David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 30 (3):257-282 (2009)
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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References found in this work BETA
George Bealer (1982). Quality and Concept. Oxford University Press.
David Bell & W. D. Hart (1979). The Epistemology of Abstract Objects: Access and Inference. Proceedings of the Aristotelian Society 53:153-165.
Keith Campbell (1990). Abstract Particulars. B. Blackwell.
Alonzo Church (1940). A Formulation of the Simple Theory of Types. Journal of Symbolic Logic 5 (2):56-68.
Citations of this work BETA
Giuseppe Primiero (2013). Offline and Online Data: On Upgrading Functional Information to Knowledge. Philosophical Studies 164 (2):371-392.
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