Ordered categories and additive conjoint measurement on connected sets

Suppose that a binary relation is given on a n-fold Cartesian product. The study of the conditions guaranteeing the existence of n value functions such that the binary relation can be additively represented is known as additive conjoint measurement. In this paper we analyze a related problem: given a partition of a Cartesian product into r ordered categories, what conditions do ensure the representability of the partition in an additive model?     

On infinite EPR-like correlations

The paper investigates, in the framework of branching space–times, whether an infinite EPR-like correlation which does not involve finite EPR-like correlations is possible. The authors read earlier versions of this paper at the seminar ‘Chaos and Quantum Information’ at the Jagiellonian University in Kraków on April 16, 2007 and at the seminar ‘On Determinism’ at the University of Bonn on April 20, 2007.     

Gender and the infinite: On the aspiration to be all there is

International Journal for Philosophy of Religion -     

论格义的本义及其引伸

本文探讨了“格义”的两种含义,即它的基本义和引申义。格义的基本义就是它的文本义,而引申义则是后人对它作为一种文化现象研究时引出的一个概念。格义在早期佛教的传播历史上起到了不可替代的作用,并且揭示了跨文化交流中的普遍意义,于是它的义蕴得到了引申和发挥,产生了“格义佛教”这个术语。格义的本义是一种概念上的对等,但是后人提到的“格义”如“格义佛教”则是它的引申义,变成了比较哲学中的一个中心概念。     

On a hitherto unexploited extension of the finitary standpoint

P. Bernays has pointed out that, in order to prove the consistency of classical number theory, it is necessary to extend Hilbert's finitary standpoint by admitting certain abstract concepts in addition to the combinatorial concepts referring to symbols. The abstract concepts that so far have been used for this purpose are those of the constructive theory of ordinals and those of intuitionistic logic. It is shown that the concept of a computable function of finite simple type over the integers can be used instead, where no other procedures of constructing such functions are necessary except simple recursion by an integral variable and substitution of functions in each other (starting with trivial functions).     

On the young child's comparison of sets

When asked to make comparisons between sets of objects, 4-year-old children succeed when the comparison questions are symmetrical with respect to the referential status of their terms. Thus questions that request the comparison of set with set, or subset with subset (both within and between sets), are answered correctly. However, when the comparison questions are referentially asymmetrical, calling for the comparison of set with subset, either within or between sets, young children typically fail to complete such tasks successfully. In such cases, what comparisons young children arrive at is established, how they arrive at them is described, and why they respond in the ways that they do is discussed.     

On ranking sets of statements in terms of plausibility

The axioms adopted by Packard (1981) and Heiner and Packard (1983) for plausibility ranking of sets of statements are critically examined. It is shown that the informational requirement of the Heiner-Packard (1983) framework is much stronger than Packard's (1981) framework and hence both axiomatic setups are examined separately. A characterization of the leximin rule is provided in Packard's framework and the nonintuitive implications of the Heiner-Packard (1983) axioms are discussed. It is also demonstrated that in both frameworks, minor variations of some of the axioms convert the characterization results into logical impossibilities.I am grateful to Prof. P. K. Pattanaik for many helpful suggestions.     

On the extension of intuitionistic propositional logic with Kreisel-Putnam's and Scott's schemes

LetSKP be the intermediate prepositional logic obtained by adding toI (intuitionistic p.l.) the axiom schemes:S = ((? ?α→α)→α∨ ?α)→ ?α∨ ??α (Scott), andKP = (?α→β∨γ)→(?α→β)∨(?α→γ) (Kreisel-Putnam). Using Kripke's semantics, we prove:

1. SKP has the finite model property;
2. SKP has the disjunction property.

In the last section of the paper we give some results about Scott's logic S = I+S.     

On the relation provable equivalence and on partitions in effectively inseparable sets

We generalize a well-knownSmullyan's result, by showing that any two sets of the kindC _a = {x/ xa} andC _b = {x/ xb} are effectively inseparable (if I b). Then we investigate logical and recursive consequences of this fact (see Introduction).     

An extension of the exemplar-based random-walk model to separable-dimension stimuli

An extension of Nosofsky and Palmeri's (Psychol. Rev. 104 (1997a) 266) exemplar-based random-walk (EBRW) model of categorization is presented as a model of the time course of categorization of separable-dimension stimuli. Nosofsky and Palmeri (1997a) assumed that the perceptual encoding of all stimuli was identical. However, in the current model, we assume as in Lamberts (J. Exp. Psychol.: General 124 (1995) 161) that the inclusion of individual stimulus dimensions into the similarity calculations is a stochastic process with the probability of inclusion based on the perceptual salience of the dimensions. Thus, the exemplars that enter into the random-walk change dynamically during the time course of processing. This model is implemented as a Markov chain. Its predictions are compared with alternative models in a speeded categorization experiment with separable-dimension stimuli.