Earlier quoted context omitted.
> If you apply the same force as you would to a cup handle it order to pick up the cup, to a single atom of the surface of the cup, couldn't that remove the atom? No, because the forces holding the atoms of the cup together are much stronger than the forces holding the cup to the floor. That's the underlying physical reason why it makes sense to consider the cup as an "object".
Really? Not just per mass? Huh. I am somewhat surprised. Hmm, but one can scratch a cup fairly easily, can one not? (depending on the type of cup). This is removing some part of the cup. Hmm, I guess that still might take more force than picking it up? But what if one has like, a really big thing of uh, I want to say talc but I don't know how much of that one could hold up without part of it breaking off... uh, googl…
Yes. Think of it this way: if the force you used to pick up the cup could remove atoms from the cup, then you wouldn't be able to pick it up; when you tried, you would just come away with some atoms, instead of the whole cup.
> if one had a column of gypsum 254.1 meters tall, and picked an atom at the top of it to pull up with force more than that of the whole weight of the pillar, certainly the whole pillar would not rise into the air, because its weight would be too much for the tensile strength
Yes. With typical materials that cups are made of, you could probably make the column somewhat taller; but in any case, 254.1 meters is way larger than a cup, and weighs a lot more, which is why you don't have trouble picking up a cup, even though you would if you had a tall enough column of the same material.
> Yet it certainly seems like this would be termed an object.
If you choose to, sure. The term "object" is not given by physical law; it's a human convention. Obviously there are going to be edge cases where the term's application becomes somewhat strained.