Augustus
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That's not sympathetic to the idea, because it's lacking the introspection which privilege is talking about.
It's clearly sympathetic to the idea. If one recognises disadvantage this necessitates advantage. The problem is the psychological block created by the term privilege.
The approach you are advocating ignores this basic cognitive reality, then blames people for responding in exactly the way that would be expected by utilising a term with strong existing connotations.
There is plenty of scientific evidence behind this, and plenty more anecdotal evidence in this thread and related articles.
https://en.wikipedia.org/wiki/Priming_(psychology)
Framing (social sciences) - Wikipedia
“Studies of priming effects have yielded discoveries that threaten our self-image as conscious and autonomous authors of our judgments and our choices...
“This complex constellation of responses occurred quickly, automatically, and effortlessly. You did not will it and you could not stop it. It was an operation of System 1. The events that took place as a result of your seeing the words happened by a process called associative activation: ideas that have been evoked trigger many other ideas, in a spreading cascade of activity in your brain. The essential feature of this complex set of mental events is its coherence. Each element is connected, and each supports and strengthens the others. The word evokes memories, which evoke emotions, which in turn evoke facial expressions and other reactions, such as a general tensing up and an avoidance tendency. The facial expression and the avoidance motion intensify the feelings to which they are linked, and the feelings in turn reinforce compatible ideas. All this happens quickly and all at once, yielding a self-reinforcing pattern of cognitive, emotional, and physical responses that is both diverse and integrated—it has been called associatively coherent.”
D Kahneman “The association machine in Thinking, Fast and Slow.”