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Single Idea 13273
[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
]
Full Idea
A plurality is a denumerable quantity, and a magnitude is a measurable quantity. A plurality is what is potentially divisible into things that are not continuous, whereas what is said to be a magnitude is divisible into continuous things.
Gist of Idea
Pluralities divide into discontinous countables; magnitudes divide into continuous things
Source
Aristotle (Metaphysics [c.324 BCE], 1020a09)
Book Ref
Aristotle: 'Metaphysics', ed/tr. Lawson-Tancred,Hugh [Penguin 1998], p.134
A Reaction
This illuminating distinction is basic to the Greek attitude to number, and echoes the distinction between natural and real numbers.
The
26 ideas
with the same theme
[general ideas concerning numbers]:
1729
|
We perceive number by the denial of continuity
[Aristotle]
|
13273
|
Pluralities divide into discontinous countables; magnitudes divide into continuous things
[Aristotle]
|
10958
|
Perhaps numbers are substances?
[Aristotle]
|
13152
|
We can talk of 'innumerable number', about the infinite points on a line
[Newton]
|
16920
|
Numbers are formed by addition of units in time
[Kant]
|
9823
|
Numbers are free creations of the human mind, to understand differences
[Dedekind]
|
23186
|
Numbers enable us to manage the world - to the limits of counting
[Nietzsche]
|
13412
|
Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order
[Benacerraf]
|
13413
|
We must explain how we know so many numbers, and recognise ones we haven't met before
[Benacerraf]
|
9901
|
Numbers can't be sets if there is no agreement on which sets they are
[Benacerraf]
|
9912
|
There are no such things as numbers
[Benacerraf]
|
12335
|
Numbers are for measuring and for calculating (and the two must be consistent)
[Badiou]
|
12334
|
There is no single unified definition of number
[Badiou]
|
10599
|
For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1)))
[Smith,P]
|
13861
|
Number theory aims at the essence of natural numbers, giving their nature, and the epistemology
[Wright,C]
|
10027
|
Mathematics is higher-order modal logic
[Hodes]
|
8958
|
In Field's version of science, space-time points replace real numbers
[Field,H, by Szabó]
|
8865
|
If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise?
[Yablo]
|
9923
|
We should talk about possible existence, rather than actual existence, of numbers
[Burgess/Rosen]
|
9622
|
'There are two apples' can be expressed logically, with no mention of numbers
[Brown,JR]
|
17453
|
The meaning of a number isn't just the numerals leading up to it
[Heck]
|
12238
|
The Aristotelian view is that numbers depend on (and are abstracted from) other things
[Oderberg]
|
9998
|
What is the relation of number words as singular-terms, adjectives/determiners, and symbols?
[Hofweber]
|
10002
|
'2 + 2 = 4' can be read as either singular or plural
[Hofweber]
|
21644
|
Numbers are used as singular terms, as adjectives, and as symbols
[Hofweber]
|
21646
|
The Amazonian Piraha language is said to have no number words
[Hofweber]
|