Aristotle would not have supported proving anything exists simply from logic structures alone. — Gregory
Is ▢ ∃(x)(a=x) well-formed? Is it a theorem of S5? — Banno
I searched "what had model logic proved" and there was nothing
— Gregory
https://philosophy.stackexchange.com/questions/23929/what-are-the-practical-applications-of-modal-logic
https://www.sciencedirect.com/science/article/pii/S1571066114000905 — TonesInDeepFreeze
Modal logical leads to it using the ontological argument. — Gregory
Those links are about computer science — Gregory
is ▢ ∃(x)(a=x) a rendering of "a (that individual) exists in every possible world"? — Banno
B applies to a theorem, not an individual. I don't think we have an answer yet. — Banno
Is ▢ ∃(x)(a=x) well-formed? Is it a theorem of S5? — Banno
Aristotle would never take the ontological argument under consideration. But modal theorists struggle with it nevertheless — Gregory
So is the implication of ▢ ∃(x)(a=x) that, in any given model, there must be an individual that exists in every possible world? — Banno
Well, yes, in that I don't think it can be done - it woudl not be well-formed - or it would lead to contradiction.It seems you are wondering how to formalize "there is an individual that exists in every possible world'. — TonesInDeepFreeze
But logic can't say what can exist and what can't. — Gregory
All that comes from non logic. — Gregory
ML tries to rule over philosophy — Gregory
Doesn't modal logic implicitly assume it can settle these questions one and for all? — Gregory
"universe" - is that not the same as "possible world"? Or is it like "domain of discourse"? — Banno
On the other hand, whatever individual 'a' names by a model, that individual is a member of the universe for the model that names 'a'. But 'a' may name different individuals according to different models. — TonesInDeepFreeze
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