Combining Texts
Ideas for
'Individuals without Sortals', 'Thinking About Mathematics' and 'The Question of Ontology'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
9 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
12211
|
It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K]
|
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
12209
|
The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K]
|
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
8744
|
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
|
6. Mathematics / C. Sources of Mathematics / 7. Formalism
8749
|
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
|
8750
|
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
|
8752
|
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
|
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8753
|
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
|
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
8731
|
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
|
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8730
|
'Impredicative' definitions refer to the thing being described [Shapiro]
|