What is the point at which a non sequitur morphs into the incongruous? Is it predicated upon contextual ideas leading up to the statement, or is it subjective based on the conclusion of the idea being propagated? I'm just curious if there are any hard/fast rules, or is it subjective -- like finding something funny or not?
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I see it as somewhat orthogonal, though often related. incongruous means “not in harmony or keeping with the surroundings or other aspects” (New Oxford American Dictionary), while a non sequitur is something that doesn't follow logically from the premises. A non sequitur is thus often incongruous, but might not always be: in a series of collected non sequiturs, they would not be incongruous. Nor would a non sequitur be incongruous if the speaker were known to be subject to dementia.
For me, the distinctive element is: incongruous is linked to the absence of harmony, while non sequitur relates to the absence of logic.
Note : I believe there are quite a few comic strip series that follow this scheme, but can't think of any (in English), so suggestions in comments would be welcome.
A non-sequitur is always incongruous, in that it does not follow (literally) from the preceding conversation. Did you have something more specific in mind?
It is 100% subjective. The connection may make complete sense to me, the speaker, while you as the listener simply "don't know what I'm talking about". To you, it's a non sequitur, to me, I'm just speaking within my own world view and not bending my speech to ensure that it will be close enough to yours that it "makes sense".