Espels:But "fermigxi" does not mean become the close, it means "to be closed", that's the difference.

That's a problem with English here, because "to be closed" means in Esperanto both "esti fermita" and "fermiĝi".
La pordo fermiĝos je la none. = The door will be closed at nine. (The act of closing it will happen at nine). (закрoется)
La pordo estos fermita je la deka. = The door will be closed at eleven. (The door will be in a locked state at eleven, the act of closing it will have happened sometime before eleven.) (будет закрыта)

All words have roots and the roots are different. I thought it was a common fact. Why do you think the opposite?

I don't think and haven't stated the contrary. I wrote, that most roots (nememstaraj) do not belong to a certain part of speech. "Akvo" is not a main root, it is a (syntactic) word derived from the root "akv" (which is neither noun, nor verb, nor nothing else; it is a bare semantic unit). "Pala" is not a main root, it is a (syntactic) word derived from the root "pal".
The fact that "akvo" is a noun, has nothing to do with "akv", but with "o".
The fact that "pala" is an adjective, has nothing to do with "pal", but with "a".
The same thing with the adjective "akva" and the noun "palo".

Disclaimer: I am aware that there is a quite novel notion, that roots indeed have an inherent class, belong inherently to a certain part of speech. However, this idea is being discussed to and fro (also on this forum quite a lot in the past). I personally think, adding parts of speech to bare roots makes things only unnecessarily complicated.

If you prefer to suscribe to the idea of classed roots, please do so. If it helps you, even better. However, you will see that not everybody shares this notion.

But even with classed roots you won't be able to predict every derivation (as sergejm already mentioned). Esperanto (nor any human language) has a 100% precise rule set without exceptions or room to interpretation. Without context and without accepting consensus you won't be able to parse all words (e.g. fermiĝi = to become closed; frostiĝi = to freeze, to become frozen"). This isn't C or Python.

But "fermigxi" does not mean become the close, it means "to be closed", that's the difference.

As sudanglo and sergejm already stated, you cannot separate semantics from morphosyntax.
According to your interpretation, "frostiĝi" would mean "become the frost" and not "freeze, become frozen". "Lumiĝi" wouldn't mean "become the light" and not "become shining, light".

nornen:

As sudanglo and sergejm already stated, you cannot separate semantics from morphosyntax.
According to your interpretation, "frostiĝi" would mean "become the frost" and not "freeze, become frozen". "Lumiĝi" wouldn't mean "become the light" and not "become shining, light".

First, "lumi" is an intransitive verb, "fermi" and "ami" are transitive. You can't compare them like they are the same.
As for "frostigxi", if we follow the rules about root, we can see that "frost" is a noun root, and the rules say:
"An IĜ verb can also be made from a root that is normally a noun. These IĜ verbs can mean that the subject is becoming the thing indicated by the root, or that it becomes similar to the root, or that some kind of action characterized by the root is happening to it".
I don't see any contradictions here, if we follow the rules. I can't see why you denied this conception about roots. To me all of it seems very logic and helps to avoid misunderstanding.

I'm no sure, that I've understood every turn in this discussion, but…

While not originally an idea by Zamenhof quite early came up the idea (by a known esperantist René de Saussure), that roots have some character, vortokaraktero, a noun, adjective or a verb character. Later almost all dictionaries have adopted a custom to put this character-based word, a pleonasm, as the headword. Therefore frosto is the headword in PIV for the root frost/ or ami for am/.

When it comes to iĝ-verbs, I've referred a couple of times to Plena Manlibro de Esperanta Gramatiko (PMEG), which classifies the iĝ-verbs into four categories.

1. ordinaraj

All iĝ-verbs with a non-verb-character root belong to this category.
 

• glacio → glaciĝi
  
• malpura → malpuriĝi

There are also a lot of verb-character root iĝ-verbs.
 

• sidi → sidiĝi (stato, en kiu la subjekto sidas)

Some verbs take a preposition as prefix.
 

• ami → enamiĝi (stato, en kiu la subjekto amas)

They all mean transition to the state defined by the pleonastic root. The subject is the thing, that undergoes the transition.

2. faritaj el objektaj verboj

Here the iĝ-form shows an action, that happened by itself or without explicitly mentioning the direct subject. They also can be understood to show transition to a state (often a participle of adjective of the root).
 

• malfermi → malfermiĝi (iĝi malfermita)
  
• trovi → troviĝi

3. faritaj el senobjektaj transiraj verboj

This is an out-dated category in contemporary Esperanto and is expressed by other means.

4. nenormalaj faritaj el objektaj verboj

There are some verbs, that quite don't fit into the category 2, but have a meaning of ek-.
 

• scii → sciiĝi = ekscii
  
• timi → timiĝi = ektimi

 
 
Now English is notorious for lacking grammatical marking. In it a word can have multiple meanings and only the (carved-in-stone) position reveals the role of the word. See Buffalo buffalo…

Esperanto on the other hand favours clear marking and this is supported by the pre- and postfixes of the language. However one of the myths of Esperanto is the claim, that you can attach any pre- and postfix to any word. Yes, that is possible, but no, not all of combinations make any sense. Given the number of theoretically possible combinations actually most combinations don't make sense, e.g. malgesciiĝado.

How to know which combinations are ok? By the same way as in any language: use a good dictionary. PIV and Reta vortaro are good online dictionaries, and there also are printed ones. If you find a combination in them, it's ok to use it (unless of course there is a mention not to use). If you don't find, you have to analyse it (see above Sudanglo's example of enveniĝi and endormiĝi). If you don't find definition or usage of the parts, you most likely have cooked up a senseless combination.

Espels:

nornen:

As sudanglo and sergejm already stated, you cannot separate semantics from morphosyntax.
According to your interpretation, "frostiĝi" would mean "become the frost" and not "freeze, become frozen". "Lumiĝi" wouldn't mean "become the light" and not "become shining, light".

First, "lumi" is an intransitive verb, "fermi" and "ami" are transitive. You can't compare them like they are the same.
As for "frostigxi", if we follow the rules about root, we can see that "frost" is a noun root, and the rules say:
"An IĜ verb can also be made from a root that is normally a noun. These IĜ verbs can mean that the subject is becoming the thing indicated by the root, or that it becomes similar to the root, or that some kind of action characterized by the root is happening to it".
I don't see any contradictions here, if we follow the rules. I can't see why you denied this conception about roots. To me all of it seems very logic and helps to avoid misunderstanding.

But the headword in the dictionary is "lumo" and not "lumi". So it shouldn't be compared to any verb, transitive or not. Shouldn't "lumiĝi < lumo" be treated equally as "frostiĝi < frosto" according to the classed root hypothesis?

nornen:
But the headword in the dictionary is "lumo" and not "lumi". So it shouldn't be compared to any verb, transitive or not. Shouldn't "lumiĝi < lumo" be treated equally as "frostiĝi < frosto" according to the classed root hypothesis?

Absolutely.

Nornen,

I'm not a great fan of the idea of vortokaraktero either, but I do realise, that without the root character the principle of neceso kaj sufiĉo is meaningless. But please let's not initiate a meta discussion here.

nornen:

Espels:

nornen:

As sudanglo and sergejm already stated, you cannot separate semantics from morphosyntax.
According to your interpretation, "frostiĝi" would mean "become the frost" and not "freeze, become frozen". "Lumiĝi" wouldn't mean "become the light" and not "become shining, light".

First, "lumi" is an intransitive verb, "fermi" and "ami" are transitive. You can't compare them like they are the same.
As for "frostigxi", if we follow the rules about root, we can see that "frost" is a noun root, and the rules say:
"An IĜ verb can also be made from a root that is normally a noun. These IĜ verbs can mean that the subject is becoming the thing indicated by the root, or that it becomes similar to the root, or that some kind of action characterized by the root is happening to it".
I don't see any contradictions here, if we follow the rules. I can't see why you denied this conception about roots. To me all of it seems very logic and helps to avoid misunderstanding.

But the headword in the dictionary is "lumo" and not "lumi". So it shouldn't be compared to any verb, transitive or not. Shouldn't "lumiĝi < lumo" be treated equally as "frostiĝi < frosto" according to the classed root hypothesis?

Thanks for that. My dictionary said "lumi" not "lumo", but I checked PIV, and was convinced I was wrong. I thought my Android version have PIV content, but now I know it is not. Thanks again

Espels:Thanks for that. My dictionary said "lumi" not "lumo", but I checked PIV, and was convinced I was wrong. I thought my Android version have PIV content, but now I know it is not. Thanks again

And there we have the problem with this "root class" idea. Whose responsibility is it, to decide, whether a root is a noun, a verb or something else?

The author of your dictionary says, that "lum" is verbal.
The author of the PIV says, that "lum" is nominal.
Zamenhof himself in the Universala Vortaro, which is part of the Fundamento, says it is both:

lum' luire, lumière | light | leuchten | свѣтить | świecić.

"Luire" is a verb and "lumière" is a noun, so apparently the root "lum" is both verbal and nominal.

However, if you look at roots as not belonging to any part of speech, this conundrum disappears completely.

Nornen,

The idea of vortokaraktero was not by Z himself, but by René de Saussure. It is the point in La Saussure-a konstato, one of the three fundamental basics in the word construction in Esperanto. Universala Vortaro is known to contain deficiencies, e.g. the entry you refer to contains "leuchten", but not "Licht", so there is a discrepancy between the French translation and others.

nornen:

However, if you look at roots as not belonging to any part of speech, this conundrum disappears completely.

.
May be you are right, but from my side it looks like it is not a solution. If we deny the roots, it is not getting us closer to solve the problem. In that case we have no clue to decide what lumigxi (for example) means. If it is "to shine" or "to become the light". Yes it could be obvious from the context, but the idea of roots is an additional option, and it is not a complicated one to just deny it.

Don't beware about it - 'lumiĝi' via context may mean both 'to begin shine' and 'to become light'. In first case it is better use 'eklumi'.