Are these sentences interchangeable?
I think I have left my keys at home.
I must have left my keys at home.
For example: If somebody asks us "where have you left your keys?" which answer would be correct to this question, 1 or 2? and why?
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We can consider the usage naively, in terms of the speaker's intent, and as perceived by the hearer.
Naively, the first is deduction (due to think) or speculation (due to the lack of explicit facts), while the second expresses certainty (due to must).
In terms of intent, the first expresses uncertainty and the second expresses a form of certainty. The following definitions support this.
I think so 1 a. used for saying that you are not completely certain about something: ‘Is James coming tonight?’ ‘I think so, but I’m not sure.’ - Macmillan Dictionary
Must 1 used for saying that you think something is probably true because nothing else seems possible: They must have got lost or they’d be here by now. - Macmillan Dictionary
However, the reasoning assumed for must is often weak or absent in conversational use of the term. When absent, this use borders on false bravado.
To the hearer, then, both can be perceived to be uncertain, but in different ways.
Nevertheless, the terms are not interchangeable because the intent and connotations they convey are different.
I think I left my keys at home.
I must have left my keys at home.
Neither of those phrases has an "exact" meaning. The first talks about what you think may be true. A thought can just pop into our heads. The second talks about what you have concluded to be true. Conclusions take at least a little bit of reasoning.
We use "must" after we have eliminated some possibilities, for example, they're not in your other pocket either, and not in your brief case, and you don't remember locking the front door on your way out of the house. You'd probably remember locking the door if you had done so, and so the keys must still be inside the house.
Either one of those statements would be a grammatical response to the question "Where have you left your keys?" So would "It's none of your business, dude, where I left my keys."
X must Y means for some reason, X believes that Y is true or had been true and X is unaware of any reason to the contrary.
Valid reasons include:
logical inevitability: *John turned left so he must be at Mike's house (Mike lives down that street.)
you did something or saw something previously and have received no evidence to the contrary since then: "My keys must be in my top drawer (You put them there earlier)"
something bad will happen and the speaker/writer is sure you want to avoid it: "You must pay your rent."
a really strong version of should: "You must come over and play this game sometime."
sometimes used to issue commands. "You must put my keys away next time!"
X think(s) Y just means that X believes Y is true or had been true, but is leaving open the possibility he/she may be wrong.
My keys must be in the car. (For example, I am remembering that I left them there)
I think my keys are in the car. (I'm not really sure where they are but I'm saying this is likely.)
The right answer depends on how confident you are that Y is true. Must means you are very confident, think means you are not completely confident.