ftr said:
Specifically, we think of the electron as a particle...
Yes, but do remember that we're using the word "particle" in the sense of a quantum particle, not in the colloquial English sense of something like a very small grain of sand or tiny lump of matter that you can say is here or there or somewhere even if we don't know where. A quantum "particle" is something that behaves in certain ways, and one of its more important properties is that it is has no position before it is measured - not "it is somewhere but we don't know exactly where", not "it's all fuzzy and spread out in a cloud" but rather that it makes no more sense to talk about the particle's position than it does to talk about the position of an idea. Thus...
So, when not measured either have a particle with undefined position or an entity compromising all these positions.
Yes, and it's the first of these. We have an entity that for historical reasons is called a "particle", its position is undefined, and it will acquire a position when we measure it in the same way that I will acquire a lap when I sit down, or that I will acquire a fist when I curl my fingers back into my hand.
It seems to be a no brainer as the wavefunction is indicating the latter.
The wave function is indicating the former. The wave function says nothing about the position of the particle before measurement, it just tells us what the results of a measurement might be if we do measure it. Now, it is natural to think that that has to imply
something about the position before we measured, but it doesn't - at the risk of sending you off on a long and confusing digression I'm going to suggest that you google for "counterfactual definiteness" (the idea that something not measured must still have a value) and "Einstein EPR paradox" (a classic paper from 1935 in which Einstein and two colleagues developed the idea that there had to be something there before the measurement) and "Bell's theorem" (the 1965 discovery, followed by several decades of experimental confirmation) that this view is not how the world works.
Now, if we insist that it is a particle that is in "superposition" then that sound ultimate contradiction,i.e. how can something unique carry multiple values, that sound very illogical and un intuitiveness does not seem to have anything to do with it.
It does sound like a contradiction, and it is unquestionably counterintuitive. However, that's because your intuition is trained to deal with classical objects, and it doesn't want to accept the logical but very different rules that apply to quantum particles.
