Combining Texts

All the ideas for 'Sets, Aggregates and Numbers', 'Isolation and Non-arbitrary Division' and 'works'

expand these ideas     |    start again     |     specify just one area for these texts


12 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Objects do not naturally form countable units [Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
We can still count squares, even if they overlap [Koslicki]
How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
Nothing is 'intrinsically' numbered [Yourgrau]
There is no deep reason why we count carrots but not asparagus [Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
You can ask all sorts of numerical questions about any one given set [Yourgrau]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
We talk of snow as what stays the same, when it is a heap or drift or expanse [Koslicki]
14. Science / B. Scientific Theories / 1. Scientific Theory
You have only begun to do real science when you can express it in numbers [Kelvin]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin]