Well, no. The interpretation is not a part of the sentence. In formal systems the domain is not a part of the sentence, but is part of the way the sentence is used - it's in the semantics, not the syntax. The interpretation assigns elements of the domain to the various variables. "The cat is on the mat" is true only if the cat is one of the things that is on the mat. The domain and interpretation are not part of the true sentence but part of the language in which the sentence occurs, or better, the use to which it is put. That use is what "binds" the cat to "the cat". There is no need here for a picture-of-cat that sits between the cat and "the cat".Shouldn't it at the very least be a property of a pair <sentence, interpretation>? — Srap Tasmaner
The wouldn't you need an interpretation of the interpretation?Shouldn't it at the very least be a property of a pair <sentence, interpretation> — Srap Tasmaner
He's one of the best sources for questions about physics. — frank
I'm stealing that phrase.Postmodern fear of knowledge. — jkop
There are already well-developed systems of nonclassical logic that have at least a third value, so nothing new in that....defies conventional logic... — mlles
About as weak as reference as could be imagined... What the fuck is "|ψ⟩=α|nonexistence⟩+β|existence⟩"?— adapted from wikipedia — GrahamJ
Does it have a truth value before the coin toss is completed? — Janus
Seems to me that logic alone should not be able to commit us to a view on the truth functions of statements about the future. Rather if we hold that statements about the future are either true or false, we can adopt a biconditional logic, but if we think otherwise we might adopt an alternative logic. — Banno
That is indeed the 'strange loop': logical priority is a product of the brain, which in turn is a product of evolution. — Wayfarer
If "Our immensely sophisticated hominid forebrain generates the world in which there is space, time, and perspective", then there is an immensely sophisticated hominid forebrain, logically prior to there being a generated world. I can't imagine how you could reconcile these two things. The brain is a part of the world it supposedly produces.I'm considering the idea that while there are inummerable objective facts, — Wayfarer
So whether you're a realist or an anti-realist or an idealist, the bare assertion that "it is raining" is true iff it is raining says nothing to address any metaphysical issues – or even issues about truth. — Michael
...cardboard boxes have 8 corners — Michael
I've tried to be clear that ultimately neither realism nor idealism will do. The part of what you say that I agree with is that we construct our understanding of how things are; I've set this out in some detail in posts about both "counts as..." and direction of fit. The part on which it seems we disagree is that since not just any understanding will do, there is something else that places restrictions on the understanding we construct. — Banno
The substantial difference is that for us the past already happened, is thus fixed and has left its traces. The future is yet to happen and so is not (for us at least) fixed. — Janus
don’t read that as supporting metaphysical realism. — Wayfarer
What's suspicious about Tarski? — Michael
So do you interpret this? That if the language English had not developed, then there would be no gold?C2. If the sentence "gold exists" does not exist then gold does not exist — Michael
Sure. And the English language does exist. So if our domain includes English sentences, the sentence "Gold exists" is a member of that domain.The sentence "gold exists" doesn't exist if the English language doesn't exist. — Michael
I do not think it is that complicated. To make use of existential generalisation all one needs is for "there is gold in those hills" to be in the domain. A pretty minimal existential commitment to there being sentences. No need to decide if it exists like a ghost, or like a chair, or like a number.It's just the ordinary sense of "exists": the Earth exists but ghosts don't. — Michael
Someone must have done some work on this. — J
Yep. There are ambiguities here that formality might serve to iron out.The real problem here is that this hasn't been described in a formal logical or mathematical theory that it is so. — ssu
