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