Combining Philosophers
Ideas for Rescher,N/Oppenheim,P, Paul Benacerraf and Keith T. Maslin
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
13 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
|
9935
|
Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
|
13412
|
Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
|
|
13413
|
We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
|
|
9912
|
There are no such things as numbers [Benacerraf]
|
|
9901
|
Numbers can't be sets if there is no agreement on which sets they are [Benacerraf]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
|
13411
|
If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
|
|
9151
|
Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
|
13891
|
To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C]
|
|
17904
|
A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf]
|
|
17906
|
To explain numbers you must also explain cardinality, the counting of things [Benacerraf]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
|
9898
|
We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf]
|
|
17903
|
Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
|
9897
|
The application of a system of numbers is counting and measurement [Benacerraf]
|