Logical Symbols (2011)

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49 points·pplonski86··6 comments

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It should be noted that these are just _one_ of the ways of expressing the various connectives.

Among the symbols I've found used:

Conjunction: ∧ ⨉ &

Disjunction: | +

Negation: ¬ ! and "overlining" the terms

Implication: => ⇒ (most common in my experience)

Equivalence: <=> ⇔

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?

Taking 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.

There's an answer here:

https://philosophy.stackexchange.com/questions/23231/is-ther...

These were certainly not the symbols we were taught at university (and that I've seen in most mathematics texts).

We used:

∧ conjunction

∨ disjunction

⇒ implication

¬ negation

⇔ equivalence (bi-implication)

⊂, ⊃ &c. were for sets.

See also "The Markable Mark" http://www.markability.net/

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