Is saying "...so I know how science works." likely to convince people?

[Prof.Lunaphiles]

I agree with you that the current government is bad. However, there could be a government based on science that implements only the policies that are scientifically proven to be effective!

A government based on science is not necessarily going to implement only the policies that are scientifically proven to be effective. A government based on science is going to properly review the reasoning of policy and issue reports of opinions and whatever else may be appropriate.

However, many people on the Internet forums seem to have this idea of the hierarchy of sciences and that linguistics and other social sciences are "soft sciences" or somehow not real sciences. The logic is that, if you study natural sciences (the "hard sciences"), it's relatively easy to know if you are wrong, since you can see whether the predictions you've made are right very soon. And that, if you study social sciences, it's very easy get something wrong and end up never knowing that, because it's very hard or impossible to do controlled experiments and/or systematic observation.

I agree.

If you ask me that notion is very problematic, if not outright self-contradictory. So, when you talk about things that are harder to properly study, you have, by that logic, less credibility.

And the hierarchy of sciences is the hardest thing to properly study . . .

I can affirm that for you - it is a very difficult task. There are very few attempts in the past hundred and fifty years, or so; but they have been earnest. I am very confident that I have deliberated a valid formula for constructing the hierarchy, and I have commenced the general hierarchy, but it will require the cooperation of scholars to review and correct my generalities, and construct the specific areas of the hierarchy.

It took about nine months of dedicated concentration to deliberate the formula, and then another nine months of challenging it, until I allowed myself to be dedicated to the formula for constructing the hierarchy that I have developed, so far. The hierarchy is called an ontology, and I am really surprised that you have not tried to deliberate the solution to the problem that you recognized - the hierarchy of sciences is the hardest thing to properly study.
How do you know that it is hard to study?

So, what do you think, is saying "I've published three papers about linguistics in peer-reviewed journals (about...), so I can safely tell you that's not how science works." more likely to be productive or counter-productive?

You are pretty much wasting your sincerity with people at Internet forums, especially, those who use the arguments that you provided.