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Logicism, Neo-Logicism, and the Logics of Abstraction
No full textAbstraction principles play a pivotal role in the foundations of mathematics. In the foundational programs in which they have been traditionally adopted, i.e. Frege’s logicism and Scottish neo-logicism, abstraction principles, conceived as definitions, augment a system of full higher-order logic. Not only, however, does such a logical system raise concerns – both philosophical and technical – for the deployment of abstractive definitions; but, also, abstraction principles can subserve alternative logico-philosophical projects depending on variations of the background logic. We first rehearse the role and significance of definitions by abstraction in logicist and neo-logicist accounts. We then discuss the most compelling technical and conceptual issues related to the logics of abstraction: the debate on the status of higher-order logic; the distinction between predicative and impredicative frameworks, and their relation to paradoxes; the adoption of non-classical logics in contemporary conceptions of abstraction. We conclude by addressing the relations between the logical, the epistemological, and the metaphysical significance of abstraction principles
Indagine sulla percezione delle problematiche ortodontiche da parte degli studenti del CLOPD dell’Università degli Studi dell’Aquila
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