I have started reading Collingwood's An Essay on Metaphysics and I see one definition that seems to be pertinent to this discussion.

p. 27 "Def. 4. To assume it to suppose by an act of free choice.

A person who 'makes an assumption' is making a supposition about which he is aware that he might if he chose make not that but another. All assumptions are suppositions, but all suppositions are not assumptions: for some are made altogether unawares, and others, though the persons what make them may be conscious of making them, are made without any consciousness of the possibility, if it is a possibility, that others might have been made instead. When correctly used, the word 'assumption' is always used with this implication of free choice, as when it is said 'let us assume x = 10'."

What about that? It looks to be not far away from what Aleksandr Lokshin has suggested.


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