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What is the difference between 'assume' and 'presume'?

In the following sentence, do I use 'assume' or 'presume'?

Your shoes were not on the shoe rack, so I ______ you have left.
Comments  
I think 'presume' is more suitable for this sentence.

because although these two word all have the mean of accepting sth as true before there is proof,

'assume' has a meaning as pretend or display sth flasely,which is a little derogatory.

and 'presume' has another meaning as venture to do sth;be so bold as to do sth.

This sentence might be one of the speaker's appologize sentence,(maybe he/she mistakes someone has left)

It's just my own opinion.Maybe you can check it on some advanced dictionary.
I would have said the opposite.

To presume (according to www.m-w.com ) includes "to suppose to be true without proof" - and the lack of shoes were "proof" (even if it turned out to not be the right conclusion).

To assume (also according to www.m-w.com ) means "to take as granted or true."

The meaning of assume about pretending something is about an attitude you display, not a conclustioni that you have drawn.It gives the example of "assumed an air of confidence in spite of her dismay." In fact. www.m-w.com goes on to say this about assume: [it] often implies a justifiable motive rather than an intent to deceive - assumed an air of cheerfulness around the patients

You can make false assumptions, but that happens when you come to the wrong conclusion, not when you attempt to deceive.
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I agree with GG.

Now, this is not an easy one:
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presuppose

synonyms PRESUME, ASSUME, POSTULATE, PREMISE, POSIT:

presuppose indicates a taking for granted of something as true or existent, ranging from hazy, casual, uncritical acceptance or belief to certainty through the requirements of logical causation <Puritanism presupposed an intelligent clergy capable of interpreting Scripture -- American Guide Series: Massachusetts> <culture, which exists only through man, who is also a social animal, presupposes society -- A.L.Kroeber>

PRESUME may imply that whatever is taken for granted is entitled to belief until disproved; broadly it may imply casual conjecture <everyone charged with a penal offense has the right to be presumed innocent until proved guilty -- U.N. Declaration of Human Rights> <nobody in Baskul had known much about him except that he had arrived from Persia, where it was presumed he had something to do with oil -- James Hilton>

ASSUME indicates arbitrary or deliberate acceptance of something not proved or demonstrated or susceptible of being proved or demonstrated, or acceptance in accord with what evidence is available <there are many laws at present which are inequitable, because, for example, they assume a freedom of choice on the part of one party which under existing social circumstances is not there -- Norbert Wiener> <if we take the witness at his word and assume that he has this fear -- B.N.Meltzer>


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I think we have
acceptance in accord with what evidence is available (
Your shoes were not on the shoe rack)
thus assume, here.

Dr. Livingstone, I presume? = I imagine you are Dr. Livingstone; am I right?
But
I assumed he was Dr. Livingstone and called headquarters to say I had found him, without even asking him.

(basically what Marius says)
assume
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assumed
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