What are the differences between "assume", "presume" and "suppose"

I believe that "assume", "presume", "suppose" are similar in meaning of to take some facts as a truth without proof.

But it seems to me that "presume" is more formal, "assume" is less formal and "suppose" is the most general word for this meaning. Am I right? Maybe there are other differences in meaning and usage of these words?

An assumption is technically something that must be taken for granted in order for an argument to go through. Some assumptions cannot, in principle, be proven. For instance, there is probably no way to prove that anything exists outside of my own mind, but I assume this because otherwise I would quickly die as a result of walking front of a non-existent car.

Less fancifully, if I thought that physics was a good and useful thing, then no matter how much I might doubt it, I would be forced to assume that the physical world exists if I wanted to be a physicist.

"Presume" has about the same denotation but also the additional connotation, as mentioned in Webster's, of confidence. Note that to say someone is "presumptuous" commonly means that someone is overly confident of their assumption.

As mentioned above, I think in most contexts today "suppose" is used rather to express a certain amount of doubt about an assumption, and in that sense has the opposite connotation to "presume".

In this sense you might think that "assume" has relatively neutral connotations, while "presume" and "suppose", as commonly used, have roughly opposite connotations. I think that's about right.

The Merriam-Webster dictionary states for "assume":

to take as granted or true

And for "presume":

2> to expect or assume especially with confidence

3> to suppose to be true without proof

So although, the words are mostly used interchangeably, from these definitions, someone who is "presuming" something is more confident than someone who is "assuming" something.

My personal experience is otherwise, I have always thought of "presuming" something as assuming something prematurely, while "assuming" something would tend to have a stronger basis (though still a not very strong one).

For instance, I would say that if my pen was stolen, I would presume it was the first person that came into contact with me, if I thought he was averting his gaze. Whereas if someone had stolen something from me before, I would assume it was him.

Suppose is supposed to be a very near synonym to both words, but in my experience, it tends to mean that someone is a bit more hesitant at accepting something, e.g. "I suppose you are right". Or if my wife suggested I take out the garbage more often, I might say "I suppose that's what I should do."

I am very interested in hearing reading other people's opinions on the matter.

The Merriam-Webster dictionary states for "assume":

to take as granted or true

In effect, to take it for granted.

2> to expect or assume especially with confidence

3> to suppose to be true without proof

In effect, to assume without proof.

I assume Barak Obama is not against the US. Simply because he is president. However some people would presume otherwise.

Do you see the difference? I assume Obama is not against the US simply because he is president. This is an easy assumption. Some people would say that is presumption, but it isn't because it is expected for a president to be for the US. Some people would assume without proof (presume) that Obama is against the US. He never said so, so there is no proof.

Some people also presume that it was someone in the US Government that destroyed the twin towers. However, everyone assumes that Bin Laden did it simply because the media said so. Of course, using assume is also implying that it isn't absolutely proved.

I just learned from my Canadian born supervisor that 'supposed to' implies an expectation that someone will do something, or that something is expected to happen.

The students were supposed to keep quiet during the lecture.

In contrast, if you say assume, then it would be more like a possibility:

It was assumed the students were quiet during the lecture.

I will not burn my fingers on the 'to presume' discussion, I think that is well explained. I am not a native English speaker as you see ('to burn your fingers on something' is a Dutch expression that means avoiding the risk to say something about a particular issue), so I could be wrong. Let me know.