Cue abstraction and ideal prototype abstraction in estimation tasks

This study investigates abstracted processes and introduces a new prototype abstraction model adapted to estimation tasks. This prototype abstraction model assumes that the processing of whole exemplar patterns supports the detection of the underlying statistics necessary for the abstraction of two extreme prototypes on the continuous criterion dimension of the task. The prototypes are stored in memory as valid reference points for future similarity-based judgments. This prototype model was compared with the cue abstraction model, which assumes that people abstract cue weights in learning and add the cue information from exemplars to infer their criterion values varying on the continuous dimension. This study hypothesises that the training mode and the number of exemplars in training interact and affect subsequent model performance at test. The results from an experiment confirmed this hypothesis and showed that observational training supports an efficient prototype abstraction and feedback training supports an efficient cue abstraction.     

Reichenbach and Weyl on apriority and mathematical applicability

I examine Reichenbach’s theory of relative a priori and Michael Friedman’s interpretation of it. I argue that Reichenbach’s view remains at bottom conventionalist and that one issue which separates Reichenbach’s account from Kant’s apriorism is the problem of mathematical applicability. I then discuss Hermann Weyl’s theory of blank forms which in many ways runs parallel to the theory of relative a priori. I argue that it is capable of dealing with the problem of applicability, but with a cost.     

Essence and definition by abstraction

We may define words or concepts, and we may also, as Aristotle and others have thought, define the things for which words stand and of which concepts are concepts. Definitions of words or concepts may be explicit or implicit, and may seek to report preexisting synonymies, as Quine put it, but they may instead be wholly or partly stipulative. Definition by abstraction, of which Hume’s principle is a much discussed example, seek to define a term-forming operator, such as the number operator, by fixing the truth-conditions of identity-statements featuring terms formed by means of that operator. Such definitions are a species of implicit definition. They are typically at least partly stipulative. Definitions of things, or real definitions, are, by contrast, typically conceived as true or false statements about the nature or essence of their definienda, and so not stipulative. There thus appears to be an obvious and head-on clash between taking Hume’s principle as an implicit and at least partly stipultative definition of the number operator and taking it as a real definition, stating the nature or essence of cardinal numbers. This paper argues that this apparent tension can be resolved, and that resolving it sheds light on part of the epistemology or essence and necessity, showing how some of our knowledge of essence and necessity can be a priori.

     

Classical physical abstraction

An informal theory is set forth of relations between abstract entities, includingcolors, physical quantities, times, andplaces in space, and the concrete things thathave them, or areat orin them, based on the assumption that there are close analogies between these relations and relations between abstractsets and the concrete things that aremembers of them. It is suggested that even standard scientific usage of these abstractions presupposes principles that are analogous to postulates of abstraction, identity, and other fundamental principles of set theory. Also discussed is the significance of important disanalogies between sets and physical abstractions, including especiallymodal andtemporal aspects of physical abstractions, which is related to the problem of the characterizingconstancy, of colors, physical attributes, and locations in space.     

In search of abstraction: The varying abstraction model of categorization

A longstanding debate in the categorization literature concerns representational abstraction. Generally, when exemplar models, which assume no abstraction, have been contrasted with prototype models, which assume total abstraction, the former models have been found to be superior to the latter. Although these findings may rule out the idea that total abstraction takes place during category learning and instead suggest that no abstraction is involved, the idea of abstraction retains considerable intuitive appeal. In this article, we propose the varying abstraction model of categorization (VAM), which investigates the possibility that partial abstraction may play a role in category learning. We apply the VAM to four previously published data sets that have been used to argue that no abstraction is involved. Contrary to the previous findings, our results provide support for the idea that some form of partial abstraction can be used in people's category representations.     

Idealization and abstraction in scientific modeling

I argue that we cannot adequately characterize idealization and abstraction and the distinction between the two on the grounds that they have distinct semantic properties. By doing so, on the one hand, we focus on the conceptual products of the two processes in making the distinction and we overlook the importance of the nature of the thought processes that underlie model-simplifying assumptions. On the other hand, we implicitly rely on a sense of abstraction as subtraction, which is unsuitable for explicating scientific model construction. Instead, I argue that a sense of abstraction as extraction is more suitable. Finally, I suggest a different way to distinguish the two processes that avoids these problems. Namely, that both idealization and abstraction could be understood as particular modes of application of the same cognitive process: selective attention.

     

Humor, abstraction, and disbelief

We investigated humor as a context for learning about abstraction and disbelief. More specifically, we investigated how parents support humor understanding during book sharing with their toddlers. In Study 1, a corpus analysis revealed that in books aimed at 1-to 2-year-olds, humor is found more often than other forms of doing the wrong thing including mistakes, pretense, lying, false beliefs, and metaphors. In Study 2, 20 parents read a book containing humorous and non-humorous pages to their 19-to 26-month-olds. Parents used a significantly higher percentage of high abstraction extra-textual utterances (ETUs) when reading the humorous pages. In Study 3, 41 parents read either a humorous or non-humorous book to their 18-to 24-month-olds. Parents reading the humorous book made significantly more ETUs coded for a specific form of high abstraction: those encouraging disbelief of prior utterances. Sharing humorous books thus increases toddlers' exposure to high abstraction and belief-based language.     

Weyl on Fregean Implicit Definitions: Between Phenomenology and Symbolic Construction

This paper aims to investigate certain aspects of Weyl’s account of implicit definitions. The paper takes under consideration Weyl’s approach to a certain kind of implicit definitions i.e. abstraction principles introduced by Frege. Abstraction principles are bi-conditionals that transform certain equivalence relations into identity statements, defining thereby mathematical terms in an implicit way. The paper compares the analytic reading of implicit definitions offered by the Neo-Fregean program with Weyl’s account which has phenomenological leanings. The paper suggests that Weyl’s account should be construed as putting emphasis on intentionality of human mind towards certain invariant features of the elements of initial domains of discourse that are involved in equivalence relations. Definition of terms like direction, shape, number etc. is achieved by a kind of transformation of those invariants into ideal objects that is involved in intuition. Then the paper argues that at the period of 1926 Weyl’s writings on implicit definitions, he is inclined to endorse symbolic construction as a way to explicate the objectivity of certain processes as those that are carried out in case of implicit definitions.     

The effect of linguistic abstraction on interpersonal distance

It is well known that people describe positive behaviors of others close to them (e.g., in‐group member, friend) in abstract terms, but with concrete terms in the case of people who they are not close to (e.g., out‐group member, enemy). In contrast, negative behaviors of people who we are close to are described in concrete terms, but in abstract terms for people who are distant. However, the communicative impact of such subtle differences in language use on a receiver who is also the actor of the behavior being described has never been addressed. We hypothesized and found that a positive abstract message compared to a positive concrete message leads to perceived proximity to the sender, while a negative abstract message compared to a negative concrete message leads to perceived distance. The implications of this study, which is the first to show the communicative impact of biased language use, are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Mystery,abstraction, and narrative psychotherapy

Abstract

The rhythm of life involves the creation and resolution of mysteries. In the social realm, such mysteries are usually solved by the process of abstraction—linguistic devices are invented and used to coordinate patterns of communal action. Although such devices are necessary and useful, they also tend to entrap a person in a social cocoon of shared explanatory fictions. Narrative psychotherapy helps clients break free of the spell woven by the abstractions to which they have become adapted. This occurs through the process Maturana (1988) called “orthogonal interaction,” in which the therapist assists the client in stepping outside the “club rules” and seeing things anew. This process is discussed, contrasted with other interpretations of narrative work, and illustrated with a brief clinical vignette.     

Cue abstraction and exemplar memory in categorization

In this article, the authors compare 3 generic models of the cognitive processes in a categorization task. The cue abstraction model implies abstraction in training of explicit cue-criterion relations that are mentally integrated to form a judgment, the lexicographic heuristic uses only the most valid cue, and the exemplar-based model relies on retrieval of exemplars. The results from 2 experiments showed that, in lieu of the lexicographic heuristic, most participants spontaneously integrate cues. In contrast to single-system views, exemplar memory appeared to dominate when the feedback was poor, but when the feedback was rich enough to allow the participants to discern the task structure, it was exploited for abstraction of explicit cue-criterion relations.     

The abstraction of musical ideas

Music presents information both sequentially, in the form of musical phrases, and simultaneously, in the form of chord structure. The ability to abstract musical structure presented sequentially and simultaneously was investigated using modified versions of the Bransford and Franks’ (1971) paradigm. Listeners heard subsets of musical ideas. The abstraction hypothesis predicted (1) false recognition of novel instances of the abstracted musical idea, (2) confidence of “recognition” should increase as recognition items approximate the complete musical idea, (3) correct rejection of “noncases,” which deviate from the acquired musical structure. Experiment 1 investigated sequential abstraction by using four-phrase folk melodies as musical ideas. Predictions 1 and 3 were confirmed, but the false recognition rate decreased as the number of phrases increased. Listeners were sensitive to improper combinations of phrases and to novel melodies different from melodies presented during acquisition. Experiment 2 investigated simultaneous abstraction using four-voice Bach chorales as musical ideas. Listeners spontaneously integrated choral subsets into holistic musical ideas. Musically trained listeners were better than naive listeners at identifying noncases.