14238 | A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [Frege] |
9157 | The null set is only defensible if it is the extension of an empty concept [Frege, by Burge] |
9835 | It is because a concept can be empty that there is such a thing as the empty class [Frege, by Dummett] |
16895 | The null set is indefensible, because it collects nothing [Frege, by Burge] |
14113 | The null class is a fiction [Russell] |
18393 | For 'there is a class with no members' we don't need the null set as truthmaker [Armstrong] |
13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
15498 | We can accept the null set, but there is no null class of anything [Lewis] |
15503 | We needn't accept this speck of nothingness, this black hole in the fabric of Reality! [Lewis] |
15502 | There are four main reasons for asserting that there is an empty set [Lewis] |
13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
8322 | I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |