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I've never understood why ⊃, rather than ⊂, is used for implication. It has the disturbing consequence for set theory that "∀x, x ∈ A ⊃ x ∈ B" is the same stat
by JadeNB 8y ago
I've never understood why ⊃, rather than ⊂, is used for implication. It has the disturbing consequence for set theory that "∀x, x ∈ A ⊃ x ∈ B" is the same statement as "A ⊆ B". I know this goes back at least to Russell and Whitehead, and probably before. Does anyone know the rationale?
- aggerdom 8y agoTaking a wild guess, but I would figure it's about distinguishing statements about truth values and statements about sets. If you think of it as a function, takes in two booleans and returns a booleen. Likewise ⊂ takes a thing and a set and returns a booleen. I've never really been a fan of ⊃, and always personally preferred an arrow.
- theoh 8y agoThere's an answer here: https://philosophy.stackexchange.com/questions/23231/is-there-a-relationship-between-implication-and-supersets https://philosophy.stackexchange.com/questions/23231/is-ther...