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Please don't repeatedly ask other posters to answer a specific question. It almost amounts to stalking. If a poster decides to address your question they will do so; if not that's their choice. Please don't harangue them - apart from anything else it's just boring.

As to the discussion about the Incompleteness Theorem, it seems there is a basic misunderstanding here as to the meaning of "true" in general english and its meaning within a particular mathematical system. Within such a closed system the statement "This statement is true" doesn't make sense - it is not an allowed statement within the mathematical system.

I'm not surprised that amateurs get confused about these finer points of mathematics; it has a history of non-intuitive concepts. Hence we have "irrational" numbers, "imaginary" numbers, etc. These concepts go beyond the everyday experience. For example, there are far more (an infinity more!) irrational numbers than rational numbers. Yet between any two irrational numbers there is a rational number - doesn't make sense does it? It doesn't make sense in our everyday experience, but in its own context it makes perfect sense. Even the concept that there is a hierarchy of infinities is not exactly intuitive.

The Incompleteness Theorem says (in very simple terms) that in any sufficiently rich mathematical system there are some statements that are true but cannot be proven true or false (and, correspondingly, some false statements for which the same holds true). Not intuitive, but no more crazy than Heisenberg's Uncertainty Principle. In physics there are some quantities (or combinations of quantities) that we can't measure; in mathematics there are some true statements that we can't prove true. It's a bit like Donald Rumsfeld's much reviled (but actually deep) statement that "there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know.". I never understood why people didn't get what he was talking about there.

This is actually quite relevant to the concept of natural language programming. We are trying to mix here two quite disparate areas - natural language and computer programming. It's never going to work; it's like trying to apply the everyday meaning of "true" to a mathematical system. At best you end up with unimaginative programs that all follow the same pattern; at worst you have some programs that just can't be written, or that actually end up incorrect ("I'm sorry, Dave, I'm afraid I can't do that."). The joy of a good program is if it solves a problem in a way that nobody had thought of before. This requires an intellectual exercise by a human mind, not some robotic system cobbling together the same old answers to the same old questions.

Part of the issue is that most people think that mathematics is a) a single unified whole, b) about numbers somehow, though sometimes using a placeholder such as x when you don't know what the number is, and c) is some direct line to absolute truth, truth in the sense that is familiar to everyday people.

None of those things are at all the case.

Mathematics is a number of different things, really, but mostly it is a) a language (well, a family of several languages, but bear with me), and b) a protocol about how to use that language politely.

As a language - and when I say this, I don't just mean conventional mathematical notation (which I've already discussed the ideosyncracies of here, here, and here - oh, and throw in this while you're at it, too) but the whole gamut of terminology and agreed-upon notions - it exists primarily to express concepts. It is a language with a very tightly defined scope, and one which is remarkably compact and dense at times, but it is more than anything a language. As such, it has its idioms and oddities, but within the constraints of its domain of discussion, it can express nearly any idea - regardless of whether it is a reflection of the physical world or not. You can, indeed, say utter nonsense with mathematics, and people do so all the time, but conversely you can say things which sound like nonsense but still have a deeper meaning to them.

And like most other languages, it can easily convey some ideas which are much harder to express in other languages. Indeed this is precisely what the language evolved/was developed to do. At the same time, it struggles to convey certain other ideas which are facile in most other languages, mainly due to the assumptions the language was developed under.

Now, because the language originated as a way of reasoning about certain things (primarily geometry, historically speaking, but by the time of Al Khwarizmi it no longer really had any direct referents to the physical world at all; even in the days of Pythagoras and Euclid, it included such physically absurd ideas as points of one dimension and lines which extend to infinity - absurdities which are, nonetheless, quite useful absurdities) it has a set of rules of order meant to 'keep the conversations on topic' (as it were). However, those rules were not really more than guidelines until Hilbert and Co. started taking them far more literally than was actually sensible to do.

As it happens, it is really useful to use that language - and those rules of politesse - to describe things in the real world in a succinct and lucid manner, by making analogies between what you are saying in the mathematical world and what you are observing in the real world.

The problem arises, as is so often the case, when you take the metaphors literally, and ascribe them some sort of deeper meaning, rather than seeing them for what they are - a way of explaining something indirectly. Keep in mind that all abstractions leak, so none of these are ever going to be 'really real'.

Also, you can often have several different metaphors for the same thing, but with different implications. This is where you have to go and see which of them implies something about what it models which you haven't seen before, which if you can then observe it would help you decide which is the better description (vide the 1919 solar eclipse expeditions).

Where things really get heated is when people start arguing about which metaphor is 'really real', especially when they don't actually go and look at either the mathematical analogy itself, or the phenomenon which it is being used to describe.

I could go on about how the scientific method isn't really what most people take it for, either; not only isn't it a way to find objective truth - an objective truth which, to be fair, the whole system takes as a given for it to work at all - but most modern scientists would say that it can't be used to find absolute truth, only to refine the accuracy and precision of those descriptions (previously known as 'theories', though the term preferred by most working scientists today is the broader and more neutral 'model') to be a better approximation of that underlying truth. And trust me, scientists are as prone to egotism, mistakes, and bias as anyone - see the works of Stephen Jay Gould for examples, both for his lovely pop-sci descriptions of other scientists' foibles, and for the rather egregious and glaring personality flaws which are reflected in his own professional work.

(I truly adore Gould's books, but he definitely had feet of clay.)

The point is, while both science and mathematics may have started out as grand searches for The Truth, they ended up (like all human endeavors) settling on a pleasing fantasy instead. The fact that this fantasy is, at times, a fair approximation of what appears to be actually happening, is almost happenstance.

(See the works of Karl Popper for more on his assertions about why the existence of an objective physical reality cannot be proven using scientific techniques themselves, while also being a necessary assumption for the scientific method to make sense at all. To be fair, Popper's Postulates are somewhat controversial, especially the assertion that falsifiabilty is the dividing line between scientific and pseudoscientific, but it is still worth knowing what he has to say.)

I'd say that you were putting a little too much emphasis on the utilitarian aspects of mathematics. Whilst parts of it can be used as a tool to describe the world - often parts that when first developed had no foreseen application - the truth is that mathematics is just the abstract study of patterns. Some patterns are useful, some are just fun, although they may later turn out to be useful - and one of the known unknowns (or is it an unknown unknown) is whether that is true for any particular branch of mathematics. Really it's just an intellectual exercise that occasionally proves to be useful, but in no way does it represent any great truth.

To me there's no true or false involved, just a question of whether a system is consistent with itself.

iansjack wrote:I'd say that you were putting a little too much emphasis on the utilitarian aspects of mathematics. Whilst parts of it can be used as a tool to describe the world - often parts that when first developed had no foreseen application - the truth is that mathematics is just the abstract study of patterns. Some patterns are useful, some are just fun, although they may later turn out to be useful - and one of the known unknowns (or is it an unknown unknown) is whether that is true for any particular branch of mathematics. Really it's just an intellectual exercise that occasionally proves to be useful, but in no way does it represent any great truth.

OK, that's a fair point. Granted, I was indeed overly focused on application.

Qbyte wrote:When resolving this paradox, one should always address the strengthened version: "This statement is not true". So then, what is your resolution of it?

A case where something has insufficient content to be true or false, it is both not true and not false, so "not true" is not equal to "false".

DavidCooper wrote:

Qbyte wrote:When resolving this paradox, one should always address the strengthened version: "This statement is not true". So then, what is your resolution of it?

A case where something has insufficient content to be true or false, it is both not true and not false, so "not true" is not equal to "false".

In otherwise, it is undecidable.

Seriously, that's exactly what 'decidability' means in mathematics, but said in a different way. You just paraphrased what you set out to discredit.

I have no idea what, if anything, this song contributes to this discussion, but for some reason I want to post here anyway (even knowing that Trident/manhobby/QuantumRobin won't be able to understand the English words without a translator).

I suspect it says more about pop music than about AI, though.

Schol-R-LEA wrote:

DavidCooper wrote:

Qbyte wrote:When resolving this paradox, one should always address the strengthened version: "This statement is not true". So then, what is your resolution of it?

A case where something has insufficient content to be true or false, it is both not true and not false, so "not true" is not equal to "false".

In otherwise, it is undecidable.

Well, it's a bit more complicated because each well-formed sentence (in the logic sense) is either true or false but not both, assuming that the underlying system is complete and sound. It's just that the system itself cannot prove the correctness of the sentence. In meta logic, it's perfectly possible to prove that an undecidable sentence is true (or false).

The crucial point is what iansjack posted. You just cannot construct a literal formalization of "this sentence is true/false". You can construct something like \exists sentence S: S = S is provable/not provable in logic L (with the standard diagonalization argument) but in the underlying logic L, you cannot prove the truth of that sentence. In meta logic the "unprovable" version of the sentence is "obviously" true because otherwise we could produce a proof and undecidability implies that no proof exists in L (and an inconsistency in L would carry over to an inconsistency of our meta logic).

EDIT: Also, note that "S = S is unprovable" is only the same as "S = S is false" if we assume that L is sound and complete. In fact, we cannot formalize "S = S is false" directly, because to do this, we need to reason about all models of L. However, there are models of uncountable size that e.g. Peano arithmetic cannot reason about (this is implied by the Löwenheim-Skolem theorem). It is easy to formalize "S = S is unprovable" because provability relies only on the manipulation of axioms and deduction rules, i.e., finite strings.

Schol-R-LEA wrote:I have no idea what, if anything, this song contributes to this discussion, but for some reason I want to post here anyway (even knowing that Trident/manhobby/QuantumRobin won't be able to understand the English words without a translator).

I suspect it says more about pop music than about AI, though.

@Schol-R-LEA,

You said to me about forum which is actually about NLP in the following response:

Schol-R-LEA wrote:Sorry, that was a rather catty comment, I apologize.

That having been said, I do think you'd find more practical help in a forum which is actually about NLP, rather than a topic such as OS development which is almost, but not quite, completely unlike NLP.

Honestly, I've always been puzzled by your posting here, since you don't seem to have any interest in operating system development, even going back to your original account (Trident). It comes across as if you grabbed on to this forum at random and decided to stay regardless of whether you have any interest in the topic or not, which makes no sense to me. I can understand why DavidCooper is here, as he is working on an OS as part of his larger work; but so far, you don't seem to discuss the topic at all. Wouldn't a different venue - one closer to your interests - make more sense?

@Schol-R-LEA,

Again:

Yes, @Schol-R-LEA, a different venue
- one closer to my interests - make sense.

@Schol-R-LEA,

I am waiting your answers on these questions:

Again:

What are the different venues - the closer to my interests?

What are the forums which is actually about NLP?

QuantumRobin wrote:What are the different venues - the closer to my interests? What are the forums which is actually about NLP?

Uhm, I would expect that a Google or DuckDuckGo search would be the obvious place to turn, rather than asking the people here (since most of us aren't going to know any, and even DavidCooper has stated he doesn't know of any off-hand), but if you really want us to to the work for you... in an appropriately passive-aggressive manner, of course.

So, then, Let me Google 'Natural Language Processing' for you. And Let me refine that search to find message board and newsgroups, as well.

The ones which pop out at me (admittedly with some massaging and refining of the searches) are:

• r/LanguageTechnology subreddit
  Artifical Intelligence Discord Server
• Wolfram Community - Natural Language Processing
• Scholarship and Job Opportunities for NLP Engineers
• Natural Language Processing Data Community
• Fast.AI

I don't think a search on 'natural language programming' will turn up much other than this thread, and maybe The Osmosian Order of Plain English Programmers, but sure, let me Google that for you, too. (Oh, hey, look at that, there's quite a bit more than I expected. Well, well.)

Now, was that so hard? OK, so you might want to do it again yourself in Portuguese, I imagine, but still...

The David Cooper said that there might not be any forums specifically about NLP, and particularly if I am referring to natural language programming rather than natural language processing in the following response:

DavidCooper wrote:

QuantumRobin wrote:@Schol-R-LEA, @David Cooper,

What are the different venues - the closer to my interests?

Again:

What are the forums which is actually about NLP?

There might not be any forums specifically about it, and particularly if you're referring to natural language programming rather than natural language processing, but it's a topic better suited to a forum about programming in general rather than one that's specifically about operating systems, even if the two things converge in the future (with every OS being built as an AGI system too and with full support for natural language programming).

David Cooper,

The Schol-R-LEA said the following response about forums of NLP:

Schol-R-LEA wrote:

QuantumRobin wrote:What are the different venues - the closer to my interests? What are the forums which is actually about NLP?

Uhm, I would expect that a Google or DuckDuckGo search would be the obvious place to turn, rather than asking the people here (since most of us aren't going to know any, and even DavidCooper has stated he doesn't know of any off-hand), but if you really want us to to the work for you... in an appropriately passive-aggressive manner, of course.

So, then, Let me Google 'Natural Language Processing' for you. And Let me refine that search to find message board and newsgroups, as well.

The ones which pop out at me (admittedly with some massaging and refining of the searches) are:

• r/LanguageTechnology subreddit
  Artifical Intelligence Discord Server
• Wolfram Community - Natural Language Processing
• Scholarship and Job Opportunities for NLP Engineers
• Natural Language Processing Data Community
• Fast.AI

I don't think a search on 'natural language programming' will turn up much other than this thread, and maybe The Osmosian Order of Plain English Programmers, but sure, let me Google that for you, too. (Oh, hey, look at that, there's quite a bit more than I expected. Well, well.)

Now, was that so hard? OK, so you might want to do it again yourself in Portuguese, I imagine, but still...

David Cooper,

Do you agree with the Schol-R-LEA response's that I quoted above?

If not, why you do not agree with the Schol-R-LEA response's that I quoted above?

Schol-R-LEA wrote:

DavidCooper wrote:

Qbyte wrote:When resolving this paradox, one should always address the strengthened version: "This statement is not true". So then, what is your resolution of it?

A case where something has insufficient content to be true or false, it is both not true and not false, so "not true" is not equal to "false".

In otherwise, it is undecidable.

Seriously, that's exactly what 'decidability' means in mathematics, but said in a different way. You just paraphrased what you set out to discredit.

Not at all. It simply moves to a different paradox. The undecidable example is a case where it is neither true nor false, so there's nothing there to decide on.

QuantumRobin wrote: David Cooper,

Do you agree with the Schol-R-LEA response's that I quoted above?

If not, why you do not agree with the Schol-R-LEA response's that I quoted above?

Stop asking me if I agree with people and start asking yourself if you agree with them. You don't need other people to make your judgements for you.

DavidCooper wrote:

QuantumRobin wrote: David Cooper,

Do you agree with the Schol-R-LEA response's that I quoted above?

If not, why you do not agree with the Schol-R-LEA response's that I quoted above?

Stop asking me if I agree with people and start asking yourself if you agree with them. You don't need other people to make your judgements for you.

@David Cooper,

I will stop asking you if you agree with people.

Thanks for your response!

Schol-R-LEA wrote:

QuantumRobin wrote:What are the different venues - the closer to my interests? What are the forums which is actually about NLP?

Uhm, I would expect that a Google or DuckDuckGo search would be the obvious place to turn, rather than asking the people here (since most of us aren't going to know any, and even DavidCooper has stated he doesn't know of any off-hand), but if you really want us to to the work for you... in an appropriately passive-aggressive manner, of course.

So, then, Let me Google 'Natural Language Processing' for you. And Let me refine that search to find message board and newsgroups, as well.

The ones which pop out at me (admittedly with some massaging and refining of the searches) are:

• r/LanguageTechnology subreddit
  Artifical Intelligence Discord Server
• Wolfram Community - Natural Language Processing
• Scholarship and Job Opportunities for NLP Engineers
• Natural Language Processing Data Community
• Fast.AI

I don't think a search on 'natural language programming' will turn up much other than this thread, and maybe The Osmosian Order of Plain English Programmers, but sure, let me Google that for you, too. (Oh, hey, look at that, there's quite a bit more than I expected. Well, well.)

Now, was that so hard? OK, so you might want to do it again yourself in Portuguese, I imagine, but still...

@Schol-R-LEA,

Thanks for your response!

Wow, did this topic spiral into something totally different since I last read through it.
@QuantumRobin: enough. You cannot force anyone to do anything. If DavidCooper disagrees with myself and others, then that is their call, not yours. Pestering them will not win you any points in your favor and will only cause more problems for you.
As for the rest of this mess... this topic has exceeded my understanding. still believe that the points that I made a few pages back still hold, and have yet to see evidence that proves otherwise. However, its difficult for me to jump back in given the direction that this topic has taken.