new formalized model of the problem part of theory is constructed.     

古米廖夫与亨廷顿:进路与术语

20世纪90年代,我着手写一篇论文“13至19世纪高加索西北地区各民族之间的关系”。从这个项目一开始,我就遇到了两个困难:采取哪个进路,使用哪个术语。当时,俄罗斯刚刚开始出版列夫·古米廖夫的文集,他是列宁格勒大学教授,曾在劳改集中营服刑。他所应用的术语从推导上讲结构似乎     

When looks are everything: appearance similarity versus kind information in early induction

The goal of this research was to examine mechanisms underlying early induction--specifically, the relation between induction and categorization. Some researchers argue that even early in development, induction is based on category-membership information, whereas others argue that early induction is based primarily on similarity. Children 4 and 5 years of age participated in two types of tasks: categorization and induction. Both tasks were performed with artificial animal-like categories in which appearance was pitted against category membership. Although the children readily acquired category-membership information and subsequently used this information in categorization tasks, they ignored category membership during the induction task, relying instead on the appearance of items. These results support the idea that early in development, induction is similarity based.