The have + past participle formula is widespread in the Latin and Germanic languages, which is strange when you think about it.  Why use the word have, which has its own meaning, as an auxiliary?  After all, the proper meaning of have has no special property.  Why not use hear, offer, compute, or any other seemingly random choice of word?

The answer, as one might expect, lies with Latin.  At the time that the formula have + past participle came into being, it was used only sporadically.

The best example I can think of involves finding a key.

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