c. 1300, purpus, "intention, aim, goal; object to be kept in view; proper function for which something exists," from Anglo-French purpos, Old French porpos "an aim, intention" (12c.), from porposer "to put forth," from por- "forth" (from a variant of Latin pro- "forth;" see pur-) + Old French poser "to put, place" (see pose (v.1)).
Etymologically it is equivalent to Latin propositium "a thing proposed or intended," but evidently formed in French from the same elements. From mid-14c. as "theme of a discourse, subject matter of a narrative (as opposed to digressions), hence to the purpose "appropriate" (late 14c.). On purpose "by design, intentionally" is attested from 1580s; earlier of purpose (early 15c.).
word-forming element meaning "lacking, cannot be, does not," from Old English -leas, from leas "free (from), devoid (of), false, feigned," from Proto-Germanic *lausaz (cognates: Dutch -loos, German -los "-less," Old Norse lauss "loose, free, vacant, dissolute," Middle Dutch los, German los "loose, free," Gothic laus "empty, vain"), from PIE root *leu- "to loosen, divide, cut apart." Related to loose and lease.
<a href="https://www.etymonline.com/word/purposeless">Etymology of purposeless by etymonline</a>
Harper, D. (n.d.). Etymology of purposeless. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/purposeless