Is it really correct to say that some nouns are countable and others are uncountable?

Solution 1:

In [2], however, it is not the count noun plate itself but the whole noun phrase another plate that denotes an "entity"

and

When a common noun denotes a "class", how can a common noun denote an "entity", let alone "an entity that can be counted or that cannot be counted"?

  Q. What do you like eating?

  A. Sandwiches.

Doesn't the answer, sandwiches, in its isolation, prove it is a countable plural noun and denotes an entity? The number of sandwiches is unspecified but the speaker is referring to more than one sandwich.

  Q. What do you like eating?

  A. Peanut butter.

Why didn't I add the -s suffix? Because in grammar, this type of noun is labeled uncountable, we cannot physically count something that is spread with a knife.