sincerity (n.)

1530s, "pure, unmixed, unadulterated;" also "free from pretense or falsehood," from French sincere (16c.), from Latin sincerus, of things, "whole, clean, pure, uninjured, unmixed," figuratively "sound, genuine, pure, true, candid, truthful" (unadulterated by deceit), a word of uncertain origin.

There has been a temptation to see the first element as Latin sine "without." But there is no etymological justification for the common story that the word means "without wax" (*sin cerae), which is dismissed out of hand by OED, Century Dictionary ("untenable"), and others, and the stories invented to justify that folk etymology are even less plausible. Watkins has it as originally "of one growth" (i.e. "not hybrid, unmixed"), from PIE *sm-ke-ro-, from *sem- "one" (see same) + root of crescere "to grow" (from PIE root *ker- (2) "to grow"). De Vaan finds plausible a source in a lost adjective *caerus "whole, intact," from a PIE root meaning "whole."

1540s, from in- (1) "not, opposite of" + sincerity, or else from Latin insincerus "not genuine, not pure; spoiled, corrupted" (see insincere).