Talk:Scott–Potter set theory
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- Scott began with an axiom he declined to name: the atomic formula x∈y implies that y is a set. In symbols:
- ∀x,y∃a[x∈y→y=a].
Wouldn’t “x∈y implies that y is a set” be more clearly expressed as
- ∀x,y [x∈y]→∃a y=a?
(more clearly)
- ∀x,y x∈y .→ ∃a y=a
In particular, if x∈y is always false and the domain of quantification for a (but not x and y) is empty, the informal version and mine are both true, but the formal version in the article is not.
I’m reluctant to correct this, since I’m not familiar with Potter nor the formalism (in particular the domain(s) of quantification), and not sure which is wrong, the explanation or the formalization.
Definition of collection
editAs given in the article,
- a is a collection if {x : x∈a} exists. (All sets are collections, but not all collections are sets.)
Now, choose a as the empty set ∅. There is no x∈a, so ∅ is not a collection, isn't it? However this is in contradiction to 'All sets are collections'. Looks like this section might need some revision. Am I wrong? Btw what is the difference between a collection and a class? Kind regards, Ernsts (talk) 19:19, 5 December 2017 (UTC)