I'm aware of the use of the terms 'count nouns' and 'mass nouns', but this dichotomy doesn't seem to lend itself to a viable explanation to Japanese students of which nouns in English allow for counting and which don't. There are several categories for identifying countable and uncountable nouns:
1) Countable structures, characterized by the intrinsic property that they have an identifiable overall structure or shape, often related to function as in the case of chairs or tables, and, therefore, can be separated (at least visually) and counted one by one. The substance that the structures are made of are of secondary (apples) or of little if no importance (glass, aluminum, or plastic chairs).
2) An uncountable substance, which has no intrinsic shape and therefore is incapable of being separated into characteristic structures that can be counted--gasses (air), liquids (water), metals (gold)--the stuff that structures are made of. They may be quantified by volume or mass or number of containers or imposed structure (tank of, glass of, ingot of).
Rice (uncountable 'substance') is an example of a conglomerate for which the separation into countable grains is difficult and usually useless and so only the conglomerate is dealt with usually.
3) An uncountable miscellany of structures (collective) that have some common feature--furniture, greenery, stuff (in my bag)--used when we can't or don't need or desire to identify the structures/substances more precisely.
4) An uncountable object having some bilateral symmetry that apparently dominates the character of the (plural) noun--eyeglasses (two pieces of glass), scissors (two blades), pants and shorts (two legs), but not shirts--so that they are counted in pairs.
From these basic categories with prototypical examples, we can often identify the nature of more abstract concepts metaphorically and assess their countability--facts and ideas (structures/objects) vs. information (substance). We can bounce around ideas (balls) or block the flow of information (water) or let it leak out. We can talk about the greenery in a yard or the culture in a country flourishing (flowering) or decaying.
Question: Is there a systematic categorization (extension) of these ideas with a standard nomenclature that I may reference?