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Single Idea 9969

[filed under theme 9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta ]

Full Idea

The empty set is the pure abstract object par excellence.

Gist of Idea

The empty set is the purest abstract object

Source

Michael Jubien (Ontology and Mathematical Truth [1977], p.118 n8)

Book Ref

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.118

A Reaction

So a really good PhD on the empty set could crack the whole nature of reality. Get to work, whoever you are!

Related Ideas

Idea 13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]

Idea 10811 The null set plays the role of last resort, for class abstracts and for existence [Lewis]

The 17 ideas with the same theme [examples amd principles of modern abstracta]:

12939 Wholly uniform things like space and numbers are mere abstractions [Leibniz]
10309 Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Frege, by Hale]
10550 Frege establishes abstract objects independently from concrete ones, by falling under a concept [Frege, by Dummett]
18269 Logical objects are extensions of concepts, or ranges of values of functions [Frege]
8719 There can be impossible and contradictory objects, if they can have properties [Meinong, by Friend]
10543 Abstract objects must have names that fall within the range of some functional expression [Dummett]
9859 It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
9860 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
9858 Abstract objects nowadays are those which are objective but not actual [Dummett]
10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
10415 Properties make round squares and round triangles distinct, unlike exemplification [Zalta, by Swoyer]
9878 Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett]
9969 The empty set is the purest abstract object [Jubien]
10626 Objects just are what singular terms refer to [Hale/Wright]
7699 Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette]
7783 Bodies, properties, relations, events, numbers, sets and propositions are 'things' if they exist [Lowe]
10307 The modern Fregean use of the term 'object' is much broader than the ordinary usage [Hale]