What does the word how many mean

I am sure some people here will immediately say «hey, this topic should be opened in the English subforum, not here which is about «Etymology/History of languages».

But, this is a question that can not be answered, or can not be answered correctly by any person whose native language is English, either. They have not.
So, this is relevant to this part of forum, history/etymology of languages in general, of English in particular. You’ll see.

As for one who learnt English later, I was taught that, as a general rule, it is «how many» for countables and it is «how much» for uncountables.
For specific example, «money», they say «how much money» because money is «uncountable» (according to them)…

Now, we have to talk about Language&Mathematics as there is this criteria, «countability»… According to linguists(?), it seems that «money» is an «uncountable» thing as they say «how much money»…

Lets also give examples, eg, dollar and cent not to be repeated here by posters who’ll reply in this thread.

They say «how many dollars» as «dollar» is countable. And, some say «how much cent» and some say «how many cent», there is no agreement in that, at least between people who I know of, mostly Americans. Even this uncertainty in «how many cent or how much cent» shows that there is a problem, in «countability» of money which is also seen in the language English.

So, lets start.

Money is countable or uncountable, according to the linguists?
(etymology of «money» is also to be mentioned if necessary, and, I guess, necessary, to answer such a question.)

Maybe, this topic needs a little stimulation as what exactly the question here may not be clear. Lets summarize first what are known.

There are two keywords here: Money and Countability.

I’m not a linguist, so, I checked on the net:

Etymology: Money (no need to give any reference as these were written everywhere on the net)

— The word «Money» originally from the Latin word moneta, meaning ‘mint’ or ‘currency’, which was later adapted as moneie in Old French.
— Moneta was originally a title given to the Goddess Juno, in whose temple money was minted in the earlier times, in Rome.
— and there is this on a forum (I don’t know if it is speculation or not): The word «Money» is derived from «Mann» in Tamil means Land (more preciously mud)
Maybe, there are other claims, but, I leave them to people here on this forum.

Countability: In the English, related to «Much» and «Many»: Ok, it seems that, in some languages like English, two different words are used depending on the countability while in some languages, for ex in Turkic, single word (çok) is used for the both, for countable and for uncountable quantities. This differentiation in this example into two words or integration into one word is probably due to the interaction between the languages and the mathematics, so, this is about history of language and mathematics. Since there are two different words (much and many) in English, English fits better than Turkic in questioning «money is countable or not» relating language&mathematics.

Combining these, etymology of money and countability in the language:

Option «Moneta», a given title to a Goddes, as origin of «Money» makes one thinks «money is countable» if Moneta is a person. If not, it is flue.
Option «Mann», mud in Tamil, as origin of «Money» makes one thinks «money is uncountable».

From history to today. (for centuries)
Current usages of «Money» in sentences, such as «cash flow, liquidity, etc», tell that «money is uncountable» and it is considered «liquid» like «water.» That must be why we see «how much money»…

(For those who may have any objection to these and for those who may prefer to add somethings, I give a pause here to myself before stimulating further.)

Dib,
It is good you reminded «time» and «days, minutes, etc» as analogy to «money» and «dollar, etc», respectively. Our topic here will probably be more about such analogies. However, to focus on «money» and its «countability or not», yes, we also need to look also at other languages and I ask this. Is there any word in any language that means/implies «money» itself is countable?

Yes, in Turkish, we don’t say «kaç tane para? (how many money?)», but, we don’t also say «kaç tane lira? like it is normally said in English (how many dollar?)
Also, in Turkic, there is no opposite word (for uncountables like «much») to «tane» (piece) (used for countables like «many»). So, shortly, we use «kaç» for the both (how many and how much) and it is not clear «kaç» here is for countables or uncountables and answer to «kaç?» is again one word (çok) unlike English with two words (many and much) that seperate countability clearly unlike Turkic. This doesn’t mean that there is no countability in Turkic, but, «countability» in Turkic just isn’t as clear as in English in particularly to «money». So, I stay with English when questioning about «money» and its «countability or not». And, it seems that «uncountability of money» is a general rule in any and all languages including English. So, chosing English fit the purpose here, as it reflects general stiuation (uncountability of money) in all world languages and it has a clear specific word (much) seperated clearly from countables (many.)

Lets not go into other things such as «advice», «information», etc whether they are countables or not and in which languages they are countables and uncountables.
Since «money» (or para or whatever in any other language) is «uncountable» thing in all languages (unless claimed otherwise by an example) lets focus on «money» only as it is also one of most important things, maybe, the most, for everybody in the world.

So, to focus more on «money» and «countability», and to make it a fruitful discussion, is it ok to go with analogies hereafter? Expressions such as «money is like water flow», «money is like time flow», etc. are expressions that tell about «money» and its language history sufficiently? (if this, analogy making, is ok, we can go ahead without doubt?)

Gavril,
Thanks for clarification about «cent». I guess we will also come back to it again, later, once «money» is clarified more. (I have some doubt, money itself was actually maybe a countable thing. But, I can’t bring any evidence, at least for the moment, to prove it or to get rid of my doubt. So, this topic.)

Dymn,

Thanks. I added «length» and «meter, etc» as an analogy to «money» and «dollar, etc», respectively, to my analogy list (liquid, flow, time, length — money.)

But, I am not sure if I understood your second paragraph well. On a coin collectors website, I learnt some coin currency names in ancient Romans time. For example, 1aureus=2quinarii=25denarii=50quinarii=100sestertii=200dupondii=etc… Here, the word «denarii» (plural of denarius) looks similar to the word in Catalan you mentioned «diners» (plural of denary), but, I understand «denarius» in the coin is like «cent» and «denarii» is like «cents», that’s «unit/s» of «money». So, plural tantum «diners» is somethings like that rather than «money»? Or, exactly, «diners=money»?.. I mean, as a conclusion, my question to you to be sure is that «diners» in Catalan is countable or uncountable? If I did understand correctly, «diners too is uncountable», right? (this is important because if «diners» is «countable», or if there is such a word which breaks the rule «money is uncountable», then, the generalization «money (and its any corresponding word in any language in the world) is uncountable» will fail. If this generalization to all languages about «money» is true, then, we can continue as we will have found that «uncountability of money» is valid in all languages.)

Dymn (and, et al.)

Since you frequently warned me about «countability» that may differ from language to language depending on the word (advice, etc), lets fix a thing here first, to avoid bifurcation/branching toward an undesired chaos in our conversation here.

«Countability» here in this topic is narrowed to the countability in money, that is, to «mathematical countability», like counting numbers «1, 2, 3, and so on» that is how we count money by «discretizing» it into some units such as «dollar.»

So, here in this topic, the universality is not the universality (or not) of «countability. Since it is narrowed to money we can write this sentence comfortably, right?
… «uncountability of money is universal in all languages»…
(unless stated otherwise, with a counter-example «word» in a language corresponding to «money».)

Diners in Catalan: So, from whatever it was evoluted, its final form «diners» is equivalent to «money», they both are uncountable. So, we can write analogy above (*) also for «diners as

{DINERS, pesoto/euro now} :: {( ), ( ), … } … (same can be written for any «word» for «money» in any language.)

Since we are using English here in our communication, lets use {MONEY, dollar} pair, also to simplify for those non-members who are surfing, just viewing here shortly, on the net.

Lets summarize all talks here in a single line, by rewriting analogy (*) here again, however, by chosing only one (the best one, most familiar to the common public) of subsets in the set at the right hand side of analogy (*). Result is:

{MONEY, dollar} :: {LIQUID, liter}
where the words in capital letters are uncountable while the words in small letters are countables as they are units.

Lets use «cent» instead of «dollar» as the cent is the real unit value name of that money.
(no need to go into detail of «liter» such as «milliliter, nanoliter, etc» where «milli, nano, etc» are somethings else, irrelevant to the topic.)

So, final simplified version of our analogy is:

{MONEY, cent} :: {LIQUID, liter}

This shortened version of analogy conforms also with «mathematical economy» or «economy mathematics» as they use similar terms «liquidity, cash flow, etc.» in their calculations. And, all «money mathematics» is built on this philosophy (or reality?) that says «money is like liquid which is uncountable. Its unit, eg, cent is like liter of liquid which is countable.»

Now, we can talk about this analogy, that simplifies the topic, «money’s uncountability», universal in the languages.
(If there is no any nonagreement at all among all of us, I’ll try to stimulate/stir/blurr this «crystal clear» result. However, later, a cup of coffee time for me.)

Let me rewrite final simplified version of analogy here as last line in this post, as my attemps will be to «break» this analogy «::»

{MONEY, cent} :: {LIQUID, liter}

I think, I personally agree with your sets of analogy. I am also okay with building further on the assumption:

Supposing this «assumption» (money is uncountable in all languages in the world) is valid, we can go ahead now.

as long as it is clear that this is purely an assumption — an axiom to build an axiomatic system on. The evidence presented in this thread for its actual validity is negligible. Our sample size and diversity is too low to get any such statistical confidence.

Before attempting to «break» this commonly accepted analogy above which I simply write with notation «::», let me tell a little math first for those who may say «how in the world money appears like liquid in mathematics?»

Liquid/fluid/flow. These are «continuum» things and continuum is an uncountable thing according to the physics&mathematics unless it is discretized into pieces.

Mathematicans handling «money» in their calculations see money as a «continuum», such as liquid/fluid/flow, that’s why we hear «liquidity, cash flow, etc» from economists who are using terms of mathematicans&physicist actually.

Ok, garipx, give an example?

Since «countability» is mostly related to «mathematics of numbers», lets write here one simple equation so that you can see «most important numbers» in mathematics, used also in various fields from physics to engineering to economy, etc. in one simple equation. Some of you probably know it.

It is called Euler Identity (EI): e^(i.Pi) + 1 = 0.

where
«e»=2,71828… (three dots mean «etc»)
«i»=square root of «-1», so, imaginary number.
«Pi»=3,14159…
«1» and «0» = you already know.

I won’t go into details of this equation, what the hell this equation in reality is, etc. They are not on-topic here.
I wrote this here just to show «numbers» in one simple line, purposely.

Lets pick «e» here which is called «e»uler number, which is an «irrational number», that’s, numbers after comma never end, that’s, never repeat.
So, we can say this «e» is an uncountable number. And, this «e» is used also in calculations of continuous compound interest rate for your money in the bank account.

So what? What you see in your bank account at the end of a period is, say, $7489,27, but, it is a «cut/rounded» figure. In a mathematican’s hand, this figure is, maybe, «7489,2739340231…» See difference? (forget about «negligibility» here after «0,27…» just because it is «$», we are talking here about «money» and «its un/countability».

Why such a «strange» number «7489,2739340231…» appeared in hands of mathematicans here, specifically in this interest-rate example?
Because they use, for ex, «e» (2,71828…) which is irrational, uncountable number in their money interest rate calculations. Uncountable contiuum such as Liquid/fluid/flow in mathematics appears in such numbers like «e».

So what? Using «e» in bank interest calculations is wrong? It’s another story we can talk later. Point of this post is «how uncountability of money appears in money mathematics». It appears, for ex, in use of number «e» which is uncountable number. We see this now. Money mathematics in detail is not our topic here, we can talk about it elsewhere, or some simple basic things here later.

So, isn’t it good as it fits analogy MONEY::LIQUID well? I can not use the word «certainly» when answering this…
What if this MONEY::LIQUID analogy is not a correct analogy? What happens? Money mathematics will totally fail then? No, but, there will be a «repairement» in «all money mathematics.» And, to do this, we need to be sure if there is any error to be repaired, and we cannot do anything without talking, so, «language», and it is what we are doing now. Having also said these in this post, now, lets question this analogy:

{MONEY, cent} :: {LIQUID, liter}

(Ps: Dib, I saw your post when I was writing my this post. Yes, I am aware (you probably are more aware than me as I am not a linguist) of that «sample» info here in this thread is probably insufficient to make such a generalization «uncountability of money is universal in all languages». My assumption here is based on what you posters here said and on the silence not opposing this generalization. So, if we all here and scientists (mathematicans, etc) agree in that assumption, it is not my assumption only. If there is an error or not in this assumption, «uncountability of money is universal», what we will be doing here in this thread is this, questioning, using analogy, as it is done by sciences also about money. Ok, to keep our talks shorter and in a methodology, step by step, lets write this analogy again as last line of this post:

{MONEY, cent} :: {LIQUID, liter}

(you can go to the bottom, to the last paragraph directly, if you don’t have time to read this long post.)

Instead of this analogy {MONEY, cent} :: {LIQUID, liter},

if we chose, for ex, this analogy {MONEY, cent} :: {TIME, minute},

could it be better?

Maybe, but, then, our coversation would have been more conceptual or more philosophical in money-time analogy.
In case of money-liquid analogy, this is quasi-conceptual, less philosophical as liquid has a physical form and money too has a physical form.
Their main common character of money and liquid is their uncountability and this is our main reason for making analogy between them and it is sufficient to chose liquid for our need. Their existing physical forms also keep us in reality more than that we can do with analogy money-time.

So, it is «sufficient best» to take «liquid», among available things, as an analogy to «money» for our purpose here that’s to question «money’s uncountability.»

Now, lets write it here again to focus and question this analogy:

{MONEY, cent} :: {LIQUID, liter}

Here, «cent» and «liter» are to be discussed later as they are obviously «countables»…

Since we are to learn about «money» here that we «suppose» we don’t know, then, we should look at its analogy, i.e. «liquid»…

LIQUID/FLUID/FLOW.

These are terms in the physics. Without going into modern physics, if we make classifications of materials, these are forms of materials in classical physics:
… solid, liquid/fluid, gas …

Solid and liquid/fluid are considered as «contiuum» in classical physics and their math calculations are done accordingly, while gas is considered as «particles» and its math calculations are done accordingly.

So, lets eliminate «gas» as «money» in math calculations is «not» handled like «particles», otherwise, «money» would have been considered as «countable».
Solid does not fit, either, as it doesn’t «flow».

So, we confirm «liquid/fluid», also due to its visible «flowability» character which «money» too has, another commonly accepted property of «money».

These (solid, liquid, gas) forms are forms that have been studied much by many scholars in the history and today. So, we know a lot about these.

NOW…

I’ll write here another «new» material form which has been academically much less studied than those (solid, liquid, gas) and a few years ago, one of few researcher studying that «new» form of material had called it «4th form of material» after 3 forms of materials (solid, liquid, gas).

What is that «new» material form? Don’t be surprised.

WHEAT/GRAIN.

How comes!? This is not new!… Well, that’s why I used » » when I was writing «new». (a little irony, but, still new, as it is new to the science community actually.)

How new?
Question to any person: Wheat/grain is solid? or liquid? or gas-like particle?
Depending on what you are studying, it is solid, and also liquid, and also gas.
You can see these forms in «wheat/grain» with your insight view, and, even eye-visually.
But, since we chosed «liquid/fluid» as analogy to «money», you can ask «how in the world wheat/grain can be correlated to the liquid!?»…

Have you ever seen a combine harvester «pouring» wheat in harvesting or wheat «moving» in an open channel at flour milling factory? Wheat just acts like a liquid, with an engineering approximation, it can also be called «flow» and fluid flow formulas can be used also for «wheat flow» at an engineering approximation level. («approximation» is another keyword here in «money», we may talk about it later.)

Ok, here, not many people may know these matematical formulations of flows, his words of «garipx» may not be enough. It is not necessary to know mathematics of flows, even visually, you can see wheat flow in a channel as «liquid flow», «solid flow» like mud flow in a truck trailer on which wheat flows slowly, and «gas/particle flow» when a handful of wheat is thrown into the air.

SO, BEST ANALOGY for «MONEY» is «WHEAT/GRAIN»… better than «liquid» analogy.

When wheat is handled as a solid, it is «uncountable», it is counted only by its volume/mass/weight (in cubicmeter or kg, lb, etc.)
BUT, because of this way of counting wheat by «kg, etc» in «trade», its countability of wheat/grain as particle «piece» is usually forgotten especially by «scholars» in general and by «mathematicans» in particular in sciences of related fields, again, because of their minds on economy/commerce/trade when they see «money». This countability by «piece» DOES exist also in the countability of «real money», eg, «coin».

SO, here is my claim: instead of this analogy, {Money, cent} :: {Liquid, liter}, this analogy should be used:

{MONEY, cent} :: {WHEAT/GRAIN, piece} … (this will also change «money mathematics» and «money language» as well.)

(Also, it’ll make more sense as «cent» too has a particle physical form, as «coin».)

Here you are… (waiting for your attacks, to the claim here.)

Here you are… (waiting for your attacks, to the claim here.)

My main question to you is: «What does all this have to do with Etymology, History of languages, and Linguistics», please? I hope you are getting to that aspect soon.

Apart from that … I believe, your concept of «countability» as used in Mathematics is unsound. Since there is no such concept in Mathematics as an «uncountable number» as far as I know and «countability» is defined for a set, not a number, when you say:

So, we can say this «e» is an uncountable number.

I guess, you really mean the following:
If the digits of the decimal (or any other rational-base) representation of e are put together in an ordered set (say, X), it will be uncountable.
However, that assertion would be wrong. X will be countably infinite. You can very easily define a one-to-one mapping between the elements of X and the set of all natural numbers, e.g. by using the position of the element in X. That is the classic definition of a countably infinite set.

—

Anyways, I would like to wait to find out what language-related issue this discussion brings up ultimately.

berndf,

When a person just learning English reads your examples (1, 2, 3, 4) may ask «if these told are true or not» (here, «truth» is understood mostly opposite of «lie» in languages, particularly in «spoken languages» and that person would go to the English lesson forum to learn if those (1, 2, 3, 4) are «really» said so or not.

Similarly, he would go to the English forum to learn how people whose native language is English say for «money», «much money» or «many money».

Such things are «information gathering» in «already available» things, but, unknown to a new learner.

Although I don’t speak English well either I (and also everybody here) had already passed that stage, we all already know English people are using «much money», not «many money. If it was said it is «subjective», that’s is a matter of personal/national/etc taste, it would be non-discussable. But, there is a generalization here, with respect to «countability». When it is narrowed to «money it becomes «uncountability of money is universal»… a generalization …
(Btw, I’ll keep using «uncountability» instead of «non-countability» whichever is said by English people is not our main topic here, I guess everybody understands «uncountability» as opposite of «countability.»)

So, this «uncountability of money is universal» requires a proof, a proof even in only English. That should be done like a mathematican does to prove «2+2=4» which is well known. Saying that «countability in mathematics and in linguistics is different» does not make sense, at least in this topic in which the thing we are talking is «money» which is considered same thing for the both, for the mathematican and for the linguist, for all others as well.

What are the language and the mathematics? (related to countability). With simple examples.

1tulip + 1rose = 2flowers… Here, what takes my attention is «tulip and rose», their odor/smell/beauty/etc rather than their quantities/mathematics.

1tulip + 1tulip = 2tulips… Here, what takes my attention is numbers/figures as all units/names (tulip) are same.

1money + 1money = 2money/s… Here, my eyes are opened wider because it is about «money» and people immediately «jump» to the total «2moneys» as it is bigger number (economy motivation).
,
These are about «money» and «countability» with letters/notations/symbols, partically from linguistics and partially from mathematics.

How these letters/notations/symbols are related?
Right now, I just said somethings here in my room, you didn’t hear. What did I say? Exactly what I said can never be known unless you hear with your own ears.
Still, I can try to tell what I said, from «beginning.»

I said this: [ ~~~~~~~~ ~~~ ~~ ~~~~~ ] where «~~»s are voice/sound waves (this can not be heard through the internet.)
-> (transformation operation through an electrical/electronical tool) ->
I said this: {><><><>< ><> <> ><><} where «><«are «discretized waves» (ok, this sound record option does not exist here on WR forum.)
-> (transformation operation by hand fingers using linguistics symbols and notations) ->
I said this: [yesterday, I picked one apple from a tree. Today, I got one apple in the morning and one apple in the afternoon. So, I got three apples in total.] (now, you read and you know what I said with our communication tool here with linguistics symbols/etc.]

But, it is a too long sentence, and, some maybe interested in «picking», some maybe interested in «tree», some maybe interested in «who/when», etc., but, our topic here in this thread is not about these, so, some (mathematicans) may say «hey, garipx, lets write it shorter by using some other symbols/notations.»

-> (a transformation operation of some linguistics symbols to mathematical symbols, for ex, «one to 1») ->

I said this: «1apple + (1apple+1apple) = (1+1+1)apples.» — (See initially we know only «1» as it was in sentence above as «one»)

Now, someone introduces some new symbols (by saying lets show 1+1 with a new symbol «2», etc:

I said this: «1apple + 2apples = 3apples»

Now, someone generalizes and omits «apples» as they are invariants/same:

I said this: «1 + 2 = 3″…

So, where the «countability» did start in this what I said? It started when the word «one» is used. Mathematics just used another symbol for it, as «1», so that a paragraph of letters/words/sentences/symbols can be shortened into a single line, usually called «equation». So, the linguistics and the mathematics are in the same group, according to the criteria «countability». A saying that «we linguists see countability differently than mathematicans or vice versa» doesn’t make sense in this particular case, espeically when it is related to the «money» and its «un/countability».

Now.
Instead of saying «apple» in which «countability» is clear, what if I said «wheat»?…
(same question questioned for «money»: «wheat too is un/countable» like it is said for «money» which is used to seen as «liquid», which is wrong according to the claim here.) This paragraph is the heart of this topic here as this new «money::wheat» analogy proposal can clean all errors in «money language».

Ps: btw, a math prof from a USA university, and also an «old» engineer still working at the industry, maybe viewing here as they were viewing a similar thread by «ErolGarip» on a non-commercial forum (a coin collector forum) where I put a link of this thread there in the public. If it’s not a problem to put a link of that other thread here, I can do that too. However, that other thread on another forum is less academical than here.

Ok, after some interruptions in the «flow» of this thread in which my all posts were related, but, somehow, seen unrelated by the boss here (MOD) and deleted, lets continue with what is said in last line of last post above.

How many rain droplets :: how many monies.

Some linguists and also others may «correct» this analogy and can say this:
Correct analogy is :»money::rain», «cent::rain droplet»… that is,
{money, cent}::{rain, rain droplet} … quite logical as the first element(s) is «uncountable noun(s)» and the second is «countable noun(s)»… defined so.

But, «rain» too can be in a countable set, depending on how you form a set.
Examples for countable sets:

microscopics water set={proton of water, neutron of water, etc}
rain set={rain droplets}
rain-like water set={rain droplet, vapor buble, snowflake, hail droplet, etc}
falling/raising waters kind set={rain, snow, hail, vapor, etc},
waters set={rain, river, lake, sea, a cup of water, etc},
organic materials set={water, air, tree, etc},
materials set={organic materials, metals, etc},
existing things on the earth set:{materials, non-materials/lights, etc},
planets set={earth, jupiter, etc},
galaxy set={earth, sun, etc},
universe set={this galaxy, that galaxy, etc}

… (see, sets in sets in sets in sets in… in which smallest set (smaller than atom-like particles and bigger set than the universe that we «know» are unknown… )

So, where is the «money» in these sets? Or, better to say, which set of these sets is the best set in making a best analogy to «money»? If we put it in «rain set», then, ok, we can say it in words: «money is like rain, rather than rain droplet» and this in words can be written with analogy notation «::» as
«money::rain» and «cent::raindroplet»…
But, this «chosing water set» as a more generalized set than «rain» set is only an «arbitrary» choice and mind confusing. If one choses, for example, «galaxy set», then, similary, we can say «money is like galaxy and cent is like earth» and in this case, we can show this said by using analogy notation «::» as
«money::galaxy» and «cent::earth»… (for someones like «green-man» in the space, from another galaxy and planet, who does not know what the water is, I could tell him the «money» by this way of analogy money::galaxy and cent::earth, following our main criteria the «un/countability» which results in «many money» or «much money» depending on the countability. So, which analogy («money is like rain» or «money is like rain droplet») is better to understand each others, people of this planet?

And, another definition/term is used by people: «countable nouns» and «uncountable nouns»… There is no sense in these terms. «Counting» is an act, is a verb while «noun» is only a «label» like «apple». That’s, what we are counting is NOT noun/label (apple), what we are counting by «counting apple» is apple itself, «physical apple». So, the expression «countable or uncountable noun» is senseless, unless you «mean» by «noun» as «physical object.» Therefore, we are using analogies by those physical objects to understand/learn what the money is. (green-men from another planets can laugh at us for not knowing our own product money. Not to hear their sarcasm, you can only hope them green-men don’t exist…)

So, it is necessary to chose one of sets given above and the best set is:

{money, cent}::{rain, raindroplet}… you can see, the set «money» has only one set element (cent) and the set «rain» has only one element (raindroplet).

For «continuity of countability» in time and space, during operation, this analogy maybe better:

{money, cent}::{wheat, grain/particle}… (again, wheat set too has only one element in its set, wheat={grain}…)

—-

PS: If you say «dollar» also exists in money set, that’s, if you put them in money set, i.e. money={dollar, cent}, then, «elements» of this money set, i.e.
«dollar» and «cent» must have no «countability» relation between each others, as «each element» in this set must be «independent» from each others. But, we know their relation: 1dollar=100cents. Therefore, writing this way, money:{dollar, cent} is WRONG… If we write it in this way money={100cent, cent}, you can see there is only one element «cent» in «money» set and also you see «countability» in «100» which is not necessary to write it in the set as we are talking about «countability». So, correct form of money set is money={cent only}. You can also say what about euro, etc. They are mathematically converted: for ex, 1euro=1,3dollar. It does not matter, money is still same set, a countable thing. With «euro», you are just counting less number of element in money set which has only one element, «cent». In their currency of Japan, it is more clear as they now have only one denomination name, «yen» (after cancelling «sen»), money={yen}.

Conclusion: Since «money» has only one element, «cent», in its set, money={cent}, which can also be written as «money=cent» and this can be expressed by language words as «money is cent» which is countable… Clear?

Why should we make it more complicated and doubled by involving another word?

I’ll start with your this line. You spoke… as if this «garipx» made it complicated…

IT is already complicated… Lets leave analogies (water, etc) aside as they are used to explain «money», for its «un/countability».
Meanings… of «money»… When the «money» is said what does any person in the World (say any person in USA) understand from «money»?
She/he understands from it, «dollar, quarter, dime, cent, etc.» If she/he look broader, she/he also understands «dollar, euro, yen, lira, etc.»
So, we have many different nouns here… and all these different «money names» are because of «meanings» they get, because of people whose views of «money» are different. Main reason for this is not because of countability or uncountability, it is because of «function» of «money which is «trade/exchange» with somethings else, for example, by giving apple and by taking money for some people, and by giving money and by taking orange for some others, etc. This is why people view «money» differently. It is another story, related to economy which is another stage of science. Lets not jump. We have not come to that point yet and economy, function of money, is not our topic here on a linguistics forum. We are at «nouns», not at «verbs» and at «sentences» yet. Still, the thing and its word «money» has not been studied yet. And, we are trying to do that here,

I guess this forum is rather an academical/educational/scientific forum, as it is (claimed to be) said that this forum is a «noncommercial» forum, so, the purpose here when we are talking about «money» is not «to make money» here, but, to study it from scientific point of view, including linguistics.

Various names in money such as (dollar, half, quarter, dime, nickel, cent) in USA is due to «trade/commerce» in which motivation is subjective/economical. These various names which can make one think as «money is already a complicated thing» can be simplified scientifically etc by seeing the relations between each others of them (1dollar=2halfs=4quarters=10dimes=20nickels=100cent) and all these can be simplified to (a number such as «100» and only one word «cent».) So, scientifically, money itself can be expressed simply by a pair of «number» and «cent», that’s, money={number, cent}… Here, since «number» indicates «countability», as a noun set for money, without forgetting countability, simply, we have this: «money={cent}» … since there is only one element in this set, it is equivalent to: «money=cent»… which is equivalent to in linguistics:… «money is cent»… (if cent is a countable noun, money too is a countable noun or maybe, it is better to say «counted noun», a «discrete counted whole noun» which is not equal to «integral/continuous counted noun» as we are using «discrete elements» when counting.) Here, we are talking about «countability» as there are two different words «much» and «many» related to countability, and the expression «much/many money» is being questioned here. (I claimed/proved «much money» is WRONG, it should (have) be(en) «many money».) This is scientifically important. We have not come to «what the money is for» yet, here, we are at «what the money itself is». It’s defined as «a countable noun» which is proved now it is a WRONG definition.

What we here in this thread is doing is not about how/why «money» are seen by people differently, its meaning changes from person to person is another topic, Still, I can tell a little about that too. With an abstract equation, for example, «Price» of «apple»:

Price = F(actors) x M(oney) — where F is some factors related to the economy which is not our topic here.

What people see differently is not actually about «money» (they even do not think about «money»). What people see differently is «F(actors)» in this abstract equation as it has various effects on the «Price». All studies including «money theories» I’ve seen are not really about «money», but, about «economy» which is simply that equation: Price=(economy) Factors x Money… Here, we are talking about «Money» itself only, questioning it. And, found out that «money is cent.» Names here are subjective, different names in case of «money» doesn’t matter scientifically. «Money is cent» can also be expressed as «geld ist cent» in German or as «para kurus’tur» in Turkish, etc… Scientifically, all these expressions are equivalent whether you name the thing <money> as «geld» or as «para» or as «money» or etc. Any and all of them are «countable.»

Where might «how much money» have come from? (instead of «how many money»)…

— It might have come from some «mathematicans» who «like» to study «continuity» (which is like «water/liquid» in the physics.) In their «continuity formulations», they use an ultimately small particle, «infinitesimaly» small. Whether such a small particle physically exists or not is unknown, it is a «mind» production, which can also be considered as «imaginary» concept. When these «infinitesimally small particles» are added together, it is called «integrating», an operation for «continuous» medium such as water. (For not infinitesimall small particles such as apple, «adding together» operation is a «summation» operation, is discrete summation.) Integrating (I) and discrete summation (D) are same operation, but, they differ with respect to «infinitesimally smallness»… So, for example, 1cent can be considered infinitesimally small amount of money? If you are poor with $100 only in your pocket ($1=100cents), you will probably not say «1cent is infinitesimally small.» On the other hand, if you have, say, $1billion, you will probably say «1cent is infinitesimally small»… So, your money formulation will change from «discrete summation» (like summing apples) to «integral summation» (like summing water particles which are taken as imaginarily as infinitesimally small.) Although the calculated results by these two different summation operations may not be different in the case of money, since the underlying principles in these two methods are different (infinitesimally smallnes related to continuity and finite smallness is related to discretenes), resulting expression by these two methods will be different, as «much» or «many».) Since «much money» is being used now we can say mathematicans studying continuity have dominated in «money formulations» and «much money» entered into the language instead of «many money.» This is an explanation why «money is uncountable» is said…

— It might have come from «uniqueness». Think about «Earth». Meaning of this word might be different in ancient days as discussed in «Etymology:Earth» thread. Perhaps, it meant «ground» before. But, today, in our era with more research on the space, when Earth is said people understand it as a «planet» where we are on. As far as we know till today, Earth is unique, that’s, there is only one from this planet, no any other copies/duplications/reproductions/etc which is similar to Earth. Therefore, it is meaningless to count the Earth as it is only one piece and you will not even to think about the countability of Earth although you can count planets together with Earth if you ignore the life, etc on the planets. How similar is this to the money? Suppose/imagine when the money started first time in the history, it was only one «coin» in a small blacksmith kind workshop. This is probable/possible. Since it was only one, so unique, we can not talk about its countability. Maybe, that workshop sold that first coin that he might have made, for ex, as an ornament. In that case, since it was unique we can not talk about its countability. So, even if it was only one, «that one» was a WHOLE, a concept that we can use «uncountable» when defining it. This «whole» is like a «completed» product after «much work». So, initially, original saying might be somethings like that «much work coin/money». This expression, like often done, might have been shortened in daily life speech throught the history and it has become «much money.» (However, after that first coin was reproduced by a state of the old day in many pieces (but, only one type), probably, «many coins/moneys» expression were used and such terms like «many monies» exists more in old history books/writings. After more types/kinds of money (coin, paper and different denominations) were produced and mathematicans made more economy calculations, the term «money» was handled like a «continuum» medium as told in first paragraph above and it became again «much money».) So, that kind of uniqeness of first coin/money and its call as «much work coin/money» with omitted «work» can be another explanation why «money is uncountable» is said…

So, after all, when the day is over, things in the past day are countable, but, when you are in the day things are uncountable. It is like: when you are in a lake water is uncountable. When you are in the lake you don’t see rain droplets. Only when you go out of lake you can see lakes and raindroplets etc which are countables. Similarly, if you are IN between «money» as seen in your words such as «this is a small money for me, that is a big money for me, etc», money is uncountable for you. And, when you don’t have a one 1cent in your pocket, you are IN «money», not OUT of money, therefore, you can not see its countability of money, like that you may not see rain droplets while you are in a lake… Another expression. When you are at Work, it is «too much» to be counted… When the work/day is over it is only another day past. Good night.

(Ok, this is last post here. unless some opposite. Long post. Conclusion is in the last lines.)

Another thing to see why «money» is countable…

Counting Numbers set: {1, 2, 3, … , 9999999, …., «infinite»}

«Infinite» here is «indefinite» which can be shown with any symbol, for ex «horizontal 8» as done in the mathematics or can just be kept as a word «infinite.»

So, the mathematical symbol «horizontal 8» and the word «infinite» are equivalent in the sense that they both are «indefinite.»

When it is said that «money is uncountable» it will mean that «money» is indefinite like «infinite.»
When so, when we rewrite «counting numbers set» above in that way below, (lets say «equivalency» symbol here be «==» and unequivalency symbol be «=/=»)

Money-Number Equivalency set: {Money=/=1 , Money =/=2 , Money =/=3, …, Money=/=999999, …, Money == Infinite}

That’s, «money» is equivalent to «infinite» only, not to any others» (with indefiniteness-definiteness criteria.)

This looked probably strange to you, too. It is because of putting indefinite «infinite» into the counting number set as if it «infinite» is a number in the counting numbers set which are definite numbers. By doing so, that’s, by claiming «infinite» as another number, mathematically, these operations below should be valid like it is valid for any number in that set.

1+2+3+ … = any number
which can also be written as
1+(1+1)+(1+1+1)+ … = any number
which can also be written as
1+1+1+1+1+1+ … = any number

If we put «infinite» for «any number» here, then,
1+1+1+1+1+1+ … = infinite
which can also be written as
summation of («too many» 1) = infinite.
«Too many»? Exactly how many? Unknown. Indefinite.
There are these in mathematics:
1 times «infinite» = «infinite» (this is clear here)
2 times «infinite» = «infinite» (again same, no plurality. Now, not so clear…)
3 times «infinite» = «infinite» (again same…)
… (and so on) …
infinite times «infinite» = «infinite» (again same)…

So, this is like writing for any «x»:
1x = 2x = 3x = … (see the weirdness here?…)
This can be written «only and only when x=infinite»)

Can we write this for «money»? If it is «indefinite» like «infinite», yes, we can write also for «x=money» considering that «money» is only a name like any «x» as:
1money = 2money = 3money = …

But, this expression was valid only for «infinite», so, we can conclude «money==infinite», that’s, they are equivalent in «indefiniteness».
Since they are «indefinite» we can not say any «definite» thing about them.
But, we can still say this (according to this «money==infinite»):

… 1cent (as an example) is not money, but, infinite times of summation of 1cent is equal to Money … (due to indefiniteness of money)

What do you understand from this?
You do not have «money» unless you have «infinite» cents…
Then, you can not count «money».
But, there is «infinite» in counting numbers set {1,2,3,…,»infinite»} which implies «counting numbers set is a mixture of definite numbers and an indefinite number»… And, that «indefinite so called number» which is «infinite» can be never «definite», its destiny is to stay as «indefinite»… Since it is «indefinite» we can never talk about its «countability», whether it is countable or uncountable, it will never be known.

So, similarly, since «money» too is «indefinite», talking about its «un/countability» is nonsense, as it will never be known…

With this definition «money is uncountable», we arrived at this conclusion…

I was told by «Treat» in a previous post that why I was complicating things unnecessarily?
As seen here, complication is already in this definition «money is uncountable» as «money is indefinite like infinite».
With such a definition, any study about «money» is an «endless» study like studying «infinite» due to its «indefiniteness».

What I am trying to do here is to take «money» from «indefiniteness» to «definiteness»…
And, this can be done only by disconnecting «money» from «infinite» which is infinite times summation of 1, that’s about «total».
We should stop viewing money as when «Money is TOTAL only».
When you keep viewing «Money is Total only», with mathematical notation, «Money=Total» only, in this mathematical expression, for ex.

$5 + $10 = $15

you are viewing that $5 and $10 are not Money, but, $15 is Money only.
You see? When the word «money» is used you are taking its «big» quantity and you are viewing only «big» as «money» actually.
We can see this better in this summation (each $5, $10, etc are randomly chosen):

$5 + $10 + $75 + $500 + $1200 = $1790 Total…

You are probably looking at the result «Total» only if you are viewing «money» as «total» only, aren’t you? Most people, perhaps, all do this, they look at the Total which is big money. Looking at more and more «big total», you may find yourself at «infinite» which is «indefinite» and that’s why there is this definition, «money is uncountable», which is not logical… So, unless you also call each of {$5, $10, $75, $500, $1200} as «money», you may get lost yourself in «infinity» if you go in that direction. Instead, if you go in other direction from «big total» to «smaller and smaller», the last station is «1cent» which is «definite». Smaller than 1cent is not money. Also, there is another important property of «1cent», which is its «contancy». To tell this:

Instead of writing some money from smaller to big like this (where «<» shows small/big, for ex, «a<b» means «a is smaller than b»)

1cent < 5cent < 10cent < 25cent < 50cent < 100cent (=$1) < 500cent (=$5) < etc … (which is not wrong)

but, writing it in this way, by writing 1cent seperately from all others:

1cent — 5cent < 10cent < 25cent < 50cent < 100cent (=$1) < 500cent (=$5) < etc …

shows that «1cent» is «constant» … while all others (whether they are coins or banknotes or other denominations, etc) are «variables». That’s, for example, instead of 10cent, a new denomination, for ex, 12cent can be minted, depending on the economy. BUT, this can not be done for «1cent» because it is «constant», alternativeless… So, since the «money» too is alternativeless, it is equivalent to «1cent». Linguistically, according to countability&alternativeness:

… money = 1cent … money is cent …

(this is valid for equivalents of 1cent such as 1penny, 1yen, 1kurus, etc. For ex, linguistically, these too are true: «geld ist 1cent, «para 1kurus», «money is 1penny», etc.)

I have already explained the logic of the English word money

How? This was your explanation?

«A word or, more precisely, a concept X is countable if meaning is attached to the expressions 1X, 2Xs, 3Xs, etc.»… (If not, non-countable.)

You are putting the cart before horse.

If I correct, what you said is:

«IF a word or, more precisely, a concept X is countable, meaning is attached to the expressions 1X, 2Xs, 3Xs, etc.»… (If non-countable, we can not write 1X, 2Xs, 3Xs etc.)

This is not an explanation on why «money is non-countable».
So, «non-countability of money» is not proved, yet… (maybe, a mathematican or two can contribute too as «countability» is more about mathematics)

—

Differences between languages: (Google translations of «money» to some languages below. In French, it says «argent», you say «sous», but, ok, I’ll take «sous».)

Lets use «Mon» in Esperanto, as a «new» generalized name of set with elements of all different «names» corresponding to «money» in English.

Mon = {money, sous, soldi, geld, para, raha, dinero, dinheiro, diners, okane, qian, dengi, chrimata, paisa, möngö, imali, etc…}

I don’t know their each stories of these different names, I can think of some reasons for some of them, but, talking about each of them is not our topic here.
A reason I can think of is «locality», for example, money may mean apple for some who give apple and take money, and, money may mean orange for some who give money and take orange, or sometimes sharp suddenly changes might have happened like a queen/goddess Juno Moneta might have changed the name from «xyz» to «money.»

So, maybe, because of their different views of local people or regional groups of people due to such different reasons, there are all these different words for «Mon». That’s, as I shortly talked about these reasons before, most of them are «economical reasons» which make people’s view of money differ.
It is so, because «money» also exists in «price». If we write an abstract Price formula, in this way:

Price(Total Money) = EconomyFactors(trade, power, politics, apple, orange, etc) x «Money».

When people are asked what is «money», they will tell its «function», «what it is for» rather than «money» itself which they do not think at all actually.
And, since their views (due to different economy factors) of people are different their views in «Price» which is «money», but, «total money» for a thing is different for them. Therefore, we can say that the money they are talking about is «Total Money» which is also «money», but, NOT the «Money» on right side of this abstract price/economy formulation. That «money» on the right side of equation is «money» itself, that’s, «money» WITHOUT connecting it to economy…

So, back to the topic. Lets rewrite the «Mon» set here

Esperanto «Mon» = {money, sous, soldi, geld, para, raha, dinero, dinheiro, diners, okane, qian, dengi, chrimata, paisa, möngö, imali, etc…}

What is the common character of this set? In other words, what is invariant(s) in this set? This is our interest here.
As you, and many people (I’ve not heard anyone saying otherwise) have said this directly or indirectly:

… This set «Mon» is a set with elements which are uncountable, that’s, uncountability is universal in this set «Mon»…

Prove is required for this claim… (even if it is commonly accepted… common acception too maybe wrong, who knows, we need to see.)

—

How to prove? One of ways is symbolic mathematics…

These notations&symbols (including linguistics such as letters, commas, etc) are kinds of «discrete» elements we are using to communicate here.
(even «infinitesimally» small imaginary particle which mathematicans use in continuum/analytical formulations are «discrete» even if it is very small like millimeters or nanometers, etc. Pure mathematicans can oppose this, but, it is a reality and this reality is proven by «chaos» appeared in their «deterministic» formulas which is called as «deterministic chaos». Anyway, it is not necessary to go into details of these, I just mentioned to say that our all tools we humans use/we made are «discrete tools.» This «discreteness» is one of reasons we have faced with, for ex, so-called number «Pi» (3,14etc) when calculating area of a circle, because we are «transforming» continuity of a circle to our discrete world so that we can calculate its area of circle with an «approximation» with very roughly to very preciously like we do analytically (does not matter, still discrete result even if it is analytically precious), therefore, our all calculations are discrete, our numbers are discrete, our counting too is discrete. Our language words too are discrete. For example, in mathematics, we write «1x+2x=9», this is a symbolic mathematics. This is simple, we can solve «x» here easily (x=3). Much more complex symbolic calculations can be done by symbolic mathematical softwares available today. This symbolic calculations are closely related to (written) languages as seen in using letters or words such as x, y, a, b, xyz, etc.
SO, proof of «un/countability of money» too can be done by using symbolic mathematics…

For example, (as I little done in my previous post)

1x = 2x = 3x… = x

This can be written for an uncountable «x»… Really? It is another story. Since numbers attached to uncountable «x» does not matter, why not, it can be written. However, a better proposal than 1x=2x=3x…=x is necessary, WITHOUT forgetting that «our uncountability» here is restricted to «money» only as there is this claim «Mon is uncountable set and its uncountability is its invariance, so, it is universal-ity of this set «Mon» with elements such as «money, sous, diners, para, etc»…

Proof should follow like that:

What is «x» here?

Answer: x=0 (zero) or x=infinite. They can describe «Mon» according to «countability»?
(notice that in this «1x=2x=3x…=x», all counting numbers are not solutions of «x», only «0» and «infinite» are solutions. So, we can consider «Mon» is equivalent to either «zero» or «infinite» if it is uncountable… Note that you can read «infinite» only as a word, not as a number. What about «zero»? It is a number? Such questions and answers. Symbolic mathematics. If any answer can explain «Mon», we can say it is «uncountable», otherwise, «indefinite»? Money is «indefinite»?)

This was your explanation?

«A word or, more precisely, a concept X is countable if meaning is attached to the expressions 1X, 2Xs, 3Xs, etc.»… (If not, non-countable.)

Yes, this is the definition of countability.

The English language does not assign meaning to the expression 2 monies in uses 1) and 2) and therefore the concept expressed by the word is non-countable. This is a property of this word and the English language in autonomous defining it as such; more precisely in not defining meaning for the expression and not attaching an intrinsic unit of measure, which would make 2 monies meaningful.

That is the end of the story. Nothing more to be said.

This is an email from a professor in mathematics who started to read this thread:

——-

Erol, (that is my name)

I have never heard the “how much” verses “how many” distinction before, it is not a standard way of differentiating the two.

Typically countable, which can be infinite, means it can be counted (matched up to correspond to the natural numbers). Uncountable would involve what cannot be matched up to the natural numbers. All integers are countable, but all the numbers between 0 and 1 are uncountable.

In Statistics we deal with the topics of discrete and continuous which all seem to relate to your question. Discrete means the data is countable while continuous means that the data is uncountable. All currency would be considered countable. In the U.S. while we have dollars, every amount can be counted in terms of cents. While other variables, like a person’s weight at a given instance, is continuous. We record weight as a discrete value, say 183 pounds, but a more precise measurement would give a more precise answer. We could measure weight to a tenth of a pound, a hundredth of a pound, or a thousandth of a pound which would give a more precise answer. But with currency, once we reach the smallest denomination used for that type of currency, more precise measurements do not produce a more precise number.

xxxx (his name closed)

———

Although this email does not say anything about the word «money», still say some about the thing «money.»

In his first paragraph, he says, in other words: «how much» vs «how many» comes after the distinction «countable» vs «uncountable».

His/mathematical definition of «countable» is related to «matching to the natural numbers» and it includes «infinite.» «Uncountable» cannot be matched up to the natural numbers.

Last paragraph is more about dividing/undividing of things to be counted. Currency, dividable, and once its smallest denomation (cent) is reached, more precise measurements do not produce a more precise number (that means it is unnecessary to divide the currency further and that means that even if you divide the currency into the smaller than 1cent, the smaller than 1cent is no more money — words in this paranthesis is my comment based on his words.)

I think that he did not read this thread carefully (probably, he is busy) and didn’t see the «money». Still, we can take his word «currency» as equivalent to «money» and his saying «currency is countable» is contrary to what «Treaty» said in his last line of his previous post, that’s :

(…in the dialect of people in Randomtown, «money» is uncountable even if it means «currency»). The principle won’t change.

So, lets use the word «currency» hereafter (for a while) instead of the word «money» as money is a broader term that maybe more mind confusing.

So, which is currect? … «how much currency» or «how many currency» …

I just checked on the net which of them are more commonly used… Their use (the word «currency») of People («Treaty», I refer by «their» to «… of majority of people») is: … «how much currency» … (so, the word «currency» here is like «water» in «how much water»… or, using it in field «money», «currency means money».)

But, professor said: «currency is countable»…

So, how to distinct? Lets write again, side by side:

«…. currency is countable….» and «….how much currency ….»

Principle that implies universality: …for uncountables, «how much» is said… FAILED or NOT? (specifically, within this field «money/currency.»)

So, you as a linguist, what are you saying? In English, «currency» is uncountable or countable?

Currency is countable: USD is one currency, USD and GBP are two currencies, USD, GBP and EUR are three currencies.

a new word for each of them is needed to be derived, isn’t it?

It is quite normal that different sciences use the same word in different meanings when contexts are sufficiently different. Speaking of countable sets and a countable nouns should be sufficient to differentiate the contexts.

First, let me answer «Treaty» first as his example (2.5 hours) is simple to be answered.

It is natural to say 2.5 hours («hour» is countable) in a language. However you can’t say that for a mathematical countable (because 2.5 is not a natural number). So, it would be nice if you stop using mathematical references altogether to avoid confusion.

Its explanation can be done by «familiarity» in «units». Those who use «2.5 hours» use so not because of language difference, they do so because their more familiar unit is «hour», for ex, not minute… 2.5hours=2x60minutes+30minutes=150minutes (can also be expressed in seconds, 9000seconds. Etc.). As you see, in 150minutes, we reached another natural number. Such things can be done for all numbers (except irrational numbers such as pi=3,1415etc). Similarly, 2,5USD=250cents. So, here, as prof said, what is important is «cent» in their money, not USD as unit. Although USD is more used, economy reality, «cent» is more important in scientifical reality. So, without using mathematical references, such things can’t be explained… And, mathematical countability is as math prof said, related to the natural numbers. Here, I am trying to understand «linguistics countability» as it is claimed by «berndf» they are different…

Ok, I’ll pick «important» lines of «berndf» here:

1. Concrete: I have two apples and three oranges, i.e. five fruits.
2. Abstract: Apples and Oranges are both fruits.

(+)

Currency is an abstract noun.

(+)

Currency is countable: USD is one currency, USD and GBP are two currencies, USD, GBP and EUR are three currencies.

= integrity (exists?)

That’s, is there any contradiction between descriptions/definitions of «berndf» or not? (since all these were said by same person, self-contradiction exists in «berndf»?)

To see if there is any contradiction or not, I still used a kind of operation notation «(+)» which is not a number summation operation notation, to check the integrity in those words…

(I’ll check it later. I need to go out.)

PS: In the mean time, you can change the word «currency» to «money» in those words of «berndf» and read them again. (ok, have a good day.)

That’s, is there any contradiction between descriptions/definitions of «berndf» or not? (since all these were said by same person, self-contradiction exists in «berndf»?)

Abstracts nouns can be countable. That is no contradiction: One ideas and another ideas are two ideas. Countability has nothing to do with physical quantities. The only thing it means is that meaning is defined for the expression 2 Xs.

However you can’t say that for a mathematical countable (because 2.5 is not a natural number).

Careful there. 2.5 is a rational number (can be represented as 5/2). The set of rational numbers is also countable although it is not discrete (i.e. between any two rational numbers a and b with b > a there is always another rational number c with b > c > a) — but this set of numbers is still countable. Countability in set theory really is a very special term that is not easily accessible to a non-mathematician and even mathematicians cannot seriously claim to be able to visualise what non-countable means. Very loosely speaking this means that infinity comes in different «sizes». There are sets that are «more» infinite than others. But that is completely beyond any human intuition. In number space, you have natural numbers, then the next bigger set is integer numbers (including negatives), then there are rational numbers (everything that can be represented as a fraction, that includes all integer numbers and things like 2.5), then there are arithmetic numbers (everything that solves a polynomial equation; that is all rational number plus numbers like sqrt(2)) and finally there are real numbers (all limits of Cauchy sequences; that is all arithmetic number plus all the «strange» numbers like pi or e).

The funny thing is that natural numbers, integer numbers, rational numbers and arithmetic numbers are all countable, i.e. they all are the same «size» of infinity. Only when you include the «strange» numbers like pi or e, the set of numbers becomes non-countable. I.e. there are «more infinite» «strange» numbers than «ordinary» ones.

Abstracts nouns can be countable. That is no contradiction: One ideas and another ideas are two ideas. Countability has nothing to do with physical quantities. The only thing it means is that meaning is defined for the expression 2 Xs.

I understand what you meant by «abstract noun.» You are not counting «apples» physically, you are counting its name/noun «apple» without thinking its physics.
A more clear example about what you mean is «love», only a concept, with no any physical body (though some biologists/physicists may not completely agree in this, by claiming there are small particles/cells/whatever that are related to the «love», our common understanding in «love» is not a material thing whether it is true or not, so, «love» fits better in your «abstract noun» as «love» has no physical body, unlike «apple» which is not so easy for anyone to isolate its label «apple» from physical «apple».) Having said these, what you are doing by «linguistics counting» is nothing else than «counting nouns». So, question is:

How many «nouns» are there in English and in all languages?
Since there are probably many things undiscovered yet, there will be more nouns when they are discovered and again, another question is how many nouns will there be, for ex, till next year?

No, of course, you should not answer these questions. But, even if they are «abstract nouns», you will need a set of numbers such as {1,2,3,…} so that you can answer (by mapping your set of abstract nouns to that number set) such a question «how many nouns»… Without having a number set (with its minimum «1» or in word «one»), you can not count anything whether «abstract noun» has also a physical body like «apple» or has no physical body like «love». (While we are at «love», let me say also this. If you are IN love, it is uncountable. If you are OUT of love, for ex, it can be countable and by looking at other people in love, you can say «this love (of this person)», «that love (of that person)» by pointing them by using your fingers which are one of basic things used in counting.

So, without knowing how many nouns there are and without knowing how many numbers we need, to be able to count, we need both sets:

nouns:{ … } and numbers:{1/one,…}

Fill … with all nouns available in all languages and with all numbers available and map them.
No, this is not our topic here because talking such will be like talking about «infinity» where we may get lost.
No, don’t fill … also with nouns in English. Again, it may go to talking about «infinity».
Yes, lets take only nouns related to «money» which is our topic here and «money» is a more familiar thing to everybody from kids to olds who do «counting» everyday.

Lets start with the «money noun» set: (as I wrote before. I used their general name as «Mon» in Esperanto)

Mon = {money, sous, soldi, geld, para, raha, dinero, dinheiro, diners, okane, qian, dengi, chrimata, paisa, möngö, imali, etc…}

How many names/nouns are there in this set? We need to use this set: {1/one} and this set numbers: {1/one, 2/two, 3/three,…,infinite} (see there is operation «+» in this counting numbers set elements, eg, 2=1+1.
Anyway, lets say we finished counting these nouns/names in «Mon» set and lets say the result is, «213», that is a finite number…
Okay? Set «Mon» is already counted or not?
Probably, it is not clear. So, lets narrow our set from «Mon» to «Currency» as abstract nouns again.

We have this set:

Currency set: {usd, gbp, euro, lira, yen, etc… }
How many currency nouns are there in this set? Probably some people know it already, I don’t know, blowing again, lets say it is «195»..
So, «currency set» is counted? Yes, and this answer fits what is said here, that’s, «currency is countable»…
…. why didn’t you say this same thing for «Mon» set… in which «money» as a noun element too exists… ?

That’s, saying «MONEY is UNCOUNTABLE» and «CURRENCY is COUNTABLE» is a CONTRADICTION…

WHY NARROWING our topic here TO «MONEY»? IT is more clear now with NARROWING to CURRENCY.
This «currency» noun set with «nouns» elements again DIFFER from all other «noun» sets BECAUSE there is some «calculatable» relations between its elements, eg. there is a convertibility ratio between usd and gbp and others. (To my claim, some other «more complex calculatable» relations exist between «money and «sous» and all others, but, it is not so easy to see it now.)

LETS NARROW FURTHER to Currency in USA: (to see relations between elements in their money set)

USA Currency nouns:{dollar, half, quarter, dime, nickel, cent} (they have these nouns/names)
How many nouns are there in this set? I can count easily, «6». Counted? Yes, so, it is countable and this is clear.

BUT, now, I’ll do a series of operations (because I know relations between these noun elements, such as 1dollar=2half…=20nickels=100cents)
Then, our new set becomes:

USA Currency nouns: {100cent, 50cent, 25cent, 10cent, 5cent, 1cent}
Now, lets count again, how many «nouns» in this set? Still 6? NO… It is ONLY 1, in words, ONE… What else left in the set? Numbers… And, those numbers too are all related to each others, eg, 5=1+1+1+1+1… So, what do we have now in this set? We have this:

USA Currency set: {cent, 1/one, +}

where «+» is a clear number summation operation notation, which is a function/verb/»work»… and «1/one» (whether you call it a word or number) and «cent» a clear noun… So, if «currency» is an abstract noun, it corresponds ONLY to «cent» or «one cent»…
Linguistically… «currency is one cent » … without forgetting «one» that is about countability, it can also be written as:

CURRENCY is CENT…

Lets go backward. What was the «currency» in another word? It was «money»…

So, «MONEY is CURRENCY is CENT»… (This is «local universality» in «any currency/money».)

(We can go wider, to «Currencies» set, and wider to «Mon» set, but, «relations between elements» of those sets are more complicated than «pure mathematical» relationship between elements of a «certain» currency. First, we need to reach an agreement in this «local universality» first, that is, «currency=cent», eg, in USA.)