A saw is an old saying

Saying

A saying is something that is said, notable in one respect or another, to be "a pithy expression of wisdom or truth."There are a number of specific types of saying:...

 or commonly repeated phrase or idea; a conventional wisdom. While "old saw" is a common cliché

Cliché

A cliché or cliche is an expression, idea, or element of an artistic work which has been overused to the point of losing its original meaning or effect, especially when at some earlier time it was considered meaningful or novel. In phraseology, the term has taken on a more technical meaning,...

, some consider it a tautology

Tautology (rhetoric)

Tautology is an unnecessary or unessential repetition of meaning, using different and dissimilar words that effectively say the same thing...

.

Among various synonym

Synonym

Synonyms are different words with almost identical or similar meanings. Words that are synonyms are said to be synonymous, and the state of being a synonym is called synonymy. The word comes from Ancient Greek syn and onoma . The words car and automobile are synonyms...

s for "saying", dictionaries from 18th century singled out "saw" as a vulgar, uneducated wisdom, often based in supersititions. This flavor is seen in the expressions "old women's saws" and "old wife's saws."