more from this thinker
|
more from this text
Single Idea 12920
[filed under theme 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
]
Full Idea
There is no multiplicity without true units.
Gist of Idea
There is no multiplicity without true units
Source
Gottfried Leibniz (Letters to Antoine Arnauld [1686], 1687.04.30)
Book Ref
Leibniz,Gottfried: 'The Leibniz-Arnauld Correspondence', ed/tr. Mason,HT/Parkinson,GHR [Manchester UP 1967], p.121
A Reaction
Hence real numbers do not embody 'multiplicity'. So either they don't 'embody' anything, or they embody 'magnitudes'. Does this give two entirely different notions, of measure of multiplicity and measures of magnitude?
Related Idea
Idea 9147
Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction [Fine,K on Leibniz]
The
21 ideas
with the same theme
[a series of isolated 'ones' on which counting is built]:
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]
|
24036
|
I can only see the proportion of two to three if there is a common measure - their unity
[Descartes]
|
24035
|
Unity is something shared by many things, so in that respect they are equals
[Descartes]
|
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
[Fine,K on 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]
|
7207
|
Counting needs unities, but that doesn't mean they exist; we borrowed it from the concept of 'I'
[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]
|