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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set

[status of a set having no members]

29 ideas
A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [Frege]
The null set is only defensible if it is the extension of an empty concept [Burge on Frege]
It is because a concept can be empty that there is such a thing as the empty class [Dummett on Frege]
The null set is indefensible, because it collects nothing [Burge on Frege]
The null class is a fiction [Russell]
For 'there is a class with no members' we don't need the null set as truthmaker [Armstrong]
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
The empty set may look pointless, but many sets can be constructed from it [Enderton]
We can accept the null set, but not a null class, a class lacking members [Lewis]
The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis]
The null set plays the role of last resort, for class abstracts and for existence [Lewis]
We can accept the null set, but there is no null class of anything [Lewis]
There are four main reasons for asserting that there is an empty set [Lewis]
We needn't accept this speck of nothingness, this black hole in the fabric of Reality! [Lewis]
Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD]
The null set was doubted, because numbering seemed to require 'units' [Tait]
We only know relational facts about the empty set, but nothing intrinsic [Chihara]
In simple type theory there is a hierarchy of null sets [Chihara]
The null set is a structural position which has no other position in membership relation [Chihara]
Realists about sets say there exists a null set in the real world, with no members [Chihara]
I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe]
Usually the only reason given for accepting the empty set is convenience [Potter]
The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
The empty set is something, not nothing! [Oliver/Smiley]
We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
Set theory makes a minimum ontological claim, that the empty set exists [Friend]
The empty set avoids having to take special precautions in case members vanish [Walicki]
The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]