## What is the difference between ∃ (existence) and A (actuality)?

3

1

The existential quantification can, it seems, be used with modal logic. Now excuse my naivety, but:

• if so, what is the difference between being actual and existential quantification?

I'm just asking cos I wondered if it makes sense to talk about worlds which aren't this one being real.

1Do you mean like in first order modal logic? – Eliran – 2016-04-16T20:19:01.137

i don't know, i will google it – None – 2016-04-16T20:22:40.917

1

Yes, in what is called quantified modal logic http://plato.stanford.edu/entries/logic-modal/#QuaModLog That is the one that Quine had misgivings about, which were formally resolved by Kripke. Interpretational issues with quantification into modal contexts remain controversial however, Kripke's approach requires undesirable ontological commitments (essentialism).

– Conifold – 2016-04-16T20:30:55.880

@Conifold - In that article doesn't "A" just stand for some arbitrary proposition, rather than being a specifically modal logic related symbol? The list of modal logic symbols in part 1 at the very top of the article doesn't give "A" as a symbol. Or is it possible MATHEMETICIAN was talking about the upside-down A symbol? – Hypnosifl – 2016-04-16T22:30:21.180

@Hypnosifl it's mentioned about half way down ? A similar phenomenon arises in modal logics with an actuality operator A (read ‘it is actually the case that’). – None – 2016-04-16T22:54:35.797

Ah, I was just looking in section 14 which Conifold linked to, while the sentence you quote is from section 10. As far as I can tell the rest of the article doesn't give any examples of how the actuality operator is used though...aside from that one mention, it seems like when they use the symbol "A" they're generally just using it to represent some arbitrary proposition in predicate logic. So I suppose one would have to look elsewhere to learn more about it, or how it might relate to the quantified modal logic that Conifold brought up. – Hypnosifl – 2016-04-17T00:30:42.683