Dissimilarity cumulation theory in arc-connected spaces

This paper continues the development of the Dissimilarity Cumulation theory and its main psychological application, Universal Fechnerian Scaling [Dzhafarov, E.N and Colonius, H. (2007). Dissimilarity Cumulation theory and subjective metrics. Journal of Mathematical Psychology, 51, 290-304]. In arc-connected spaces the notion of a chain length (the sum of the dissimilarities between the chain’s successive elements) can be used to define the notion of a path length, as the limit inferior of the lengths of chains converging to the path in some well-defined sense. The class of converging chains is broader than that of converging inscribed chains. Most of the fundamental results of the metric-based path length theory (additivity, lower semicontinuity, etc.) turn out to hold in the general dissimilarity-based path length theory. This shows that the triangle inequality and symmetry are not essential for these results, provided one goes beyond the traditional scheme of approximating paths by inscribed chains. We introduce the notion of a space with intermediate points which generalizes (and specializes to when the dissimilarity is a metric) the notion of a convex space in the sense of Menger. A space is with intermediate points if for any distinct there is a different point such that (where D is dissimilarity). In such spaces the metric G induced by D is intrinsic: coincides with the infimum of lengths of all arcs connecting to In Universal Fechnerian Scaling D stands for either of the two canonical psychometric increments and (ψ denoting discrimination probability). The choice between the two makes no difference for the notions of arc-connectedness, convergence of chains and paths, intermediate points, and other notions of the Dissimilarity Cumulation theory.     

Kaufmann on the Probabilities of Conditionals

Kaufmann has recently argued that the thesis according to which the probability of an indicative conditional equals the conditional probability of the consequent given the antecedent under certain specifiable circumstances deviates from intuition. He presents a method for calculating the probability of a conditional that does seem to give the intuitively correct result under those circumstances. However, the present paper shows that Kaufmann’s method is inconsistent in that it may lead one to assign different probabilities to a single conditional at the same time.     

意见收敛定理与休谟问题

意见收敛定理是主观主义概率论的一条重要定理,它表明随着证据的增加,验前概率的主观性将被验后概率的客观性所代替。意见收敛定理被看作主观概率的动态合理性原则,因而被用来解决休谟问题,即归纳合理性问题。然而,哈金有说服力地表明,意见收敛定理证明的是条件概率Pr（h／e）的收敛,而不是验后概率Pre（h）的收敛。主观主义概率论暗中接受的一个等式是：Pre（h）=Pr（h／e）,通常称之为“条件化规则”。这样,归纳法的合理性问题变成条件化规则的合理性问题。为此,本文提出一个新的合理性原则,即“最少初始概率原则”,将它同“局部合理性”观念结合起来便可为条件化规则的合理性加以辩护。     

Logics with the Qualitative Probability Operator

The paper presents several strongly complete axiomatizationsof qualitative probability within the framework of probabilisticlogic. We show that in the proposed semantics qualitative probabilitiesare characterized by probability functions, so they also arecomparative probabilities.     

The Basic Constructive Logic for a Weak Sense of Consistency defined with a Propositional Falsity Constant

The logic B_Kc1 is the basic constructive logic in the ternaryrelational semantics (without a set of designated points) adequateto consistency understood as the absence of the negation ofany theorem. Negation is introduced in B_Kc1 with a negationconnective. The aim of this paper is to define the logic B_Kc1F.In this logic negation is introduced via a propositional falsityconstant. We prove that B_Kc1 and B_Kc1F are definitionally equivalent.     

Empirical metaphysics: the role of intuitions about possible cases in philosophy

Frank Jackson has argued that only if we have a priori knowledge of the extension-fixers for many of our terms can we vindicate the methodological practice of relying on intuitions to decide between philosophical theories. While there has been much discussion of Jackson’s claim that we have such knowledge, there has been comparatively little discussion of this most powerful argument for that claim. Here I defend an alternative explanation of our intuitions about possible cases, one that does not rely on a priori extension-fixers. This alternative explanation provides a vindication of our reliance on intuitions, while blocking Jackson’s abductive argument for a priori semantic knowledge. In brief, I argue that we should regard our armchair intuitions as providing an important, a priori source of evidence for hypotheses about the contents of our implicit referential policies with regard to our terms. But all such hypotheses have a potential falsifier that is only discoverable empirically. In other words, gold-standard evidence for such hypotheses is always empirical.

Autonomous construction of ecologically and socially relevant semantics

This article presents a synthetic modeling approach to the problem of grounded construction of concepts. In many computational models of grounded language acquisition and evolution, meanings are created in the process of discrimination between a chosen object and other objects present on the scene of communication. We argue that categories constructed for the purpose of identification rather than discrimination are more suitable for the detached language use (talking about things not present here and now). We describe a semantics based on so-called identification criteria constructed by extracting cross-situational similarities among instances of a category, and present several computational models. In the model of individual category construction, the instances are grouped to categories by common motor programs (affordances), while in the model of social learning, focused on the influence of naming on category formation, entities are considered members of the same category, if they are labeled with the same word by an external teacher. By these two mechanisms, the learner can construct interactionally grounded representation of objects, properties, relations, changes, complex situations and events. We also report and analyze simulation results of an experiment focused on the dynamics of meanings in iterated intergenerational transmission.     

Talking About a Universalist World

The paper defends a combination of perdurantism with mereological universalism by developing semantics of temporary predications of the sort ’some P is/was/will be (a) Q’. We argue that, in addition to the usual application of causal and other restrictions on sortals, the grammatical form of such statements allows for rather different regimentations along three separate dimensions, according to: (a) whether ‘P’ and ‘Q’ are being used as phase or substance sortal terms, (b) whether ‘is’, ‘was’, and ‘will be’ are the ‘is’, ‘was’, ‘will be’ of identity or of constitution, and (c) whether ‘Q’ is being used as a subject or predicate term. We conclude that this latitude is beneficial, as it conforms with linguistic reality (i.e., the multiple uses actually in place) and also enables one to turn what is ordinarily perceived as a problem for universalist perdurantism viz., a commitment to all sorts of weird and gerrymandered temporally extended entities, into an advantage, for the richness in questions allows us to make sense of the many different readings of sentences of the same grammatical form.     

Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of Negation

The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation,–intuitionistic negation and some of its generalizations: minimal negation of Johansson and semi-negation.We discuss also the impact of Rasiowa works on the theory of non-classical negation.A lecture presented at the International Conference Trends in Logic III : A. Mostowski, H. Rasiowa and C. Rauszer in memoriam, Warsaw, Ruciane-Nida September 23-26, 2005.