Reasoning--especially reasoning, without technical knowledge--must be put aside, in cases of this kind. It cannot assist the inquirer. It will lead him, in the most logical progression, to what, in the eyes of artists, would be a most illogical conclusion. Thus: bad drawing, bad proportion, bad perspective, indifference to truthful detail, color which gets its merit from time, and not from the artist--these things constitute the Old Master; conclusion, the Old Master was a bad painter, the Old Master was not an Old Master at all, but an Old Apprentice. Your friend the artist will grant your premises, but deny your conclusion; he will maintain that notwithstanding this formidable list of confessed defects, there is still a something that is divine and unapproachable about the Old Master, and that there is no arguing the fact away by any system of reasoning whatsoever.
I can believe that. There are women who have an indefinable charm in their faces which makes them beautiful to their intimates, but a cold stranger who tried to reason the matter out and find this beauty would fail. He would say of one of these women: This chin is too short, this nose is too long, this forehead is too high, this hair is too red, this complexion is too pallid, the perspective of the entire composition is incorrect; conclusion, the woman is not beautiful. But her nearest friend might say, and say truly, "Your premises are right, your logic is faultless, but your conclusion is wrong, nevertheless; she is an Old Master--she is beautiful, but only to such as know her; it is a beauty which cannot be formulated, but it is there, just the same.
Mark Twain, A Tramp Abroad, Chapter 48.
Of course, strictissimo modo, it can't be the case that the premises are right and the logic faultless but the conclusion wrong; however, if we are using 'logic' in a looser sense (which we usually do), it's a reasonable claim: the premises are good -- as far as they go -- the argument is reasonable -- as far as it goes -- but something is missing. It's interesting to compare this to something Hume says about je-ne-sais-quoi:
Besides all those qualities, which render a person lovely or valuable, there is also a certain je-ne-sçais-quoi of agreeable and handsome, that concurs to the same effect. In this case, as well as in that of wit and eloquence, we must have recourse to a certain sense, which acts without reflection, and regards not the tendencies of qualities and characters. [Treatise 188.8.131.52]
In other words, je-ne-sais-quoi is not discovered by reasoning (e.g., about 'tendencies of qualities and characters', i.e., utility) but by a sense of the agreeable, 'which acts without reflection'; from a a Humean perspective, this is what is missing from the sort of reasoning Twain notes: the cultivated sense or taste that discovers this indefinable quality of agreeableness.