Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Internalism Exposed' and 'The Possibility of Metaphysics'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
9 ideas
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]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887
|
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891
|
Arithmetical undecidability is always settled at the next stage up [Koellner]
|
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
8297
|
Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe]
|
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
8266
|
Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe]
|
8302
|
Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe]
|
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
8298
|
Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe]
|
8311
|
If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe]
|
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
8310
|
Does the existence of numbers matter, in the way space, time and persons do? [Lowe]
|