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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units

[a series of isolated 'ones' on which counting is built]

21 ideas
Two can't be a self-contained unit, because it would need to be one to do that [Democritus, by Aristotle]
The unit is stipulated to be indivisible [Aristotle]
If only rectilinear figures existed, then unity would be the triangle [Aristotle]
Units came about when the unequals were equalised [Aristotle]
A unit is what is quantitatively indivisible [Aristotle]
Unit is the starting point of number [Aristotle]
Unity is something shared by many things, so in that respect they are equals [Descartes]
I can only see the proportion of two to three if there is a common measure - their unity [Descartes]
Only whole numbers are multitudes of units [Leibniz]
There is no multiplicity without true units [Leibniz]
Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction [Fine,K on Leibniz]
Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill]
You can abstract concepts from the moon, but the number one is not among them [Frege]
Units can be equal without being identical [Tait on Frege]
Frege says only concepts which isolate and avoid arbitrary division can give units [Frege, by Koslicki]
We need 'unities' for reckoning, but that does not mean they exist [Nietzsche]
Multiplicity in general is just one and one and one, etc. [Husserl]
Classes have cardinalities, so their members must all be treated as units [Armstrong]
A number is a multitude composed of units [Dummett]
A one-operation is the segregation of a single object [Kitcher]
Objects do not naturally form countable units [Koslicki]