I am in an uncomfortable position. I am beginning to do research in a particular area within my field. The body of related works are mostly done by students of a single professor. And, nearly all of it makes a crucial mistake. The works are borrowing/applying concepts and techniques from other, more theoretical and mathematical fields, yet in a way that doesn't make logical sense. Specifically, they are conflating terms, utilizing them as good sounding buzzwords, and (through an incorrect interpretation) as a criterion for the design and value of their techniques.
My work heavily uses the same concepts, yet my arguments are completely contradictory to those of my peers. So I am trying to figure out the best course of action.
I could start by submitting a paper correcting their mistakes, but it would feel a little cruel, and would likely turn my peers against me. I could publish my works, and try to point out their flaws politely, but the flaws are so prevalent that it would still likely cause a lot of discomfort to them. I could send an email to them explaining the problems with their work, but I'm not sure how that would go. It's quite a problem, because it really invalidates the reasoning and conclusions of dozens of papers and even a text book. The professor is distinguished and well known in his field. I really don't want to be the one to stir things up, but the issue must be addressed in some way or another in order for me to publish my work.