The reason the word obviously does argumentative work

Placed in front of a contestable proposition, obviously adds no evidence and changes the cost of objecting. The claim is presented as already shared, so a challenge is no longer a disagreement about the proposition. It is a disclosure about the challenger, and disclosures of that kind are expensive in a room.

What everyone sees

The word is read as emphasis or as filler, the verbal equivalent of underlining. Emphasis is part of it. But emphasis operates on the claim, while this operates on the audience’s position relative to the claim, which is why it appears most often exactly where support is weakest.

What is actually happening

Stalnaker described assertion as an operation on the common ground: an utterance proposes to add content to what participants treat as mutually accepted, and presuppositional devices smuggle content in as already accepted rather than offering it for evaluation. Brown and Levinson supply the cost of resisting: challenging what has been marked as shared threatens the face of both parties, so listeners frequently allow it to stand even when unconvinced. The effect is not to strengthen the argument. It is to reprice the objection, moving it from a cheap intellectual move to an expensive social one.

Why it stays hidden

The device hides because silence resembles agreement and is recorded as such. Nobody objected, so the proposition passes into the shared record and is available as a premise later. The listeners who doubted it are aware only of having chosen not to interrupt, which does not feel like having conceded anything.