scholarly journals Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics

2018 ◽  
pp. 145-171
2020 ◽  
Vol 43 ◽  
Author(s):  
Chris Fields ◽  
James F. Glazebrook

Abstract Gilead et al. propose an ontology of abstract representations based on folk-psychological conceptions of cognitive architecture. There is, however, no evidence that the experience of cognition reveals the architecture of cognition. Scale-free architectural models propose that cognition has the same computational architecture from sub-cellular to whole-organism scales. This scale-free architecture supports representations with diverse functions and levels of abstraction.


2007 ◽  
Author(s):  
Amy Perfors ◽  
Charles Kemp ◽  
Elizabeth Wonnacott ◽  
Joshua B. Tenenbaum

2012 ◽  
Vol 21 (2) ◽  
pp. 223-243
Author(s):  
Irit Degani-Raz

The idea that Beckett investigates in his works the limits of the media he uses has been widely discussed. In this article I examine the fiction Imagination Dead Imagine as a limiting case in Beckett's exploration of limits at large and the limits of the media he uses in particular. Imagination Dead Imagine is shown to be the self-reflexive act of an artist who imaginatively explores the limits of that ultimate medium – the artist's imagination itself. My central aim is to show that various types of structural homologies (at several levels of abstraction) can be discerned between this poetic exploration of the limits of imagination and Cartesian thought. The homologies indicated here transcend what might be termed as ‘Cartesian typical topics’ (such as the mind-body dualism, the cogito, rationalism versus empiricism, etc.). The most important homologies that are indicated here are those existing between the role of imagination in Descartes' thought - an issue that until only a few decades ago was quite neglected, even by Cartesian scholars - and Beckett's perception of imagination. I suggest the use of these homologies as a tool for tracing possible sources of inspiration for Beckett's Imagination Dead Imagine.


Author(s):  
Angela Furfari ◽  
Sílvio Brito ◽  
Valeria Caggiano

Several studies demonstrate that Schwartz’s (2006) theory of human values is valid in cultures previously beyond its range. We measured the 10 value constructs in the theory with the Portrait Values Questionnaire (PVQ), a new and less abstract method. This study explores the influence of values in a professional choose, focusing on the associations between social and professional background. The findings support the construct validity of the test. The results suggest, there is a matching between values and occupational choose, there are evident differences between gender and age. These results confirm the international literature about different gender and value system’s. Its theoretical meaning in the context of Schwartz’s culture-level value theory is discussed.


Author(s):  
Wai-Tat Fu ◽  
Jessie Chin ◽  
Q. Vera Liao

Cognitive science is a science of intelligent systems. This chapter proposes that cognitive science can provide useful perspectives for research on technology-mediated human-information interaction (HII) when HII is cast as emergent behaviour of a coupled intelligent system. It starts with a review of a few foundational concepts related to cognitive computations and how they can be applied to understand the nature of HII. It discusses several important properties of a coupled cognitive system and their implication to designs of information systems. Finally, it covers how levels of abstraction have been useful for cognitive science, and how these levels can inform design of intelligent information systems that are more compatible with human cognitive computations.


2020 ◽  
Vol 31 (2) ◽  
pp. 213-229
Author(s):  
Ewa Dąbrowska

AbstractWhile many linguists view language as either a cognitive or a social phenomenon, it is clearly both: a language can live only in individual minds, but it is learned from examples of utterances produced by speakers engaged in communicative interaction. In other words, language is what (Keller 1994. On language change: The invisible hand in language. London: Taylor & Francis) calls a “phenomenon of the third kind”, emerging from the interaction of a micro-level and a macro-level. Such a dual perspective helps us understand some otherwise puzzling phenomena, including “non-psychological” generalizations, or situations where a pattern which is arguably present in a language is not explicitly represented in most speakers’ minds. This paper discusses two very different examples of such generalizations, genitive marking on masculine nouns in Polish and some restrictions on questions with long-distance dependencies in English. It is argued that such situations are possible because speakers may represent “the same” knowledge at different levels of abstraction: while a few may have extracted an abstract generalization, others approximate their behaviour by relying on memorised exemplars or lexically specific patterns. Thus, a cognitively realistic usage-based construction grammar needs to distinguish between patterns in the usage of a particular speech community (a social phenomenon) and patterns in speakers’ minds (a cognitive phenomenon).


Semiotica ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Michael Ranta

Abstract The theoretical debate on the nature of narrative has been mainly concerned with literary narratives, whereas forms of non-literary and especially pictorial narrativity have been somewhat neglected. In this paper, however, I shall discuss narrativity specifically with regard to pictorial objects in order to clarify how pictorial storytelling may be based on the activation of mentally stored action and scene schemas. Approaches from cognitive psychology, such as the work of Schank, Roger C. & Robert P. Abelson. 1977. Scripts, plans, goals and understanding. Hillsdale, NJ: Lawrence Erlbaum; Mandler, Jean Matter. 1984. Stories, scripts, and scenes: Aspects of schema theory. London/Hillsdale, NJ: Lawrence Erlbaum; Schank, Roger C. 1995. Tell me a story: Narrative and intelligence. Evanston, IL: Northwestern University Press, suggest that cognition crucially depends on the storage and retrieval of action scripts or schemata, that is, narrative structures, which may occur at various levels of abstraction. These schemas incorporate generalized knowledge about event sequences, such as the order in which specific events will take place; causal, enabling, or conventionalized relations between these events, and what kind of events occur in certain action sequences. There also are scene schemas that are characterized by spatial rather than temporal relations. Further kinds of schemas seem also to play a decisive role. Drawing upon considerations from schema and script theory, I will focus on some concrete examples of pictorial narration, more specifically depictions of the Annunciation of the Virgin Mary, where narrative schema structures become involved and, indeed, the comprehensibility of the pictures as such presuppose mental script representations.


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