Ok so.. this is complicated. Phenomenology I think is often a hard thing to wrap your head around, or it was for me when I first learnt.

It's definitely not the same thing as Hume's Idea, worlds apart.

Phenomenology is the study of the structure of consciousness and our lived experiences, it doesn't really have anything to do with math or logic, if anything it would be the opposite.

but isn't a viewpoint that considers human consciousness very relativistic, as each human thinks differently? Or is that wrong, since he only focuses on "essential structures" ie facets of consciousness all humans should have?

In Phenomenology it's called inter-subjectivity. We're all having independent subjective experiences but all of our experiences are the same, so to speak. Not concretely the same obviously, but we are all operating under the same structures, we're all presumably conscious. We might think differently, have different beliefs, but we all think, we all have beliefs, only the content changes.

Phenomenology, or more accurately, Husserl's position arose out of methodological skepticism. He saw what Descartes was trying to do but didn't think that he went far enough in its application. His approach is trying to reduce things to its absolute basics, and bracketing everything else (taking any questions not relating to the structure of consciousness or direct lived phenomenal experience and putting them aside for much later).

Husserl does talk about logic in his criticism of what he saw as an overreaching of psychology into the realm of philosophy, but it doesn't directly relate to the basic aim of phenomenology as far as I'm aware, it's been a long while.

http://plato.stanford.edu/entries/husserl/ http://plato.stanford.edu/entries/phenomenology/