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Is it possible for an intelligent person to care about whether a top physicist or top philosopher is more intelligent?
Yes, in my experience intelligent people are often interested in questions of ranking. They serve as a focal point for fleshing out other ideas.
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Originally Posted by VeeDDzz`
This is really what we're all asking, and a far more interesting question.
Also, is it possible for the intelligent to care about being recognised as superior to another?
It's not only possible, it's common.
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Is intelligent action motivated by egotistical motives?
Yes, much intelligent action is motivated by egotistical motives.
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If it is, then we maybe ought to redefine intelligence.
Why? Intelligence is a capacity for processing information, modelling complexity in a functional way, creating abstraction, parsing meaning, etc.
It has nothing to do (or not do) with ego or any other human emotional or character traits. It's a capacity/ability, like hand/eye coordination or VO2 max. It is only tangentially related to wisdom.