What do you call someone or the action of a person who in an argument says one thing, but provides information to something that has nothing to do with what he was trying to prove?
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That argument is called a "straw man fallacy" or sometimes a "straw man argument." If I were to do that to you, I'd make it seem like you said something you never said, something I could easily disprove, then I would proceed by doing so.
The word sophistry applies quite nicely;
NOUN (plural sophistries) [MASS NOUN] 1 The use of clever but false arguments, especially with the intention of deceiving: trying to argue that I had benefited in any way from the disaster was pure sophistry (OED)
However this does lack the connotation of under research or lack of evidence