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Plagiarism is the reuse of other's materials without proper credit and acknowledgement [1]

Credible sources are vaguely defined, but it can be attributed to verifiable facts in the literature [2]

I want to ask that, in a situation, when an academician found an "inspiring" idea (not necessarily well-defined) on the non-academic part of the Internet, such as some blogs, or discussion on the social networks, a Youtube video, or some crude Python scripts, etc, and work out on their own to shape up an explicit scientific study or, for example, write up a sophisticated numerical package, then two there are two things here: (1) the source does not provide a scientific study, nor in an academic form, thus it cannot be considered as "credible source", so usually it cannot be cited, (2) but it provides a crude idea that one formulates a scientific problem based on it, so not citing it should be considered as plagiarism.

What is the way to deal with it? Whether to cite or not to cite? For a casual discussion on the Internet to inspire research might be rare in reality, at least it is me who hasn't seen a case, but what if this situation came into reality?

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    When using someone else's idea, you should cite it, whether or not it's "credible" or "academic". I disagree with your assertion that a non-credible source usually cannot be cited. In fact, if I write a paper explaining why someone else's paper is nonsense, then I have to cite that other paper even while explicitly saying it's nonsense.
    – Andreas Blass
    Commented Aug 29, 2020 at 14:48
  • "Credible source" is just a judgement call. Cite it. You cause no harm in citing, but possibly do in avoiding it. Harm to your own reputation.
    – Buffy
    Commented Aug 29, 2020 at 15:34
  • What is the way to deal with it? --- I don't know what field you're in, but it's fairly common to see "personal communication" or some such in bibliographies of mathematics papers. In the introductory/motivational part of the paper you could say something along the lines of A (your informal source) observed B, which suggests that method C could be a useful way of approaching D, and this paper is the result of carrying this out.
    – Dave L Renfro
    Commented Aug 29, 2020 at 18:36
  • Giving "credit" has nothing with the sources being "credible". You seem to be confusing the two concepts due to the words having the same root. Plagiarism is plagiarism whether the source that is ripped off is credible or not.
    – Kaz
    Commented Aug 30, 2020 at 3:01
  • In some academic situations, it is not acceptable to use someone's work even if the source is credited. For instance, in an examination, you cannot copy the neighboring student's answer even if you add a footnote saying 1. From my neighbor's exam paper; used with permission.
    – Kaz
    Commented Aug 30, 2020 at 3:03

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I'm not sure where you heard that you should only cite "credible" sources. Credibility is a judgement call, best avoided. You should always cite things that you have found and used, even if they were ill formed when found. The ideas are those of others that you have developed further. But the idea didn't originate with you, so you are open to charges of plagiarism if you don't cite. The likelihood of a formal charge may be slim, but other academics might doubt you if you cut corners.

That doesn't, however, mean that you have to accept the veracity of the things you cite. In fact, you can, and in some cases should, discuss the doubts you have or the ill state in which you found a resource that you use.

I'll note that in mathematics, we sometimes have to cite papers that contain serious errors so that we can correct those errors. But our work is still based on the work of the earlier mathematicians, even if we correct it.

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    Agreed. When I assess student work, I have no problem with students citing sources with poor quality assurance, as long as the students show appropriate caution about believing everything those sources say. That caution may include seeking out a second, independent source to confirm or refute what the first source says; or it may include the student, on his/her own behalf, going through the chain of logic in the first source with a fine-tooth comb to make sure it all adds up. But even without that caution, citing a source with poor quality assurance is better than citing no source at all.
    – user128581
    Commented Aug 29, 2020 at 16:30

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