Combining Philosophers
Ideas for Roderick Firth, Michael Walzer and James Robert Brown
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
19 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9604
|
Mathematics is the only place where we are sure we are right [Brown,JR]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9622
|
'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / n. Pi
9648
|
π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
9621
|
Mathematics represents the world through structurally similar models. [Brown,JR]
|
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
9646
|
There is no limit to how many ways something can be proved in mathematics [Brown,JR]
|
9647
|
Computers played an essential role in proving the four-colour theorem of maps [Brown,JR]
|
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
9643
|
Set theory may represent all of mathematics, without actually being mathematics [Brown,JR]
|
9644
|
When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
9625
|
To see a structure in something, we must already have the idea of the structure [Brown,JR]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9628
|
Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR]
|
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
9606
|
The irrationality of root-2 was achieved by intellect, not experience [Brown,JR]
|
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
9610
|
Numbers are not abstracted from particulars, because each number is a particular [Brown,JR]
|
9612
|
There is an infinity of mathematical objects, so they can't be physical [Brown,JR]
|
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
9620
|
Empiricists base numbers on objects, Platonists base them on properties [Brown,JR]
|
6. Mathematics / C. Sources of Mathematics / 7. Formalism
9629
|
For nomalists there are no numbers, only numerals [Brown,JR]
|
9630
|
The most brilliant formalist was Hilbert [Brown,JR]
|
9639
|
Does some mathematics depend entirely on notation? [Brown,JR]
|
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
9608
|
There are no constructions for many highly desirable results in mathematics [Brown,JR]
|
9645
|
Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR]
|