Abstract
The paper’s aim is to determine and discuss in which sense, if any, Frege’s and neo-Fregean logicism are responding to the epistemological challenge concerning our arithmetical knowledge. More precisely the paper analyses what the epistemological significance of Frege’s logicist programme amounts to, namely, the objective justificatory connections obtaining between arithmetical and logical statements. It then contrasts this result with the self-understanding of the neo-Fregeans who allegedly follow Frege’s steps, but in fact take a rather different direction.
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Notes
- 1.
- 2.
Wright, On the philosophical significance of Frege’s theorem, p. 210.
- 3.
Wherever possible, the Grundlagen quotations are taken from (Beaney [1]); alternatively they are from Austin’s translation.
- 4.
- 5.
See e.g., Burge [3].
- 6.
The principle has been called Hume’s Principle by Boolos (in “The consistency of Frege’s Foundations of Arithmetic”, in [2]). Boolos gave it this title because it recalls a remark in Hume’s Treatise (Book I, Part iii, Section 1, par. 5), and because Frege quotes Hume in Grundlagen (§63):
when two numbers are so combin’d, as that the one always as unite answering to every unite of the other, we pronounce them equal …
- 7.
See e.g., Hale [7].
- 8.
Hale and Wright [10, p. 169].
- 9.
Ebert and Shapiro [5, p. 421].
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Acknowledgements
Acknowledgments Portions of this were presented at the conference in Dubrovnik in May 2010. Many thanks to the participants for their comments: Stewart Shapiro, Per Martin-Löf, Alan Wier, Berislav Žarnić, Stephen Reed. Many thanks as well to Nenad Smokrović and especially to Nenad Miščević.
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Trobok, M. (2012). Debating (Neo)logicism: Frege and the Neo-Fregeans. In: Trobok, M., Miščević, N., Žarnić, B. (eds) Between Logic and Reality. Logic, Epistemology, and the Unity of Science, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2390-0_5
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