I did say that "maybe it's simpler to just understand T(q) as 'q is a true proposition'." — Michael
Since "proposition" and "true proposition" are not in your argument itself — TonesInDeepFreeze
T(q) ≔ q is a true proposition
P(q) ≔ q is a proposition — Michael
The semantic turnstile as opposed to the proof turnstile is not important in this context. You don't even need any turnstile. — TonesInDeepFreeze
Depending on the context, 'proposition' stands for something different from 'sentence'. But you use 'p' for a sentence (you negate it, so it's a sentence). I don't see how one would figure out anything about platonism or anti-realism from your argument. — TonesInDeepFreeze
'utterance' means speaking out loud. Or do you have a different sense in mind? — TonesInDeepFreeze
1. Tq <-> p ... premise — TonesInDeepFreeze
Realists would argue that there is no connection; that there is some possible world where it is raining but where nothing is uttered. — Michael
That's all fine, but the more general point I mentioned is that we need to move to modal logic to have existence as a predicate. — TonesInDeepFreeze
Are you referring to the E formula from FOL= (and similar systems), such that Exists(x) =df ∃y y=x? — Kuro
(1) AxEy y=x is a theorem — TonesInDeepFreeze
Ey y=x in FOL= as a definiens for Exists(x). It would be pointless — TonesInDeepFreeze
(2) My point is the opposite: FOL= does not have an existence predicate. — TonesInDeepFreeze
most logics with existence predicates are not modal — Kuro
But modal logic is the more common one to study than all the others combined. (That's not an argument that modal logic is "better" or anything like that, just that it's natural enough to first turn to modal logic, as a common subject, to see what it offers, while not precluding that the number of other approaches is potentially inexhaustible too.) — TonesInDeepFreeze
I'm just unsure why you're characterizing modal logic as ones that deal with existence predicates — Kuro
most modal logics are standardly extensions of FOL with K and some of the additional modal axioms, and therefore do not express nontrivial existence predicates. — Kuro
It's been a while since I studied this, but, if I recall correctly, Hughes & Cresswell and L.T.F. Gamut do define an existence predicate in modal logic that is an extension of classical FOL=. (I'll happily stand corrected though if I my memory is incorrect.) — TonesInDeepFreeze
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