Ideas from 'Counting and the Natural Numbers' by Jeffrey H. Sicha [1968], by Theme Structure
[found in 'Philosophy of Science' (ed/tr -) [- ,]].
green numbers give full details |
back to texts
|
unexpand these 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
|
|
|
|
Full Idea:
What is really essential to being a natural number is what is common to the natural numbers in all the functions they perform.
|
|
|
|
From:
Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)
|
|
|
|
A reaction:
I could try using natural numbers as insults. 'You despicable seven!' 'How dare you!' I actually agree. The question about functions is always 'what is it about this thing that enables it to perform this function'.
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
|
17424
|
Counting puts an initial segment of a serial ordering 1-1 with some other entities
|
|
|
|
Full Idea:
Counting is the activity of putting an initial segment of a serially ordered string in 1-1 correspondence with some other collection of entities.
|
|
|
|
From:
Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)
|
|
17425
|
To know how many, you need a numerical quantifier, as well as equinumerosity
|
|
|
|
Full Idea:
A knowledge of 'how many' cannot be inferred from the equinumerosity of two collections; a numerical quantifier statement is needed.
|
|
|
|
From:
Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 3)
|