But even on the continuum, there will be usually areas. If you consider the trolley problem and you're dealing with a threshold deontologist, having zero persons on the track will likely result ("I don't throw the guy over the bridget", hopefully) in a different answer then having one person on the track, and at some point the answer will shift again. We'll only need to reduce the problem to find the points of change (or areas, as few people will probably say "well, at 99? no, but for a 100 lives, yeah, I'll throw him over"), we don't need to keep a 1:1 mapping of all possible input values with the output values.
To use things, we usually reduce the single parts and use abstractions to deal with what's important (to us in that context). You don't deal with individual atoms, you look at clusters and clusters of clusters etc and understand and use them alltogether as a pen, just like you've similar pens before, even though they were 100% completely different if you look close enough.
This in itself can be see as problematic, as one can say that trying to reduce "concepts, ideas, or beliefs into abstractions" is futile, as those "things" are not black and white, they do not conform to Aristotelian logic of one thing/concept being either "true" of "false", there's a "continuum" (for lack of a better word) when trying to define each and everyone of those terms.
In other words one cannot be moral or not-moral (to go back to the trolley problem), there's a moral "continuum" which even varies with time (I know I'm less "moral" before I had the chance to drink my coffee early in the morning).