(Note: I wanted to write this after reading the discussion here about hostility towards popular questions from people with little experience in math).
The SE community is great but I would like to discuss an aspect with the answers to some questions that I have asked here, and to hear your opinion about it. I will take as an example my last question which struck me in particular. In this question, I wrote a passage about my understanding of Gödel's incompleteness theorems regarding the axiomatization of Euclidean geometry. As it turns out, my understanding had serious flaws, but the comments I got were not all enlightening. An established user with reputation over 100k, who has since deleted all his comments, said that what I wrote could just as well imply that Gödel's incompleteness theorems were equivalent to "delicious pickled gherkins". After trying to seek further clarification, his resulting comments were not much more helpful, and culminated with the following:
I have no idea why you would believe anything like that. If that was the case then the incompleteness theorem would not state that the theory has to be a first-order theory. Why on earth did we waste all this time for eight decades focusing only on first-order theories when it comes to GIT? Or maybe, just maybe, it has a lot to do with the logic that you are working in? I don't know. You tell me.
I take this up because I see experienced mathematicians make comments such as this sometimes. Is it really necessary to say things like "I have no idea why you would believe anything like that"? When I try to explain things to people who have less experience than me and they say something inaccurate, I try to make neutral statements such as "This is not entirely true because of..." (or perhaps better: "you made a mistake regarding..."). I think that doing so could lead to more friendly discourse where more learning takes place, and could therefore be beneficial in this community.
Another user answered my question "Is this accurate?" with the following:
Clearly not. Your interpretation of Gödel's completeness is very specious. This theorem only says : any first-order consistent theory admits a model.
This is completely correct as I later learned. However, I question the uses of words like "clearly", "obviously", etc, on websites such as SE. It is not clear to me that my understanding is wrong, otherwise I would not have posted the question. So "clearly" to whom? The person who answers the question? The general public? I think those are value-laden words that could often be avoided, but they are used sometimes on math-SE in answers to questions. I would like to hear your opinion about the use of such words.
(On a side node, another user later wrote an answer to my question that is, in my opinion, an ideal way to answer questions of this type. I think it's a good idea to read it for comparison to the above.)