Logic is simply an arrangement of neurons inside the brain and makes no sense outside the scope of the mind. If a person is inclined to think logically, they do nothing but to bend reality to fit that way of thinking. Arguments based on logic alone have absolutely no value, as they only reflect the internal structure of the mind and not what it's being discussed externally to it.
While being a great tool, logic is a dead end in terms of evolution and can be explained by the nature of logic itself: it tends toward simplicity.
Simplicity doesn't have the same potential as complexity. Take any object and divide it and you'll eventually find fundamental particles and be unable to further divide it. This is, there is a limit. Complexity, on the other side, is limitless.
So there is no reason to think that intelligence is a tendency toward logic, because organisms tend toward complexity and there is a direct relationship between complexity and intelligence. So why the association then?
Complexity makes it difficult for us to interact externally, like with other people. One can expect to be misunderstood if a complex idea is forced to become simple, just like a digital picture that loses resolution. So the importance of logic inside intelligence relies on it's ability to adapt a complex idea into a simple container, like language, and vice versa.
This can be confirmed empirically, as richness of language is usually a good indicator of intelligence. By richness I mean that the person is capable of using ever more precise terms to denote the finer details of the idea that is being transfered. For example, talking about water is not the same as talking about vapor and ice, and talking about ice is not the same as talking about snow. Snow and water are exactly the same thing, we just happen to give the concepts a meaning, and this is a manifestation of subjectivity on top of logic.
However, the backbone of intelligence remains something else than logic, something I like to call "intuition", a tendency toward complexity, which is the opposite of logic. Intuition drives the mind away from generalities and makes it capable of handling specifics, which is what the real universe is all about.
Mathematical averages dissort our perception of the world and are unfortunately the base of reasoning of many sciences. Saying that when throwing a ball it describes a parabolic path is as absurd as saying that, when there is a birth rate of 2.1%, we get two full children and one leg.
Typology is an excellent example of the fallacy of logic, as it assumes that the mind is so simple that it belongs to a certain "type". That it switches from one way of thinking to another without going through intermediary steps. The brain is, however, composed by trillions of data paths that change constantly... and a bit too complex for that. The concept of typology is a direct result of our compulsion to make the world fit our view and not the opposite.
Our uniqueness as complex organisms is perhaps the only thing worth being taken as a root to reality. Just think about it.