Whether or not: the explicature ("He is coming, whether you like it (or not)"

It's best to formalise the conjunction "whether" with the horseshoe (Grice, 'if').

'whether' is used to introducing a direct interrogative question (often with correlative "or") which indicates doubt between alternatives.  

1526, William Tyndale, trans. Bible, Mark II:

"whether ys it easyer to saye
to the sicke of the palsey, thy
synnes ar forgeven the: or to saye,
aryse, take uppe thy beed and walke?

1616, William Shakespeare, King John, I.i:

Whether hadst thou rather be a Faulconbridge, [...]
Or the reputed sonne of Cordelion?

Also, "whether" is used to introduce an indirect interrogative question that consists of multiple alternative possibilities (usually with correlative "or").

"He chose the correct answer, but whether by luck or by skill I don't know."

Without a correlative, used to introduce a simple indirect question; if, whether or not.

"Do you know whether he's coming?"
"Do you know whether he's coming or not?"

"Whether" is also used to introduce a disjunctive adverbial clause which qualifies the main clause of the sentence (with correlative "or").

"He's coming, whether you like it or not."

But hardly: "He's coming, whether you don't like it."

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Note that there is some implicatural overlap in usage between Usage 2 and Usage 3, in that a "yes-or-no" interrogative content clause can list the two possibilities explicitly in a number of ways:

"Do you know whether he's coming or staying?"

"Do you know whether he's coming?"
"Do you know whether he's coming or not?"

"Do you know whether or not he's coming?

Further, in the first two of these examples, the "or staying" and

"or not"

may be added as an implicatural (cancellability-oriented) afterthought (sometimes indicated in writing with a comma before), such that the "whether" may be uttered in Usage 3 and then amended to Usage 2.

Usage 4 does not have a counterpart that introduces only a single possibility;

*"He's coming, whether you like it" is felt by many to be ungrammatical.

In traditional grammar, the clauses headed by whether in Usages 2 and 3 are classified as noun clauses. Those headed by whether in Usage 4 are classified as adverb clauses.