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Single Idea 12939
[filed under theme 9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
]
Full Idea
Things which are uniform, containing no variety, are always mere abstractions: for instance, time, space, and the other entities of pure mathematics.
Gist of Idea
Wholly uniform things like space and numbers are mere abstractions
Source
Gottfried Leibniz (New Essays on Human Understanding [1704], 2.01)
Book Ref
Leibniz,Gottfried: 'New Essays on Human Understanding', ed/tr. Remnant/Bennett [CUP 1996], p.109
A Reaction
I presume that being 'mere abstractions' denies them ontological status, and makes them creations of thought. If so, I like this idea a lot.
The
17 ideas
with the same theme
[examples amd principles of modern abstracta]:
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12939
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Wholly uniform things like space and numbers are mere abstractions
[Leibniz]
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10309
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Frege says singular terms denote objects, numerals are singular terms, so numbers exist
[Frege, by Hale]
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10550
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Frege establishes abstract objects independently from concrete ones, by falling under a concept
[Frege, by Dummett]
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18269
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Logical objects are extensions of concepts, or ranges of values of functions
[Frege]
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8719
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There can be impossible and contradictory objects, if they can have properties
[Meinong, by Friend]
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10543
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Abstract objects must have names that fall within the range of some functional expression
[Dummett]
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9859
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It is absurd to deny the Equator, on the grounds that it lacks causal powers
[Dummett]
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9860
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'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object
[Dummett]
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9858
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Abstract objects nowadays are those which are objective but not actual
[Dummett]
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10489
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We deal with abstract objects all the time: software, poems, mistakes, triangles..
[Boolos]
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10415
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Properties make round squares and round triangles distinct, unlike exemplification
[Zalta, by Swoyer]
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9878
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Contextually defined abstract terms genuinely refer to objects
[Wright,C, by Dummett]
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9969
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The empty set is the purest abstract object
[Jubien]
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10626
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Objects just are what singular terms refer to
[Hale/Wright]
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7699
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Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals
[Jacquette]
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7783
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Bodies, properties, relations, events, numbers, sets and propositions are 'things' if they exist
[Lowe]
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10307
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The modern Fregean use of the term 'object' is much broader than the ordinary usage
[Hale]
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