The correct use of these correlatives is intuitive for me, but I've been trying for a long time to articulate the difference in a simple way that accounts for most/all usage. Roughly speaking:

Tiu goes with a noun (or in compound words, with an adjective or adverb): Tiu libro. Tiu seĝo. That book, that chair. In compounds: tiutempa, of that time, tiumaniere, in that way. If, in English, you want to say "that X", you need tiu X-o.

Think of tiu as an adjective - used to modify a noun.

Often the noun that tiu attaches to can be omitted and is implied. Al mi plaĉas tiuj libroj. Kiom kostas ĉi tiu [libro]? - I like these books. How much does this one cost?

The other use for tiu is as a generic pronoun to refer to people. Tiu diris, ke... - That person said, that ...

Tio, however, is used standalone, and cannot go with a noun - it already is the noun. Tio ĝenas min, that bothers me. Compare to tiu problemo ĝenas min.

Tempodivalse:The correct use of these correlatives is intuitive for me, but I've been trying for a long time to articulate the difference in a simple way that accounts for most/all usage.

If you think of a simple way to explain it then please do because I still don't get this fully.

I could be wrong, but I think it works like this:

Tiu - For specific things

Tio - For unspecific things

Imagine you are watching TV. You see an actor wearing a shirt that you like. If you say mi volas tiun then it means that you want the actor to take off his shirt and mail it to you. You want the specific shirt that the actor was touching.

If you say mi volas tion then it means that you want the shirt, but it is okay if it is a replica that is sold in a store. It doesn't have to be the one that the actor physically touched.

If you have two things which are identical and you say tio then it could mean either one. If you say tiu then you being very specific regarding the one you are mentioning.

Tiu - That specific one
Tio - That class of object

Iu - Some particular thing or person.
Io- Something - This could be anything because it isn't specific.

Mi volas iun - I want something and I am picturing it in my mind
Mi volas ion - I want something but I don't know what it is.

It is similar to how the definite and indefinite articles are used within a language.

Someone correct me if I am wrong.

Alkanadi:

Tempodivalse:The correct use of these correlatives is intuitive for me, but I've been trying for a long time to articulate the difference in a simple way that accounts for most/all usage.

If you think of a simple way to explain it then please do because I still don't get this fully.

To me the simplest explanation is the following.

* io/kio/tio/ĉio/nenio stands alone without any noun.
* iu/kiu/tiu/ĉiu/neniu cannot stand alone without a (maybe implicit) noun.

Alkanadi:If you think of a simple way to explain it then please do because I still don't get this fully.

Hint: If you can't decide whether -u or -o is correct, try saying it in English, but substituting the correlative with the word "something". If the resulting English sentence sounds acceptable, use -o. If the word "something" makes the sentence sound weird, you should be using -u.

Say you wanted to say I want that book in Esperanto. Tio libro or tiu libro? Well, replace the word with the word "something".

I want something book. -> This sounds weird, so you shouldn't be using the -o correlative.

Ignore this post folks, We hash through the differences between tiu and tio, work out some misunderstandings, and finally come to what I think are 3 very good rules for when to use Tio vs when to use Tiu on page 3 or so.

Probably best to skip to page 3

Read the post where Tempodivalse starts from the beginning and gives us three simple rules.

Tempodivalse:

Hint: If you can't decide whether -u or -o is correct, try saying it in English, but substituting the correlative with the word "something". If the resulting English sentence sounds acceptable, use -o. If the word "something" makes the sentence sound weird, you should be using -u.

Say you wanted to say I want that book in Esperanto. Tio libro or tiu libro? Well, replace the word with the word "something".

I want something book. -> This sounds weird, so you shouldn't be using the -o correlative.

What if you see a book in the window of a bookshop and you say, "I want that book", but you don't actually want that particular book; any copy will do. You want some printing/copy/edition/instance of that book, but not that particular book in the window. Do you still use tiu?

What if I have a rock on a table in front of me and I'm pointing right at it with my finger and I want to say, "That is mine". If I replace that with something, I get "Something is mine"; a perfectly acceptable sentence in my opinion. Should I say "Tio estas la mia." instead of "Tiu estas la mia."?

eshapard:

johmue:

To me the simplest explanation is the following.

* io/kio/tio/ĉio/nenio stands alone without any noun.
* iu/kiu/tiu/ĉiu/neniu cannot stand alone without a (maybe implicit) noun.

I think this may be the simplest explanation, but I don't think it works.

It does.

I'm pretty sure either version can stand alone. "look at that." (If the person is pointing at something in particular, I think we can agree that we'd use tiu for this).

Hardly. If you say "Rigardu tiun." and it is not clear what you are talking about. I would ask you "Kion tiun?" Actually "Look at that." would translate to "Rigardu tion" where as "Rigardu tiun." would be "Look at that one."

"That is what I think" (tio, or tiu? I think most would agree to use tio)

That there is something being pointed out is implicit in both words (they are pronouns after all). No matter what 'that' refers to in a sentence, I think we can always come up with some noun for it.

If there is a clear implicit noun that can we just don't say because it's cleat by context, then it's "tiu". If not it's tio. Come up with context examples and I will explain you.

e.g. That idea is what I think.

If there have been several ideas been discussed in the context, then it's "tiu".

Here are some example sentences from A Complete Grammar of Esperanto, by Ivy Kellerman Reed:

Ĉi tiu estas la mia. (This is mine.)

No noun here, so clearly tiu can stand alone. We know that we must be talking about something, and you could probably come up with a noun for whatever it is we're talking about, but doesn't the word 'that' always point to something? So isn't some kind of noun always implicit?

No. If someone says "Tiu estas mia." it has to be clear what noun is implicitly standing with "tiu". Otherwise it's "tio".

Se tio estas vidota, li estas punota. (If that is going to be seen, he is going to be punished.)

Tio stands alone here, but isn't it implicit that it refers to something. I mean, there must be something to see. And all things can be named with nouns. So this must be saying something like, "If that evidence is going to be seen (in the court trial), he is going to be punished." So according to the standalone/implicit noun rule, this would be tiu right? We're talking about a specific piece of evidence.

You actually could construct a context where "Se tiu estas vidota, li estas punota." is correct. But again, there has to be a noun that naturally can be attached to "tiu".

I think the rule may be that tiu is used when you are pointing out some specific concrete physical object, and you use tio in every other situation.

Wrong. You obviously have not understood the difference. That's why you say my explanation does not work. It simply does not explain your wrong understanding.

"Look at that" - tiu - I'm pointing at some object for you to see.

Wrong: It's "Look at that" is "Rigardu tion".

"That's what I think." - tio - You can't point at an idea.

It's correct to use "tio" here. But your explanation is wrong.

"That is mine." - tiu - You're pointing out some specific object that you own.

It depends. It's "tiu" only in the case, when you could clearly say what the person is talking about and actually add a noun.

"Ĉu iu el tiuj libroj estas via"?
"Jes tiu [libro], estas mia [libro]."

If you just talk about some unspecified object you'd say "Tio estas mia."

Now let's say you're talking about the intellectual property rights to a cartoon character you created; "Mickey Mouse? That is mine." Now I think the that in 'that is mine' should be tio because you aren't pointing out any specific image or toy or something; you're pointing to the concept of Mickey Mouse or maybe the use of Mickey Mouse (both very much not specific concrete physical objects).

Wrong:

Jen du kantoj:
Mastiku la fendojn; tiu estas mia.
Alia aventuro; tiu estas de LPG.

"If that is to be seen..." - Tio when talking about some collection of damning evidence that we are aware of; Tiu when that collection is in front of you and you are actually pointing to it.

"Tiu" when you clearly could attatch some noun to it. Otherwise "tio". No matter whether you can physically point at it or only imaginary mention it.

If I'm right, then ...

But you are wrong.

Correct me if I'm wrong

I did.

eshapard:
What if you see a book in the window of a bookshop and you say, "I want that book", but you don't actually want that particular book; any copy will do. You want some printing/copy/edition/instance of that book, but not that particular book in the window. Do you still use tiu?

I think that's fine, just as in English you can say "I want that one!" - in response to "Which book in the store window do you want? We can buy one on the internet."

What if I have a rock on a table in front of me and I'm pointing right at it with my finger and I want to say, "That is mine". If I replace that with something, I get "Something is mine"; a perfectly acceptable sentence in my opinion. Should I say "Tio estas la mia." instead of "Tiu estas la mia."?

I would use tio. You could in principle use tiu if you were already talking about/looking at different kinds of rocks, and wanted to say that this particular rock is yours. In that case, the referent is unsaid but left strongly implied: tiu ŝtoneto estas mia. But in most situations this isn't going to sound good.

Johnmue's suggestion is best: if it goes with a noun, use -u. If there is no noun, use -o. If you are talking about a person, a standalone -u correlative is OK, as in Tiu promesis telefoni min.

Sometimes I think Slavs have an super unfair advantage with this stuff.

eshapard:What if you see a book in the window of a bookshop and you say, "I want that book", but you don't actually want that particular book; any copy will do. You want some printing/copy/edition/instance of that book, but not that particular book in the window. Do you still use tiu?

Yes. "Mi volas tiun libron."

What if I have a rock on a table in front of me and I'm pointing right at it with my finger and I want to say, "That is mine". If I replace that with something, I get "Something is mine"; a perfectly acceptable sentence in my opinion. Should I say "Tio estas la mia." instead of "Tiu estas la mia."?

"Tio estas mia."

You'd say "Tiu estas mia." only if there are other rocks around and you want to point out that this one is yours.

"Tiu estas mia." = "This one is mine."

johmue:
If you just talk about some unspecified object you'd say "Tio estas mia."

Thanks for your response!

I'm having trouble understanding when anyone would ever talk about an uspecified object.

Whenever I use the word 'that', there's always something I'm talking about.

Can you give me an example of when you would use 'that', but not have something in mind?