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It feels weird to think of premises as being "sent ahead". It makes more sense to think of premises as being put down, like in the etymology of the English thesis or French thèse quoted below.

premise [14]

Premise comes via Old French premisse from medieval Latin praemissa, a noun use of the past participle of Latin praemittere ‘send ahead’. This was a compound verb formed from the prefix prae- ‘before’ and mittere ‘send’ (source of English admit, commit, mission, transmit, etc). It first entered English as a technical term in logic, in which its underlying meaning is of a proposition ‘set before’ someone. But it was also used in the plural as a legal term, meaning ‘matters stated previously’. In a conveyance or will, such ‘matters’ were often houses or other buildings referred to specifically at the beginning of the document, and so the term premises came to denote such buildings.

Word Origins (2005 2e) by John Ayto, p 392 Right column.

thesis [14]

Greek thésis meant literally a ‘placing’ or ‘laying down’ (it was derived from the verb tithénai ‘put, place’, which also gave English apothecary). It evolved metaphorically to ‘proposition’, and passed in this sense via late Latin thesis into English.

Op cit, p 504 Left column.

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Old French didn't "borrow" from Latin, Latin evolved to what became Old French (among other languages.)

Anyway, there is no problem with premisse etymology being "sent ahead".

The premisses are the propositions "sent" ahead, i.e. transmitted, expressed first while the conclusion is what is expressed next.

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