When applied to discourse, dismissal is a method of processing out the opponent’s discourse, on the brink of refutation and destruction.

1. Dismissal as the concluding stage of refutation

An argument can be dismissed after due consideration. In that case, dismissal is the last step of a conclusive refutation.
The standard forms of refutation are based on a substantial examination of the content of the rejected speech, or on more or less relevant considerations about the person holding it. Even in the latter case, the rejection is, however badly argued, at least backed by some justificatory discourse.

2. Dismissal without consideration of the dismissed argument
(ad lapidem)

The opponent can dismiss a discourse simply by declaring that the bad quality of the proposed argument is self-evident and self-denouncing:

No comment.
Your arguments are shabby, insufficient, miserable, distressing
I will not give your statement the honor of a refutation.
What you say is not even false.

Uncle Toby’s reaction, “whistling half a dozen bars of Lillabullero”, is a case of such reaction “when any thing, which he deem’d very absurd, was offerd”,  S. Ab, ad –, ex.

In ancient rhetoric, this move declaring the argument to be “childish” or “obviously absurd or practically null”, is called apodioxis, (Dupriez 1984, Apodioxis; Molinié 1992, Apodioxis), S. Pathetic argument.

The opponent can dismiss an argument as self-refuting in perfectly good faith, which can lead to paradoxical situations. If the discourse of Big Jones is really self-denouncing, then:

One should give Big Jones a greater say, the more he speaks, the more foolish he appears, the fewer votes he will get.

But this is a perilous strategy, inspired more by the arguer’s self-confidence than by any self-evidence about the discourse.

To top it all off, the opponent may adopt a strategy of irony, and contribute to the dissemination of the opponent’s speech. This is the extraordinary case reported by Wayne Booth about events taking place in his university, where students were clashing with their University administration:

At one point, things got so bad that each side found itself reduplicating broadsides produced by the other side, and distributing them, in thousands of copies, without comment; to each side it seemed as if the other side’s rhetoric was self-damning, so absurd had it become. (Booth 1974, p. 8-9)

S. also Dismissal (Companion

Obviously, the other side cannot even hear such a disqualification, which targets third parties. Used in particularly contentious argumentative situations, such a maneuver makes any deal between the discussants impossible, S. Conditions of discussion.

From the ethotic perspective, such a (non-) arguer displays a kind of moral indignation, whereas the opponent can accuse her of arrogance and contempt.

Ad lapidem argument (Lat. lapis, “stone”)

The name of this argument is derived from a famous incident in which Dr. Samuel Johnson claimed to disprove Bishop Berkeley’s immaterialist philosophy (that there are no material objects, only minds and ideas in those minds) by kicking a large stone and asserting ‘I refute it thus’ (after Wikipedia, Ad lapidem).

This clear contempt of verbal argument is akin to “the proof of the pudding is in the eating”, a practical proof by facts and action.