Countability and unmarked plurals

Recently, I've run into a few situations that have called for some clarification of what it means for a noun to be countable. You may be curious about just where I run into these things. Do people buttonhole me at parties? Grill me at conferences? Stop me on the street? Sadly, no. Most often these issues come up during some sort of net-mediated interactions.

Anyhow, one particularly observant and self-aware correspondent writes:

"One of the thrills of creating material for students is discovering new areas of my own lack of knowledge. When designing a worksheet on countable and uncountable terms, my examples didn't really work out right.

I had neatly laid out three zones on the sheet: countable, uncountable and those that can be either (like paper and hair), and assigned examples of each from the students' vocabulary lists.

The nouns 'sheep' and 'fish' are not given 's' or 'es' when applied to plural use (in North American English), so I've simply referred to them as 'uncountable' in the past, and placed them into the uncountable zone. But almost instantly, I realized they didn't fit the patterns I was trying to illustrate.

There might be 'many sheep' in the field, but there darn sure aren't 'very much sheep', to my ear anyhow. There are 'a few fish' in the tank, but not 'a little fish'. These seem to act stubbornly as countable categories.

Which tells me that some noun categories are countable, but their labels (like fish and sheep) just don't get a plural form adjustment.

What are the correct terms and categories for these items? What else am I missing?"

Of course, he's quite right that countability of nouns is best looked at by considering the determiners they will allow rather than their morphology. Nouns like sheep simply have a plural form that is identical in shape to their singular form. These are often referred to as unmarked plurals. An analogy with verbs would be something like put, for which the plain form, plain present tense, past tense, and past participle all share a shape. Most verbs have past tense forms and past participle forms that share a shape (shape here encompasses both spelling and pronunciation).

Another issue is that most nouns have both countable and uncountable senses, though typically one sense dominates. Almost all "uncountable" nouns have a plural sense indicating types (e.g., Belgium produces many fine beers.)

There are few nouns that are singular only. I once believed that equipment was one, but I was mistaken. The following are a few that I can think of, but feel free to prove me wrong:

• crockery, footwear, perseverance, nonsense
  
• italics, linguistics, mumps, news
  

There are also a few plural only nouns. I think I got these examples from the Cambridge Grammar of the English Language, though I don't honestly recall.

• belongings, clothes, genitals, pants, remains
• cattle, police, vermin

In some language like Chinese, it is my understanding that no basic nouns are countable. All must be identified with a counter (e.g., two cups of water, one rod of pencil, three sheets of cookie).

Finally, it's interesting to note that even among languages that make a countable/uncountable distinction, there is little agreement on what is counted (again, examples may be from the CGEL or perhaps from Pinker's The Stuff of Thought).

• spaghetti: countable in Italian but not in English
• hair: countable in French but not in English
• peas: now countable in English, but previously uncountable pease
  

Indeed, we can look at almost anything both ways:

• opinions, advice
• stories, fiction
• facts, knowledge
• holes, space
• songs, music
• naps, sleep
• lies, bullshit