Combining Philosophers
Ideas for Herodotus, Michael D. Resnik and Harr,R./Madden,E.H.
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 / b. Types of number
|
15273
|
Points can be 'dense' by unending division, but must meet a tougher criterion to be 'continuous' [Harré/Madden]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
|
15274
|
Points are 'continuous' if any 'cut' point participates in both halves of the cut [Harré/Madden]
|
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 / d. Platonist structuralism
|
6302
|
Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
|
|
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]
|
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
|
15211
|
There is not an exclusive dichotomy between the formal and the logical [Harré/Madden]
|