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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
42 ideas
from 'Letters to Antoine Arnauld'
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15955
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I think the corpuscular theory, rather than forms or qualities, best explains particular phenomena
[Leibniz]
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12903
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Wise people have fewer acts of will, because such acts are linked together
[Leibniz]
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5031
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Everything which happens is not necessary, but is certain after God chooses this universe
[Leibniz]
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5030
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Miracles are extraordinary operations by God, but are nevertheless part of his design
[Leibniz]
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12904
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If varieties of myself can be conceived of as distinct from me, then they are not me
[Leibniz]
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12905
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I cannot think my non-existence, nor exist without being myself
[Leibniz]
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13089
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To fully conceive the subject is to explain the resulting predicates and events
[Leibniz]
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12906
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Truths about species are eternal or necessary, but individual truths concern what exists
[Leibniz]
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12907
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Each possible world contains its own laws, reflected in the possible individuals of that world
[Leibniz]
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13077
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Basic predicates give the complete concept, which then predicts all of the actions
[Leibniz]
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11981
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If someone's life went differently, then that would be another individual
[Leibniz]
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19334
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I can't just know myself to be a substance; I must distinguish myself from others, which is hard
[Leibniz]
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19333
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A truth is just a proposition in which the predicate is contained within the subject
[Leibniz]
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12910
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The predicate is in the subject of a true proposition
[Leibniz]
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12908
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Essences exist in the divine understanding
[Leibniz]
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12912
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Immortality without memory is useless
[Leibniz]
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12909
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Everything, even miracles, belongs to order
[Leibniz]
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12911
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Concepts are what unite a proposition
[Leibniz]
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12913
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Nature is explained by mathematics and mechanism, but the laws rest on metaphysics
[Leibniz]
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12914
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Metaphysics is geometrical, resting on non-contradiction and sufficient reason
[Leibniz]
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12915
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Definitions can only be real if the item is possible
[Leibniz]
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12916
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A body is a unified aggregate, unless it has an indivisible substance
[Leibniz]
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12918
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Animals have souls, but lack consciousness
[Leibniz]
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12917
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The soul is indestructible and always self-aware
[Leibniz]
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12919
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Unity needs an indestructible substance, to contain everything which will happen to it
[Leibniz]
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5032
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It seems probable that animals have souls, but not consciousness
[Leibniz]
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5033
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Nothing should be taken as certain without foundations
[Leibniz]
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12920
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There is no multiplicity without true units
[Leibniz]
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12319
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What is not truly one being is not truly a being either
[Leibniz]
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12704
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Aggregates don’t reduce to points, or atoms, or illusion, so must reduce to substance
[Leibniz]
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12745
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Philosophy needs the precision of the unity given by substances
[Leibniz]
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12921
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Accidental unity has degrees, from a mob to a society to a machine or organism
[Leibniz]
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12746
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We find unity in reason, and unity in perception, but these are not true unity
[Leibniz]
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12922
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A thing 'expresses' another if they have a constant and fixed relationship
[Leibniz]
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12923
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Every bodily substance must have a soul, or something analogous to a soul
[Leibniz]
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5034
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Mind is a thinking substance which can know God and eternal truths
[Leibniz]
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12924
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Motion alone is relative, but force is real, and establishes its subject
[Leibniz]
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12925
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Beauty increases with familiarity
[Leibniz]
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13079
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A substance contains the laws of its operations, and its actions come from its own depth
[Leibniz]
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12927
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Happiness is advancement towards perfection
[Leibniz]
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12926
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Wisdom is the science of happiness
[Leibniz]
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12706
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Bodies need a soul (or something like it) to avoid being mere phenomena
[Leibniz]
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