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Ideas of Jeffrey H. Sicha, by Text
[American, fl. 1968, At Amherst College.]
1968

Counting and the Natural Numbers

2

p.407

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'.

2

p.407

17424

Counting puts an initial segment of a serial ordering 11 with some other entities




Full Idea:
Counting is the activity of putting an initial segment of a serially ordered string in 11 correspondence with some other collection of entities.




From:
Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)

3

p.410

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)
