IMHO, the context of this sentence is important.
"Here was a man some twenty thousand miles from home, by the way of
Cape Horn, that is- which was the only way he could get there- thrown
among people as strange to him as though he were in the planet
Jupiter; and yet he seemed entirely at his ease; preserving the utmost
serenity; content with his own companionship; always equal to himself.
Surely this was a touch of fine philosophy; though no doubt he had
never heard there was such a thing as that. But, perhaps, to be true
philosophers, we mortals should not be conscious of so living or so
striving. So soon as I hear that such or such a man gives himself out
for a philosopher, I conclude that, like the dyspeptic old woman, he
must have "broken his digester."
The discussion is about Queequeg's fine philosophy and equanimity. The
hidden allusions are (g)astro-logical, for they associate Jupiter (and
Sagittarius) with philosophy and digestion. Jupiter is our solar
system's big belly. In Moby-Dick, Queequeg is clearly linked with
Sagittarius. This sign is traditionally associated with long-distance
travels, higher education, philosophy and religion. Here, Ishmael
seems to contrast two views on philosophy: a "natural" and "true"
philosophy (that of the savage), and a "dyspeptic" one (that of the so-
called civilized). I infer, from previous chapters (i.e. the Carpet-
Bag), that "northern lights" are synonymous with German (dyspeptic,
that is, indigest) transcendental idealism.
It all sounds like Melville's own "Critique of Pure Reason".
Nick
PS. Ahab, too, wants to “break a digester"...