Student or Learner
Does "formal science"'s "formal" mean "marked by form or ceremony" or "of or relating to the appearance, form, etc, of something as distinguished from its substance "? "Formal" has several meanings, and in this case, the translation goes as the latter, but I have the feeling of the former more.
ex)The convention of communication between scientists is formal and Verification Process of Formal Science. If new discoveries are to be taken seriously by other scientists, certain rigid criteria must be met. This means, before the new finding can be published and accepted, the experiment must be repeated and verified according to accepted procedures. Then, the finding is almost always communicated through a formal scientific paper or a journal article. The most important new findings may appear in a journal of general interests to all scientists, such as Science or Nature. In either case, the article will not be published until it has undergone the examination of the journalís editor and of two or three anonymous volunteer referees. This is one of the extensive safeguards of formal science.
Something closer to the first definition. It goes through a proper process, it follows a form. Real science is done using scientific methods, peer review, etc. The findings are published in scientific journals.