I had to look up saw myself, best definition that fit the theme was as follows:
A proverb or maxim, as inΒ Mom's always repeating the old saw, "Haste makes waste."Β This term usesΒ sawΒ in the sense of "saying," andΒ oldΒ in the sense of "wise" rather than old-fashioned. [Second half of 1400s]