Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Philosophy of Mind (Encylopedia III)' and 'Ontology and Mathematical Truth'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

2 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers

9965	There couldn't just be one number, such as 17 [Jubien]
	Full Idea: It makes no sense to suppose there might be just one natural number, say seventeen.
	From: Michael Jubien (Ontology and Mathematical Truth [1977], p.113)
	A reaction: Hm. Not convinced. If numbers are essentially patterns, we might only have the number 'twelve', because we had built our religion around anything which exhibited that form (in any of its various arrangements). Nice point, though.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

17890	There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
	Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable).
	From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
	A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway]