I feel that pure ability to calculate, compare data, and perform linear thinking is one element of thought; while on the other hand, recalling information with clarity, connecting concepts (including recognizing people and places), and intuition, is a separate one. So if someone is a very good mathematician, they would most likely by good at other processes where something can be derived from an algorithm. Someone who is good at recognizing faces is also unlikely to be lost anywhere they have been before. There are exceptions to those rules, but these can be handled with either special abilities, or giving a unique character an oddly balanced skill set.
And as a negative example, it is a common trope for someone to be a mathematical genius who semi-regularly gets lost in the Lab's closet, or someone who never forgets a face but who isn't exactly a mental heavyweight. I find that this even works for more offbeat characters. For instance, a ranger who is never lost doesn't seem like a personable person, but if they ever get a grudge, you can bet that they will never loose their target. It's not that the ranger is bad at recognizing people, but that he just doesn't treat people as something to recognize. This could be again handled by skills, and by roleplaying (The ranger's player never has the ranger use his intuition with people in the same way a barbarian's player doesn't use his agility to dance. Often)
So, in short, I'd have at least those two mind stats, which for shorthand we could call Intellect and Intuition (IQ and TU).
These could still be separate from a third mental stat, which may represent a degree of charisma or something. This would presumably tie into acting, projection, manipulation, and possibly self-control. With that, then we could cut it down to six attributes.
I feel that may be enough if we then provide other ways to define the character along the lines of advantages and disadvantages like "unerring direction" for someone with low TU who doesn't get lost, or a "Maniac Calculator" for someone who is a idiot savant only capable of adding up numbers but not figuring out what day it is.
When these atts are used, I'm thinking that most skill rolls would be based on about two atts, any relevant advantages or disadvantages, and naturally skill. So for a sword attack, perhaps Str and Agi, perhaps modified by the fighting style (A lithe acrobat is better at dueling with a rapier than a barbarian warrior is, but if they're both using pig iron claymores...). Talking to a merchant about prices could involve all three mental stats, but mainly the social one and TU, since not only are we intuitively figuring out what the merchant wants and acting like we're going to give it to them, we are also making logical arguments about how we need something in exchange.
With all those bases covered, I don't see a place for the social stats that isn't at least partially handled by the mental ones and the traits.