This discussion brings to mind a basic psychology course that I audited in the mid 90s. About halfway through the course we were covering the 'traits paradigm' and intelligence in particular. One of the subtopics we delved into was Howard Gardner's
theory of multiple "intelligences" that he classified as follows: linguistic intelligence, logical/mathematical intelligence, musical intelligence, bodily-kinesthetic intelligence, spatial intelligence, interpersonal intelligence, intrapersonal intelligence. At some point it struck me that this was touchy-feely, navel-gazing, liberal nonsense and I proceeded to inform the class of my view (not in those words) that, in brief, intelligence is intelligence; it is not athleticism, self-awareness, musical talent, sociability, etc. If anything, the need to classify these other abilities as "intelligence" merely revealed (whether proper or not) the higher valuation that society places upon intelligence by comparison to other traits .
In any case, there are two types of knowledge (and knowledge is knowledge; it is not revelation, etc.):
1) empirical knowledge: What we have directly observed.
2) inferential knowledge: What logically follows.
The degree of certainty is based upon the reliability of the observation and the soundness of the logic.
intelligence is intelligence I'm sure your classmates were impressed. Intelligence is one of those wonderful things that's hard to define without going circular.
Q: What is intelligence?
Psychologist: It's what my test measures.
Q: So what does your test measure?
Psychologist: Intelligence.