Critical Studies / Book Reviews [Book Review]

Philosophia Mathematica 6 (1):90-90 (1998)
The over-arching theme is that we can redeem Frege's key philosophical insights concerning (natural and real) numbers and our knowledge of them, despite Russell's famous discovery of paradox in Frege's own theory of classes. That paradox notwithstanding, numbers are still logical objects, in some sense created or generated by methods or principles of abstraction— which of course cannot be as ambitious as Frege's Basic Law U. These principles not only bring numbers into existence, as it were, but also afford a distinctive form of epistemic access to them. The usual mathematical axioms governing the two kinds of numbers are to be derived as results in (higher-order) logic. These derivations will exploit appropriate definitions of the primitive constants, functions, and predicates of the brand of number theory concerned. (For example: 0, 1; s, +, x; (; N(z); R(z).) No supplementation by intuition or sensory experience will be needed in the derivations of these axioms. The trains of reasoning involved will depend only on our grasp of logical validities, supplemented by appropriate definitions. Result: logicism is vindicated; and the mathematical knowledge derived in this way is revealed to be analytic, not synthetic
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/6.1.90
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 16,667
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles
Peter Sullivan & Michael Potter (1997). Hale on Caesar. Philosophia Mathematica 5 (2):135--52.
Erich H. Reck (2005). Frege on Numbers: Beyond the Platonist Picture. The Harvard Review of Philosophy 13 (2):25-40.
Fraser MacBride (2003). Speaking with Shadows: A Study of Neo-Logicism. British Journal for the Philosophy of Science 54 (1):103-163.

Monthly downloads

Added to index


Total downloads

23 ( #128,632 of 1,726,249 )

Recent downloads (6 months)

3 ( #231,316 of 1,726,249 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.