"Table" is just a word. If you want to know what the word means, you have to observe the structure of the patterns in it's usage. Words acquire meaning through usage (in context.)
There is no such thing as an "approximate table" per se, just things that can be approximately described by the word "table". It makes no sense to talk about a 'real table'. Every thing that exists is real, whether you call it a table or not.
I'm also confused why you'd think the concept of continuity is blurry on this issue. Continuity means that similar inputs give nearby outputs, and this is perfectly consistent with how computation works: if you construct two results through similar algorithms, they will have closely related types. Types become a measure of similarity of different computations, and thus you can use them to group things with similar linguistic structure, and thus similar meaning.
Either way, Aristotle and Plato were both ancient people with not even a tenth the information we have today, so I wouldn't consider them authorities on any part of this discussion.
There is no such thing as an "approximate table" per se, just things that can be approximately described by the word "table". It makes no sense to talk about a 'real table'. Every thing that exists is real, whether you call it a table or not.
I'm also confused why you'd think the concept of continuity is blurry on this issue. Continuity means that similar inputs give nearby outputs, and this is perfectly consistent with how computation works: if you construct two results through similar algorithms, they will have closely related types. Types become a measure of similarity of different computations, and thus you can use them to group things with similar linguistic structure, and thus similar meaning.
Either way, Aristotle and Plato were both ancient people with not even a tenth the information we have today, so I wouldn't consider them authorities on any part of this discussion.