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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]

19 ideas
 16146 Two can't be a self-contained unit, because it would need to be one to do that [Democritus, by Aristotle]
 17844 The unit is stipulated to be indivisible [Aristotle]
 17845 If only rectilinear figures existed, then unity would be the triangle [Aristotle]
 17859 Units came about when the unequals were equalised [Aristotle]
 12369 A unit is what is quantitatively indivisible [Aristotle]
 12273 Unit is the starting point of number [Aristotle]
 12956 Only whole numbers are multitudes of units [Leibniz]
 12920 There is no multiplicity without true units [Leibniz]
 9147 Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction [Leibniz]
 9801 Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill]
 8641 You can abstract concepts from the moon, but the number one is not among them [Frege]
 9989 Units can be equal without being identical [Tait on Frege]
 17429 Frege says only concepts which isolate and avoid arbitrary division can give units [Frege, by Koslicki]
 20361 We need 'unities' for reckoning, but that does not mean they exist [Nietzsche]
 9576 Multiplicity in general is just one and one and one, etc. [Husserl]
 18392 Classes have cardinalities, so their members must all be treated as units [Armstrong]
 9895 A number is a multitude composed of units [Dummett]
 18071 A one-operation is the segregation of a single object [Kitcher]
 17435 Objects do not naturally form countable units [Koslicki]