PERSONAL POINT OF VIEW:
Just because science has to be extraordinarily rigorous doesn't mean that we cannot use the power of imagination. Is it fantasy? Is it delusion? Is it blissful ignorance? Is it a combination of all these? Whatever it is, in my opinion, we should not divest ourselves from this innate capacity that we humans have. So long as we are able to separate evidence-based / hard logically-driven knowledge from mental flashes, I am convinced that there is no harm in doing so. As a matter of fact, I find it far more damaging to one's personal development suppressing such thoughts than encouraging them. I just so happen to think of this in terms of potentially new neural connectivity, one that has to be kept on its on realm of happy speculation, but alive nonetheless.
Professor Dan Everett says there are no such things as intuitions (https://youtu.be/7wqHAZSSklA), only inferences, but I will use this term here as this is the common non-technical use and sense of the word that everybody understands ("the meaning of words is its use").
1. Patterns and Mental Universals
How do we know if a pattern is a system or a coincidence (systematic or coincidental)? (coincidence understood as random events that simply cluster here and there because they have to end up somewhere, not because they had to be right there where we see them...).
So, for instance, prototypical transitivity (seems to me) is given by the natural constrains of the world we live in, not by some mental universal (I'm not saying there are no mental universals, but we should not deem everything that happens universally an innate mental universal).
Take for instance "pyramids"; we were not born with a chunk of brain designed to build pyramids, but given the constraints of the physical world in which we live, they just so happen to be one of the most common structures around the world, but that structure is just a coincidence imposed by the laws of physics and resources available to human beings.
3. Correlación, causalidad o casualidad
(correlation, causality or coincidence)