There's never a statement in any given language that is both definitely true according to the rules of that language and also not provable in that language, because to be definitely true according to the rules of a language just is to be provable in that language. — Pfhorrest
Thank you. I thought it rather a stylish presentation. I like that guy’s channel. — Wayfarer
What you say just seems wrong for the simple reason that the truth of statements that are not provable cannot be ruled out; we don't know if they are true or not. In other words there can be truths which we cannot determine to be such, or at least it cannot be ruled out that there are. — Janus
this is a particularly clear pop-explanation — Banno
Almost no pop explanations ever mention Godel numbers in their presentation of the results. — StreetlightX
visual comments and props are the requirements of the media. — Wayfarer
It basically just boils down to how any language capable of formulating e.g. a proof of arithmetic is also capable of formulating self-referential sentences to which there cannot be assigned only one or the other boolean truth value: they must be assigned by the language either neither truth value (so the language is incomplete) or else both truth values (so the language is inconsistent). — Pfhorrest
If we were to take away anything of philosophical import from Godel, it would be that we should be using either a paraconsistent logic (where statements can be both true and false without explosion) or an intuitionist logic (where statements can be neither true nor false). — Pfhorrest
Kudos! Thanks again. — TheMadFool
Did you notice what went wrong? — TheMadFool
Aw shucks.... :yikes: — Wayfarer
I must confess that I didn't. I've not studied symbolic logic, and my mathematics is rudimentary, but I'm interested in why Godel's Theorems 'are unquestionably among the most philosophically important logico-mathematical discoveries ever made' (says this article.) I feel as though I intuitively understand why that is, but when I read up on it, I find it very hard to follow. Which is why I found that video was helpful although as we see, opinions are divided. — Wayfarer
I'm not saying that unprovable statements are definitely false, so this is a non-sequitur. — Pfhorrest
There's never a statement in any given language that is both definitely true according to the rules of that language and also not provable in that language, because to be definitely true according to the rules of a language just is to be provable in that language. — Pfhorrest
There's never a statement in any given language that is both definitely true according to the rules of that language and also not provable in that language, because to be definitely true according to the rules of a language just is to be provable in that language. — Pfhorrest
What you say just seems wrong for the simple reason that the truth of statements that are not provable cannot be ruled out; we don't know if they are true or not. In other words there can be truths which we cannot determine to be such, or at least it cannot be ruled out that there are. — Janus
the version in the video — TheMadFool
Get your hands on an introductory course on logic. — TheMadFool
Godel uses the liar paradox to wit, the sentence L = This sentence is false — TheMadFool
If you can correctly extract from the video that Godel's argument is circular, then the video is wrong. — TonesInDeepFreeze
I defer to your better judgement — TheMadFool
is it any good? — fishfry
can you tell me if it's giving people false ideas? — fishfry
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