From Sam Harris' website, survey results show that atheists and Christians responding to the survey have similar psychological beliefs. The area of greatest difference in this survey appears to be worry about the future.
The thing is that we can't really measure intelligence that way. Logical intelligence? mathematical skills? Good at languages? Quick at grasping the basics of a topic?
The feeling of being more intelligent cannot be defined, because you can feel intelligent over another person on different things. We cannot define intelligence. When people say intelligence you assume "logical thinking" but it was also quite well accepted that women would be less smart. It is also noticeable that you can have it easier understanding things depending on your learning process (auditory, kinaesthetic or visual).
You know, the thing is, if I would score on an IQ test today like Mensa, chances are I would get a mediocre score and probably score very poor on the mathematical part, because I have never been very strong at maths (probably also because it favor visual learning). However, I can equally speak to a guy who scored 130+ on the Mensa test, what does it say about my intelligence overall? I score poor doing sit down exams and tests, so poor I would barely be considered average intelligent (I have done tests where you can basically measure that). Still yes, I would say A LOT of people I have met are incredibly stupid. They are stupid in many ways. Stupid because they are blatantly ignorant. Stupid because they cannot seem to grasp or understand even in my eyes the simplest of things.
Indeed, I would say most people are biased in terms of IQ, but I don't think IQ is the way to measure intelligence.
I cannot entirely suggest a better definition, but I think we are really looking at something far broader and more profound. The fact one can increase one's IQ just by attending school is just... meh.
Well, I do believe every human being has the same possibilities becoming smart (hey, Einstein had a very small brain) except if you are born with your brain being impaired, such as with the case of Down's Syndrome.
It's true that it's difficult to define and measure intelligence, but it's less difficult to define and measure one or more aspects of abilities which combine to make up intelligence.
So what we can do is, say, measure people's maths ability, or their spatial awareness, or their information processing speed, and then ask them how they think they compare to other people on those measures.
But ultimately most people have a fair idea of what IQ tests measure, if they've taken such a test themselves. So regardless of how well an IQ test measures intelligence, if we're asked how we think we compare to others in terms of IQ, we should be able to place ourselves appropriately.
But of course we can't because we tend to have an over-inflated view of ourselves in relation to others, at either the individual or group level (i.e., we tend to think the group that we're a member of is better than other groups). So whenever we have limited information about those we're comparing ourselves to, we favour ourselves.
(the whole IQ thing would be much simpler if everyone knew that 100 was an average score)
Regarding the possibilities of becoming smart, if you consider ways people differ that are milder than your example of Down's Syndrome, you might not agree. And there is a lot of variation in the genetic foundations upon which our intelligence is built. There's a limit to how far above that genetic foundation any individual can stretch, so while most people who aren't severely impaired can do quite well, someone who is genetically predisposed to being not-very-bright would not be able to reach the same level as someone predisposed to being very bright.
But as you said, intelligence isn't about just one thing. So that not-very-bright person will probably be much better at some skills than the very-bright one.
That is exactly my biggest issue. It's enough to say that you are smarter just because you have more developed nerves in your brain, that you might've developed after becoming a musician. I understand that genes play a role, social standards play a role too. There is a huge difference in how lower class and middle/upper class families educate their children. The latter classes will obviously also get smarter children because they for example read them bed time stories, ask them abstract questions, make them watch documentaries on TV etc.
It has just become the general consensus to say that smart means logically smart, but even that is hard to truly define since I do easily grasp abstract topics and like I said, can easily follow the train of thought of someone who scored 130+ on the Mensa test (he also loves maths and is good at maths) but if I would do it myself, it would either be average or even downright poor.
There is also the issue that A LOT of tests ONLY favor visual learning. This really gives a wrong picture of people who do not belong into the category, such as myself. Indeed, I would believe I would score way better if I could make my tests verbally.