History and Philosophy of Logic 34 (3):225-41 (2013)

Authors
Gregory Lavers
Concordia University
Abstract
This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the independent existence of abstract objects, Frege and Carnap held remarkably similar views. I close with a discussion of why, despite all this, Frege would not accept the principle of tolerance.
Keywords Frege  Carnap  Philosophy of mathematics  Explication  Arithmetic
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DOI 10.1080/01445340.2013.806396
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References found in this work BETA

Logical Foundations of Probability.Rudolf Carnap - 1950 - Chicago, IL, USA: Chicago University of Chicago Press.
Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
The Foundations of Arithmetic.Gottlob Frege - 1884/1950 - Evanston: Ill., Northwestern University Press.
Empiricism, Semantics and Ontology.Rudolf Carnap - 1950 - Revue Internationale de Philosophie 4 (11):20-40.

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Citations of this work BETA

Explication.Moritz Cordes, and & Geo Siegwart - 2018 - Internet Encyclopedia of Philosophy.
Weberian Ideal Type Construction as Concept Replacement.Raphael Riel - forthcoming - European Journal of Philosophy.

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