Ideas from 'Counting and the Natural Numbers' by Jeffrey H. Sicha [1968], by Theme Structure
[found in 'Philosophy of Science' (ed/tr -) [- ,]].
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
17423
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The essence of natural numbers must reflect all the functions they perform
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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.
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From:
Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)
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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'.
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17425
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To know how many, you need a numerical quantifier, as well as equinumerosity
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Full Idea:
A knowledge of 'how many' cannot be inferred from the equinumerosity of two collections; a numerical quantifier statement is needed.
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From:
Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 3)
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17424
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Counting puts an initial segment of a serial ordering 1-1 with some other entities
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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.
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From:
Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)
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