Combining Philosophers
Ideas for H.Putnam/P.Oppenheim, Euripides and Gottfried Leibniz
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 / 2. Geometry
13163
|
Circles must be bounded, so cannot be infinite [Leibniz]
|
13008
|
Geometry, unlike sensation, lets us glimpse eternal truths and their necessity [Leibniz]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
9147
|
Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction [Fine,K on Leibniz]
|
12956
|
Only whole numbers are multitudes of units [Leibniz]
|
12920
|
There is no multiplicity without true units [Leibniz]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
19390
|
Everything is subsumed under number, which is a metaphysical statics of the universe, revealing powers [Leibniz]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
19406
|
I strongly believe in the actual infinite, which indicates the perfections of its author [Leibniz]
|
13190
|
I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
19375
|
The continuum is not divided like sand, but folded like paper [Leibniz, by Arthur,R]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
18080
|
A tangent is a line connecting two points on a curve that are infinitely close together [Leibniz]
|
18081
|
Nature uses the infinite everywhere [Leibniz]
|
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
12937
|
We shouldn't just accept Euclid's axioms, but try to demonstrate them [Leibniz]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
23026
|
We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz]
|