Combining Texts
Ideas for
'Natural Kinds and Biological Realism', 'Structuralism and the Notion of Dependence' and 'What are Sets and What are they For?'
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 / 4. Using Numbers / g. Applying mathematics
|
14246
|
If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
|
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
|
14247
|
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
|
14085
|
'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
|
|
14086
|
'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
|
|
14084
|
Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
|
|
14087
|
'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
|
14089
|
Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
|
14083
|
Structuralism is right about algebra, but wrong about sets [Linnebo]
|
|
14090
|
In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo]
|