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Single Idea 9572

[filed under theme 4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set ]

Full Idea

In the Gödelian realistic view of set theory the statement that there is a null set as the assertion of the existence in the real world of a set that has no members.

Gist of Idea

Realists about sets say there exists a null set in the real world, with no members

Source

Charles Chihara (A Structural Account of Mathematics [2004], 11.6)

Book Ref

Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.343

A Reaction

It seems to me obvious that such a claim is nonsense on stilts. 'In the beginning there was the null set'?

The 22 ideas from Charles Chihara

8758 We could talk of open sentences, instead of sets [Chihara, by Shapiro]
10265 Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
8759 We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
10264 Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
18151 Could we replace sets by the open sentences that define them? [Chihara, by Bostock]
10192 We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
9547 Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara]
9549 The set theorist cannot tell us what 'membership' is [Chihara]
9550 We only know relational facts about the empty set, but nothing intrinsic [Chihara]
9551 What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara]
9552 Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara]
9553 Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]
9559 If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara]
9561 The mathematics of relations is entirely covered by ordered pairs [Chihara]
9562 In simple type theory there is a hierarchy of null sets [Chihara]
9563 A pack of wolves doesn't cease when one member dies [Chihara]
9566 No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara]
9568 I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara]
9571 ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
9573 The null set is a structural position which has no other position in membership relation [Chihara]
9572 Realists about sets say there exists a null set in the real world, with no members [Chihara]
9574 'Gunk' is an individual possessing no parts that are atoms [Chihara]