My uncle Toby would never offer to answer this by any other kind of argument than that of whistling half a dozen bars of Lillibullero.—You must know it was the usual channel through which his passions got vent, when anything shocked or surprised him;—but especially when anything which he deemed very absurd was offered.[Laurence Sterne, The Life and Opinions of Tristram Shandy, i. xxi.]
As not one of our logical writers, nor any of the commentators upon them, that I remember, have thought proper to give a name to this particular species of argument, I here take the liberty to do it myself, for two reasons: first, That, in order to prevent all confusion in disputes, it may stand as much distinguished for ever, from every other species of argument—as the Argumentum ad Vericundiam, ex Absurdo, ex Fortiori, or any other argument whatsoever:—and, secondly, that it may be said, by my children's children, when my head is laid to rest,— that their learned grandfather's head had been busied to as much purpose once as other people's;—that he had invented a name,—and generously thrown it into the TREASURY of the Ars Logica, for one of the most unanswerable arguments in the whole science. And, if the end of disputation is more to silence than convince,—they may add, if they please, to one of the best arguments too.
I do, therefore, by these presents, strictly order and command, That it be known and distinguished by the name and title of the Argumentum Fistulatorium, and no other;—and that it rank hereafter with the Argumentum Baculinum and the Argumentum ad Crumenam, and for ever hereafter be treated of in the same chapter.
As for the Argumentum Tripodium, which is never used but by the woman against the man;—and the Argumentum ad Rem, which contrariwise, is made use of by the man only against the woman,—as these two are enough in conscience for one lecture —and, moreover, as the one is the best answer to the other—let them likewise be kept apart, and be treated of in a place by themselves.
Argumentum fistulatorium means, roughly, 'argument by piping'. Ad verecundiam, ex absurdo, and ex Fortiori are, respectively, argument from authority, from the absurdity of the position, and from the truth of a stronger conclusion. They would have been found in real lists of argument-types at the time. All the rest are jokes, but argumentum baculinum was an old one by Sterne's time; it occurs when you resolve an argument by beating your opponent with a club or a stick. Remarkably, later, more humorless lists of fallacies (which are descendants of the argument-classifications Sterne is mocking) will often list an argumentum ad baculum as an actual fallacy, namely, one in which you try to end a conversation by threatening someone. Argumentum ad Crumenam would be appeal to the purse. Argumentum Tripodium and Argumentum ad Rem are bawdy, involving references to genitalia. The second one is rather clever; literally it means something like, 'argument to the point or purpose', i.e., a relevant argument, and so he manages simultaneously to be bawdy and make the age-old and otherwise tired joke about how only men stick to the point.
You can hear Lillibullero here. The song mocks Irish Catholics and the tune became popular among English soldiers (hence Uncle Toby's familiarity with it). The tune, which long predates the words, is still popular; the Orange Order still use it, with new words, in The Protestant Boys, and the BBC used it for certain programs in WWII. It's also the official regimental march of the Corps of Royal Electrical and Mechanical Engineers.