Combining Philosophers
Ideas for John Buridan, Michael D. Resnik and JP Burgess / G Rosen
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
10 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
6304
|
Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9923
|
We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
6300
|
Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
|
6303
|
Sets are positions in patterns [Resnik]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
9925
|
Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
6295
|
There are too many mathematical objects for them all to be mental or physical [Resnik]
|
6296
|
Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
|
6301
|
Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
|
6302
|
Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
|
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
9934
|
Number words became nouns around the time of Plato [Burgess/Rosen]
|