So far as I can tell, the Gettier problem is exactly the same as "I believe in Science" - There's a fallacy of false equivalence in "X is a justified argument,

So far as I can tell, the Gettier problem is exactly the same as "I believe in Science" - There's a fallacy of false equivalence in "X is a justified argument, X||Y is therefore justified because of the justification in X", or something like that, I'm not sure what to call that fallacy. When you evaluate the truth of the whole argument, you'll find that it's not a "Justified True Belief" because the truth does not flow through the justified prepositions.