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Single Idea 14112
[filed under theme 9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
]
Full Idea
In a class as many, the component terms, though they have some kind of unity, have less than is required for a whole.
Gist of Idea
A set has some sort of unity, but not enough to be a 'whole'
Source
Bertrand Russell (The Principles of Mathematics [1903], §070)
Book Ref
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.69
A Reaction
This is interesting because (among many other things), sets are used to stand for numbers, but numbers are usually reqarded as wholes.
The
18 ideas
with the same theme
[whether a mere assemblage of parts can be unified]:
3357
|
Democritus denies reality to large objects, because atomic entities can't combine to produce new ones
[Benardete,JA on Democritus]
|
15851
|
Parts must belong to a created thing with a distinct form
[Plato]
|
13272
|
Things are one to the extent that they are indivisible
[Aristotle]
|
17842
|
Indivisibility is the cause of unity, either in movement, or in the account or thought
[Aristotle]
|
17860
|
Things are unified by contact, mixture and position
[Aristotle]
|
14046
|
A 'body' is a conception of an aggregate, with properties defined by application conditions
[Epicurus]
|
17555
|
'One' can mean undivided and not a multitude, or it can add measurement, giving number
[Aquinas]
|
16770
|
It is absurd that there is no difference between a genuinely unified thing, and a mere aggregate
[Duns Scotus]
|
17248
|
If a whole body is moved, its parts must move with it
[Hobbes]
|
17188
|
A thing is unified if its parts produce a single effect
[Spinoza]
|
17028
|
Particles mutually attract, and cohere at short distances
[Newton]
|
12699
|
A body would be endless disunited parts, if it did not have a unifying form or soul
[Leibniz]
|
12921
|
Accidental unity has degrees, from a mob to a society to a machine or organism
[Leibniz]
|
14112
|
A set has some sort of unity, but not enough to be a 'whole'
[Russell]
|
17571
|
Every physical thing is either a living organism or a simple
[Inwagen]
|
16072
|
'The rock' either refers to an object, or to a collection of parts, or to some stuff
[Burke,M, by Wasserman]
|
10726
|
Things can't be fusions of universals, because two things could then be one thing
[Oliver]
|
10725
|
Abstract sets of universals can't be bundled to make concrete things
[Oliver]
|