Combining Philosophers

All the ideas for Archimedes, Stephen R. Grimm and Jeffrey H. Sicha

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

---

7 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers

17423

The essence of natural numbers must reflect all the functions they perform [Sicha]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17425

To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha]

17424

Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha]

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

13007

Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]

11. Knowledge Aims / A. Knowledge / 2. Understanding

19691

Unlike knowledge, you can achieve understanding through luck [Grimm]

19690

'Grasping' a structure seems to be modal, because we must anticipate its behaviour [Grimm]

19692

You may have 'weak' understanding, if by luck you can answer a set of 'why questions' [Grimm]