Whether or not: the implicature

The word "whether" implies (or rather, entails) two alternatives:

a. “whether so,” and
b. “whether not.”

Thus, "or not" is redundant and “usually unnecessary” (NYPL).

However, M-WDEU testifies to the use of whether or not by authoritative writers for over a century and insists that the usage is legitimate.

IRA authors are urged to avoid the unnecessary “or not.”

Griceian editors should use discretion in deciding whether (or not?) to delete the phrase, especially in Tamil.