Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Letters to Antoine Arnauld' and 'Reference and Necessity'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
12920 There is no multiplicity without true units [Leibniz]
     Full Idea: There is no multiplicity without true units.
     From: Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.04.30)
     A reaction: Hence real numbers do not embody 'multiplicity'. So either they don't 'embody' anything, or they embody 'magnitudes'. Does this give two entirely different notions, of measure of multiplicity and measures of magnitude?
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]