Thanks this is great but why do you look like The Divine Miss M

Essa não ironicamente foi uma boa introdução

“This statement cannot be proved using axioms and rules.” Consider as part of the understanding that from which the statement was formulated, i.e., to back-engineer it. This statement mirrors Quine’s liar paradox, “this statement is false”, which in my view was pure sophistry and meaningless. The contradiction arises from the defiance of the very logic also used in its definition/formulation. The term “statement” is a set definition though empty of members so there is no reference object that might present meaning in its use. “False” is the adjective meant to judge it though is kept from that task in that it becomes in its place in the statement, both the cause and effect at once of the paradoxical function. So to introduce this into mathematics is no less a scam than it was for Quine. “This statement cannot be proved by the axioms and rules” was formulated from a statement which either proposed a truth and by the clever structure of the Goedel numbers gave rise to the statement above or was a hodgepodge of mathematical symbols (of no particular meaning in a mathematical context) which when manipulated, meant to result through Goedel’s translation scheme to formulate his statement. If the former, it means that the mathematical statement had to have expressed that which we would be obliged to consider true, but for which there was no proof. How is it that such a mathematical formula could have escaped the notice of those in the profession for centuries? How could they not have seen that there were formulae for which there were not axioms and rules by which to provide their proofs? To have generated such a statement as “this statement cannot be proved by the axioms and rules” from mathematical formulae and axioms, which made sense in the discipline prior to Goedel’s translation seems a bit unlikely. One is driven to conclude that this ridiculous paradox of Quine’s would only act to corrupt mathematics as it did philosophy. How could a mathematical statement which when translated by Goedel’s numbers into a semantic statement make any sense in the context of mathematics? So, if we obey that suggested by the statement “this statement cannot be proved by the axioms and rules”, which is that it is a true statement (or what is the point of the discussion?), we must accept that it is either a statement standing on its own in judgment and thus self-referencing or it references the mathematical statement from which it was derived. The problem remains the same in either case. If it is not self-referencing, the statement from which it was translated had to have actually stated something in mathematical terms which made mathematical sense. I find it hard to believe that this is the case in that there is no structure to mathematics which is mirrored by the structure of language. Creating this statement out of the translation of disconnected mathematical statement fragments proves nothing. Such a mathematical statement would merely define something out of context of any associated mathematics axioms/rules normally employed. If this is not so, then the world of mathematicians would have known readily that such mathematical statements existed and were unprovable and there would have been no need of Goedel. Something seems wrong here. Three points to consider; • If there is a statement that is claimed true then it has to be known as to how and why it is true and that would be the proof. If we are to understand that this Goedel statement references a mathematical statement (from which it was derived) that is true, how is it that we can make such a claim? By what means can we understand it as true? • If there are simply bits of mathematical formulae or axioms, etc., which are manipulated that by the Goedel numbering system formulate this statement, of what consequence is that? It is able to make no claim about any incompleteness of math or logic. • This statement cannot be proved…generated by the translation of bits of math via the numbering system, means nothing if the terminology employed in the conclusion does not have counterparts in the language of mathematics. I seem to always come back to indict Goedel because of his stated admiration of Quine and his paradox which was pure nonsense. What do you think?

Starts a 3:05

You explain almost everything so clearly, but then near the end, the most important steps are not commented at all, you just dump symbols onto the screen with music and hope that people understand it. It would have been nice to have explanations of what each step means.

Well done.

You've done excellently with this video

this video is perfection, it makes me so sad to go on your channel and see there are no more videos!! Please keep em coming!! This is an absolute treasure!

Simply amazing video.

This is such a comfort video for me. I feel like I have learnt so much from it.

Fricken brilliany, please revive this channel!

This is legit funny tho. You have a great sense of

High quality content

Sorry for asking something so broad, but I would be very interested in hearing your personal thoughts about what intuition is? I believe this facet of our mind is what Penrose uses in his book "the emperors new mind", if I'm not mistaken (haven't gotten into reading it yet). Do you think there is anything to be said about intuition in regards to Gödels theories, or for any other reason?

I'm in for a treat. I absolutely love incompleteness, and I have many philosophical ideas upon it.

Not a mathematician by any means (I study jazz, and also Bach, I’m a musical nerd haha), but I’ve always been fascinated by pure mathematics and theoretical physics, it’s a huge interest of mine. And as someone who isn’t at all a professional I have to say this is one of the best and also most fun explanations I’ve seen. It is so approachable and makes such an abstract concept easier to comprehend. That’s all I can say as an outsider haha

Make a small video nerd

I mostly agree with your ending opinion, but not with your using the chinese room as an example. All the chinese room proves is that the book is a static intelligence of sufficient complexity/capability, and the man in the room is nothing but the computational substrate in the problem. Its basically a red herring that has convinced half or more of the great thinkers in the world.

Heyy I love your channel and may I ask a question: If in set theory, I can create a relation which takes a set of elements which are propositions (like set a is a subset of set b) and map it to a set of elements containing “true” and “false”, then why is it said that set theory itself can’t make truth valuations? I ask this because somebody told me recently that “set theory cannot make true valuations” Is this because I cannot do what I say above? Or because truth valuations happen via deductive systems and not by say first order set theory ?

This video brings a level of depth and rigor that's missing from a lot of math KZbin content. You've got a great concept here. I'm a video editor and if you make more of these, I can show you some things to make them more punchy and algorithm-friendly.

great job! and funny too. You should keep making these kinds of videos

Try some wd40 to get rid of Hoopla.

. Connectives? Conjunction Junction, what's your function? "And", "But" and "Or" get you pretty far! . -- (School House Rock)

. 🙂 Thanx for pointing out that the term "formal" is similar to the term "spherical" when used in the context you're discussing here. . Now I fully understand the term "formal logic".

I enjoyed the video. But, now I feel incomplete ...

Very impressive

watching this a year late and your channel is right up my alley, dreading checking the rest of the channel and finding you havent posted since. hope you're doing well

The opening is by far the best explaination of Godels incompleteness lol i love it so much

I struggle with multiplication...but here we go!

bit of an objection to the C vs Python comparison - even once you understand C, Python is still a far more powerful and expressive tool for getting programs written (even if it leaves a little to be desired in the speed of running them). Perhaps a more natural comparison would be C vs a functional language, like Haskell - in C, you give a series of instructions, from a fairly small and mostly fixed set of instructions of what to do (like individual inferences of natural deduction) whereas in functional languages you start with a small set of built-in functions and define new functions by modifying existing functions (with these modifications themselves being functions). In fact, the Curry-Howard isomorphism states that function application follows the same rule "A, A->B becomes B" as modus ponens (albeit with no analogue to negation)

great motivation for me to formally look into formal logic

Seeing human reason as superior to, or unachievable by machines ignores the fact that the difference is in our penchant for flawed logic. I think it has already been demonstrated adequately that learning models are amply capable of flawed logic (although we are still and will always remain the masters of that realm). What it may demonstrate is that attempting to eliminate such flaws, while probably a fool's errand anyway, might also not achieve all of our goals for the technology.

Nail polish remover is a great hoopla solvent.

Maths and physical reality overlap, but they are not one. But wait . . . what is one?

This is pretty brilliant work and I hope you end up making more stuff for this channel

I sat here and watched this end-to-end in one sitting and was enthralled. Very, very well done.

You appear rather young to be so well-acquainted with these topics and at such a depth. Kudos to you.

That intro though.

Was worth it just for the introduction. 😂. Ty.

As a first year applied math major, this is woke. And did not go over my head. I promise.

As a first year applied math major, this is woke. And did not go over my head. I promise.

This must be the best explanation of Godel's Incompleteness Theorems that I've ever seen! Glad to have found this gem.

With the question is mathematics invented or discovered - there is also a 3rd alternative which is the position of mathematical nominalism which is that mathematic is integrated into the nature of our physical reality. Nice good silly video though.