, Volume 80, Issue 3, pp 487–503 | Cite as

Logicism as Making Arithmetic Explicit

  • Vojtěch KolmanEmail author
Original Article


This paper aims to shed light on the broader significance of Frege’s logicism (and hence the phenomenon of modern logic) against the background of discussing and comparing Wittgenstein’s ‘showing/saying’-distinction with Brandom’s idiom of logic as the enterprise of making the implicit rules of our linguistic practices (something we do) explicit (by something we say). The main thesis of this paper is that the problem of Frege’s logicism lies deeper than in its inconsistency (which has since turned out to be reparable, as the neologicists have shown): it lies in the basic idea that in arithmetic (and prospectively in language in general) one can, and should, express everything that is implicitly presupposed so that nothing is left unsaid. This, in fact, is the target of Wittgenstein’s critique. Rather than the Tractatus, with its claim that logicism attempts to say something that can only be shown (e.g. what ‘object’, ‘function’ or ‘number’ are), it is the Philosophical Investigations, with its argument by regress against the thesis that every rule which one can follow must be of an explicit nature, that is of real significance here.


Definite Description Logical Object Recursive Rule Definitive Logic Implicit Feature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Work on this paper has been supported by Grant No. P401/11/0371 of the Grant Agency of the Czech Republic. The author would like to thank the paper’s two anonymous reviewers for their suggestions and constructive comments.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Faculty of Arts, Institute of Philosophy and Religious StudiesCharles University, PraguePrague 1Czech Republic

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