Consistency and konsistenz

Erkenntnis 26 (1):1 - 43 (1987)
A ground-motive for this study of some historical and metaphysical implications of the diagonal lemmas of Cantor and Gödel is Cantor's insightful remark to Dedekind in 1899 that the Inbegriff alles Denkbaren (aggregate of everything thinkable) might, like some class-theoretic entities, be inkonsistent. In the essay's opening sections, I trace some recent antecedents of Cantor's observation in logical writings of Bolzano and Dedekind (more remote counterparts of his language appear in the First Critique), then attempt to relativize the notion of Inkonsistenz to self-sufficient theories T which interpret themselves. In effect, I argue that Gödel's diagonal lemma suggests a sense in which metatheoretic notions of proof, well-foundeness and satisfaction are object-theoretically inkonsistent. With respect to Cantor's Inbegriff, for example, the lemma yields that any object-theoretic reconstruction of thinkability generates an antidiagonal sentence , which one can paraphrase asSelf-referential application of the assertion that.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/BF00166348
 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
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 28,106
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Set Theory and Physics.K. Svozil - 1995 - Foundations of Physics 25 (11):1541-1560.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

20 ( #248,475 of 2,171,798 )

Recent downloads (6 months)

1 ( #326,702 of 2,171,798 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums