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9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta

[examples amd principles of modern abstracta]

17 ideas
Wholly uniform things like space and numbers are mere abstractions [Leibniz]
Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Hale on Frege]
Frege establishes abstract objects independently from concrete ones, by falling under a concept [Dummett on Frege]
Logical objects are extensions of concepts, or ranges of values of functions [Frege]
There can be impossible and contradictory objects, if they can have properties [Friend on Meinong]
Abstract objects must have names that fall within the range of some functional expression [Dummett]
Abstract objects nowadays are those which are objective but not actual [Dummett]
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
Properties make round squares and round triangles distinct, unlike exemplification [Swoyer on Zalta]
Contextually defined abstract terms genuinely refer to objects [Dummett on Wright,C]
The empty set is the purest abstract object [Jubien]
Objects just are what singular terms refer to [Hale/Wright]
Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette]
Bodies, properties, relations, events, numbers, sets and propositions are 'things' if they exist [Lowe]
The modern Fregean use of the term 'object' is much broader than the ordinary usage [Hale]