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Can you explain to me how you would do that outside of a laboratory setting? The real answer is that it's an amorphous fluid. It is a single object rather than discrete quanta.
What's happening is that you're trying to identify the exception and make it the rule. Yes, you can figure out how many moles of water are in a volume at a certain temperature and pressure. That's not really the point, is it? When people pour glasses of water, they aren't thinking in terms of moles. The word is noncountable because it was invented by humans far before any sort of chemistry was discovered. That usage can change, sure, but do you really think that the average person will ever see it that way?
Alternatively, are you thinking in terms of measuring volume? That's definable, but it's also not what is meant here.
One correction to my previous reply: water and water are not homonyms like you said, it is one word with multiple ways to use it. On to your next question.
Outside of lab equipment, you could measure your water in many easy ways: for example in the Die Hard movie they had to measure water.
Just because it is harder to arrive at a number of atoms doesn't mean that water isn't countable. It's also difficult to count the grains of sand on a beach! Water is countable! And is was a big scientific breakthrough when this was discovered! That's why I'm trying to hard to correct your misconception.
The easiest way to get the number of water molecules without a lab would be with just one measurement: a simple measuring cup. From knowing the volume of water, you can get its mass from the density, which we can estimate as 1 g/mL . From grams, divide by the molar mass of water, which you can find online: 18.01528 g/mol. This gives you an approximation of how many water molecules are in your sample! And all you had to do was use a measuring cup, look up a reference value, and do a calculation. That's pretty cool, and before 1776 and Amedeo Avogadro, no one knew you could count water this way. It is a discreet quanta, but before this, no one knew. That is the point!
Did you know light is also countable in this way? There are some chemical reactions that use photons as reagents in the chemical equation. If you know the output of a standardized halogen bulb, and shine it for a known amount of time, you can know, within the limits of your uncertainties, how many photons you sent into your sample. That's also pretty amazing!
You say "when people are pouring water into glasses, they aren't thinking about moles", and I'll agree with that. But just like when you're walking on the beach, you're not thinking about the number of grains of sand, they're still countable. Or when you climb the stairs, you don't usually count how many you took. But you can! And water is just as countable as these, at a fundamental level. Even if the molecules are very small, they are distinct, discrete, quantized.
So even if language doesn't treat water as a countable thing, even if the word "water," in that specific usage, isn't used for counting, fundamentally, water is countable. Just like air. And light. And grains of sand, or trees in a forest.
Ok this will be my last attempt.
You state that you can count the grains of sand on a beach. I disagree. You can count the grains of sand that you pick up and put into another vessel. Until you do that, the sand also remains an amorphous fluid. Same with water. You can count the water molecules in your glass, but you cannot count the water in the ocean. Scientists can make some really great estimations of how much water there is, but it will never be precise. It should also be noted that nobody anywhere ever outside of a scientific setting would ever speak in that sort of precision, yet you want all human language to operate that way.
Your argument is that if you can count an amount that would fit in your hand, you can count them all. This isn't how things work, though, because there is no method by which every grain of sand on the beach or every molecule of water in the lake can be counted. You're looking for deductive truth when induction is the only thing available.
Your issue isn't with me, it's with human language. I will leave you with these:
If you still disagree, you should try to convince them instead of me.
It looks like we are not going to agree on what makes something countable, but I did appreciate the exchange.
Mathematicians talk about "countable infinity" and "uncountable infinity". The integers are countable, 1, 2, 3, ... forever. There is no way to count them all. But they can be counted.
Compare that to uncountable infinity: there are more Real Numbers in the uncountable infinity of fractions between 0 and 1 than in the entire countable infinity of the integers! Because they are not discrete like the integers. Discrete is not the right word. I'm not a mathematician. They're not countable.
In both of these cases, no human can count them all. But the countable infinity can be counted. Just like the water in the ocean, or the sand on the beach. God could count them, for instance.
In the end, we're using the word countable differently. We might have different worldviews about the nature of water and its importance. I'm ok with that :)
It sounds like you have a mathematics or science background. I’m actually a linguist with multiple degrees and who studied internationally at the postgraduate level. I’m speaking from the perspective of a linguist and referring to the semantic aspects of word usage. Count versus mass / countable versus uncountable is a very fundamental aspect of human language and in any pragmatic usage is very inflexible. When moving into specialist language use, pragmatics fall away and that precise usage can enter the space. My original comment is on the pragmatic use.
I think I may have realized in this thread that linguistic intuition is something that is sometimes counterintuitive to the average person in the way metaphysics can be, and perhaps challenging to acquire in a way that I have forgotten. You were probably the third person to make the same point and I may have been annoyed at having to defend something that is basic and recognized by anyone who studies language in pretty much any capacity.
Cheers
Yes, I do have a science background, which is why I love thinking about how a cup of water is full of molecules :)
Speaking only for myself, I understand that 'water' might not be a countable noun, but that doesn't make the underlying thing we call "water" uncountable as a real, tangible thing, and that was what I was trying to convey.
It seems like people might reasonably disagree about whether something is physically countable or not, but it was deeper than linguistics for me.
You might appreciate this: although a lot of scientists don't like people calling insects "bugs," I love how so many languages have a word for "small creepy-crawly animal" and I highly endorse the popular usage of bugs to include spiders, roly-polies, insects, etc. For this, I don't get why some biologists insist on applying the specialist description of living things to the semantic (?) grouping. Maybe you would put 'countable' in that category too. But to me, the idea that water is molecules makes it countable at a deep level, regardless of how our language talks about it.
I'm going to look up and learn more about countable/mass nouns now -- sorry to start out as part of that annoying group. Thanks for the thread :)
In the bugs topic, I also love how virtually nothing called “berry” is a berry and tons on things that you don’t think are berries (watermelon, bananas) are berries. Someone probably defined the term long after it was applied to everything.