History and Philosophy of Logic 30 (3):257-282 (2009)

Authors
Giuseppe Primiero
Università degli Studi di Milano
Abstract
This article presents an historical and conceptual overview on different approaches to logical abstraction. Two main trends concerning abstraction in the history of logic are highlighted, starting from the logical notions of concept and function. This analysis strictly relates to the philosophical discussion on the nature of abstract objects. I develop this issue further with respect to the procedure of abstraction involved by (typed) λ-systems, focusing on the crucial change about meaning and predicability. In particular, the analysis of the nature of logical types in the context of Constructive Type Theory allows elucidation of the role of the previously introduced notions. Finally, the connection to the analysis of abstraction in computer science is drawn, and the methodological contribution provided by the notion of information is considered, showing its conceptual and technical relevance. Future research shall focus on the notion of information in distributed systems, analysing the paradigm of information hiding in dependent type theories
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DOI 10.1080/01445340902872630
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References found in this work BETA

The Epistemology of Abstract Objects: Access and Inference.David Bell & W. D. Hart - 1979 - Proceedings of the Aristotelian Society, Supplementary Volumes( 53:135-165.
The Method of Levels of Abstraction.Luciano Floridi - 2008 - Minds and Machines 18 (3):303-329.
Quality and Concept.George Bealer - 1982 - Oxford University Press.
The Limits of Abstraction.Kit Fine - 2002 - Oxford University Press.

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