hmm... could you provide me with some examples clearly showing the difference? (I have a thesaurus, but it doesn't give any examples) How am I supposed to know how such nuances work like? Sorry for being a pain in the ass...
For instance, in the following sentence I wouldn't know which one fits best:
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Even if one is to assume/presume/presuppose and
accept the fact that the American psyche has been possibly irremediably
distorted/malformed by the 9/11 attacks and might perhaps be biased, it would
be incommensurable to deny/gainsay the prevailing...