@Alexander. Translation: “I can not find anything wrong with your post either, but I want to register my dislike of you.”

I don't know anything about you, @Carsogrin. How could I dislike you?

It's a genuine suggestion. I think improving a post is often the fastest way of getting what you want.

My core issue is that it seems that the only actual, concrete objection anyone has to my post, that would justify deleting it as opposed to down-voting it, is that it does not talk in a sophisticated way.

@user21820 seems to think that I claimed that ZFC and LOF are related. I do not recall mentioning them, and I can not see anyone else except Goldbach in the question.

@Carsogrin What part of the answer do you think gives them that impression?

I can understand people down-voting my answer just because it is not high-sounding, but it does not tell me that they understand my point.

@Alexander. I am not sure what you mean. I looked at a post earlier here, and the original question.

… by @user21820…

@Carsogrin Yeah, I've seen the answer. It's this, right?

That seems to be a link to my deleted, edited post. I am still not sure what you are talking about. People seem to think that I can improve my post by referring in detail to theories and models.

@Carsogrin That seems to be what the question was looking for.

Maybe what you wrote was deleted not because it was incorrect, but because it was not suited for the question is was posted on.

Here it is. A theory is generally not self-referring. A model, in instantiating a theory, does not do reflexive referring. In that sense, my post is about models. Again, I am not up to speed on this, and that might be wrong. I would have hoped that the OP would be able to apply my simple concept themself.

Yes, it is deemed not suitable because it is not high-sounding. Again, I have yet to see any argued claim that it is actually wrong (apart from the one about ZFC and LOF). It is supposed to be a simple, clever insight. Deleting simple, clever insights because they are simple is misguided.

@Carsogrin I think the question is asking about some very specific things, but your answer was a simplified layman's terms explanation, which in particular was broad and general. That isn't what the question was asking about.

Again (again getting personal)… as in my grievance post, my issue is that I have trouble believing that there is any chance of communicating about the problem, and the reality seems to be that on one cares to show that they actually do understand my point. (Of course, if it is simply stupid, that is understandable.)

Which specific part of the question does your answer address?

Looking at @mlk ’s answer… I do not think that Gödel’s theory is about choosing or being forced to choose; it is just about a feature of languages that include reflexive referring. I might be wrong. Also, I do not see how using integers requires or implies reflexive referring, but that might be wrong; again, I am not up to speed on this.

The point of my answer is that the issue is about reflexive referring. The problem pertains to reflexive referring. Any language that is capable of reflexive referring can construct inconsistent statements. It might apply to models. It might apply to theorems. It might apply to applying theorems to models. It just applies wherever there is reflexive referring, and not otherwise.

It looks to me that @mlk ’s answer is good (speaking as a non-expert). I just think that the reflexive referring issue is the issue.

I am theoretically logging out now.

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@Carsogrin You are wrong. There is nothing else to say on this. If you want to tell others about Godel's theorems, please make sure you yourself know all the technical details.

In particular, Godel's theorems NEVER construct any inconsistent statements, nor do they construct "reflexive referring". mlk's answer is correct because despite its gloss it does capture the correct meaning:

> The only choice we made is that of a logic that is sufficiently strong to include integer arithmetic. What Gödel then proves is that access to the integers automatically allows us to construct somewhat self-referential statements.

Both highlighted parts are important. There are numerous FOL theories that are syntactically complete, and the reason Godel's theorems don't apply to them is precisely because they are not strong enough to perform integer arithmetic. The fact that you say "do not see how using integers implies reflexive referring" shows that you do not at all understand Godel's theorems.

For example, ACF0 (the theory of algebraically complete fields of characteristic zero) is syntactically complete, and one can even write a computer program to determine whether a sentence is a tautology over ACF0 or not.

So is RCF (theory of real-closed fields), and DLOWE (theory of dense linear orders without endpoints), and Presburger arithmetic, and many others. Godel's theorems cannot apply to any of them.

mlk was also careful to say "somewhat self-referential", because they are not in fact self-referring. Many if not most popular layman accounts of Godel's theorems are deeply misleading on this very point, so it is totally useless to rely on those popular accounts.

Tanner Swett's answer even explains this point, so you should read it even if you don't want to learn the technical details of Godel's theorems.

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Anyone who wants to continue discussing that deleted post, please do so here, as it is off-topic for the other chat-room.