Are Mathematical Theories Reducible to Non-analytic Foundations?

Axiomathes 23 (1):109-135 (2013)
In this article I intend to show that certain aspects of the axiomatical structure of mathematical theories can be, by a phenomenologically motivated approach, reduced to two distinct types of idealization, the first-level idealization associated with the concrete intuition of the objects of mathematical theories as discrete, finite sign-configurations and the second-level idealization associated with the intuition of infinite mathematical objects as extensions over constituted temporality. This is the main standpoint from which I review Cantor’s conception of infinite cardinalities and also the metatheoretical content of some later well-known theorems of mathematical foundations. These are, the Skolem-Löwenheim Theorem which, except for its importance as such, it is also chosen for an interpretation of the associated metatheoretical paradox (Skolem Paradox), and Gödel’s (first) incompleteness result which, notwithstanding its obvious influence in the mathematical foundations, is still open to philosophical inquiry. On the phenomenological level, first-level and second-level idealizations, as above, are associated respectively with intentional acts carried out in actual present and with certain modes of a temporal constitution process
Keywords Axiom of Choice  Finitistic  First-level idealization  Gödel’s incompleteness theorems  Individual-substrate  Infinite  Intentionality  Second-level idealization  Skolem-Löwenheim Theorem
Categories (categorize this paper)
DOI 10.1007/s10516-012-9182-3
 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: 24,422
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
Karl Popper (1935). Logik der Forschung. Journal of Philosophy 32 (4):107-108.

View all 24 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Timothy Bays (2000). Reflections on Skolem's Paradox. Dissertation, University of California, Los Angeles
Gordon McCabe (2010). The Non-Unique Universe. Foundations of Physics 40 (6):629-637.

Monthly downloads

Added to index


Total downloads

38 ( #126,782 of 1,924,770 )

Recent downloads (6 months)

3 ( #254,761 of 1,924,770 )

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.