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Originally Posted by no5no5 
I think everyone has their own definition. And we're not really allowed to discuss (is my understanding). If you want more information, I'd recommend a visit to Hoagies' Gifted.
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I think we can say what we think giftedness is, we just can't say that we think someone else's definition is wrong or debatable.
OP, giftedness is a diagnostic criteria most often used in kindie and older school settings, typically based on IQ and achievement testing. It's also a descriptive category, and this is where there tends to be variation in definition. Advanced cognitive ability is the descriptor most aligned to the diagnostic criteria, but a range of other abilities are often described as gifted - musical and artistic ability, emotional maturity and intuitiveness, interpersonal/social skills, physical adeptness.
Hoagiesgifted.org is a great place to start, and related to advanced cognitive ability specifically you can't go wrong with a book by James T. Webb. You could also read old posts in this forum as this place is a gold mine!
IMO, unless there's a need for a diagnosis for something like finding a fit with a school setting, it's better to wait on testing. The testing process requires a lot of patience and attendance to task, things that aren't always within the scope of even the most gifted preschoolers.