History and Philosophy of Logic 19 (3):137-151 (1998)

Abstract
Frege's docent's dissertation Rechnungsmethoden, die sich auf eine Erweiterung des Grössenbegriffes gründen(1874) contains indications of a bold attempt to extend arithmetic. According to it, arithmetic means the science of magnitude, and magnitude must be understood structurally without intuitive support. The main thing is insight into the formal structure of the operation of ?addition?. It turns out that a general ?magnitude domain? coincides with a (commutative) group. This is an interesting connection with simultaneous developments in abstract algebra. As his main application, Frege studies iterations of functions. He does not yet pose the question of existence proofs. Measurement of magnitudes is also connected to numbers, but the discussion is here ambiguous in a way which calls for the systematic account of numbers in Grundgesetze
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DOI 10.1080/01445349808837305
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References found in this work BETA

Mathematical Thought From Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
Funktion und Begriff.Gottlob Frege - 1891 - Jena: Hermann Pohle.
Gottlob Frege. [REVIEW]Michael D. Resnik - 1983 - Philosophical Review 92 (1):122-125.

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