Leisureguy:What do you propose?

I would approach the whole question not from the semantic point of view, but from the syntactic.

If transitivity were directly linked to semantics (e.g. verbs of action, perception and emotion are transitive, but verbs of state or quality are intransitive), then transitivity should be (more) stable across language barriers. Which it is not. For instance in Esperanto "helpi" is transitive, in German and Russian it is intransitive, and in Spanish it started out intransitive, is now becoming transitive and nobody knows for sure how to use it. The question, whether or not it is transitive in English, is a bit moot, since the English two-case-system (rectus / obliquus) doesn't allow to distinguish between accusative objects (indicator for transitivity) and dative objects (no indicator).

From a syntactic point of view the definition is quite simple: A transitive verb is a verb which can govern arbitrary direct (accusative in nom-acc-languages, absolutive in erg-abs-languages) objects.

Is this definition useful? Not really, because it just assigns a label to verbs with a direct object, but it doesn't help us to determine, whether a given verb can govern such an object or not.

In some languages (e.g. Q'eqchi') you can spot the transitivity of verb by simply looking at it: Does the infinitive end in -b'al or -nkil? Then it is transitive. Does it not? Then it's not. In Esperanto, German, Russian, and lot more languages this trick doesn't work. We have to rely on dictionaries.

For instance, as a German speaker, without consulting a dictionary I would assume that "helpi" is intransitive as it is in German: Ich helfe ihnen (dative) -> *mi helpas al ili. (And I am quite sure, I have written this a lot in the past.)
As a Q'eqchi' speaker, I would assume it is transitive as it is in Q'eqchi': nintenq'aheb' -> mi helpas ilin.
As a Spanish speaker, I would assume it can be both: les ayudo -> *mi helpas al ili; los ayudo -> mi helpas ilin.

So the only trustworthy way of determining the transitivity of an Esperanto verb is to look it up in a dictionary. And not only transitivity, but the whole subcategorisation frame of the verb: e.g.: is it "mi dankas vin pro io" or "mi dankas vin por io", etc. However there are some hints that could help us to venture at least an educated guess thanks to syntactic functions (syntactic roles, thematic roles, Θ-roles)

When we have an agent and a patient, then more often than not the verb is transitive and the patient is its direct object: mi batas vin.

When we have an agent and a topic, then more often than not the verb is transitive and the topic is its direct object: mi diras la veron.

When we have an experiencer and a stimulus, then more often than not the verb is transitive and the stimulus is its direct object: mi vidas vin.

In summary: When we come across a new verb in Esperanto and it falls into one of the three aforementioned categories, then it is more or less safe to assume that it is transitive (we will still get false positives though). When not, use a dictionary.

That's very useful (and interesting) and I see that trying to deduce (e.g.) transitivity from logic gives unrelaiable (and often misleading) results. As with prepositions, one must just learn them, though (as you point out) some are easy to guess — bati is the canonical example. But boli? that can be transitive or intransitive (from the logic of it, speaking as an English-speaker). Certainly to have the use of a variety of cases in some ways makes things clearer: nominative, vocative, genitive, ablative, dative, accusative — and it seems that there are traces of cases lost, absorbed into others (e.g., genitive of possession and genitive or origin seem to reflect the merging of the genitive and locative cases, and the dative too seems to have gobbled up some of its compatriots).

So I'm convinced: I'll just study and learn (in)transitivity of the verbs I learn.

Now what about the oddity of la kuko gustas bone while at the same time la kuko estas bona. In both cases we're describing an attribute of the cake (but there I am doing it again, taking a semantic approach). I suppose in the first example we are describing not the cake but rather the way the verb in this case acts, conveying the idea of goodness in terms of that particular verb's area of responsibility — so we're modifying the verb. "The good/well distinct in English doesn't map to bona/bone in Esperanto because the Esperanto's verb is taking on more of the descriptive burden.

Anyway, thanks for your answer and clarification and intriguing examples.

Verbs whose subject is a stimulus are really strange in Esperanto.

La kuko gustas fiŝe. (taste)
La kuko sonas fiŝe. (sound; ok, i know cakes generally don't make any sound, but exempli gratia)
La kuko aspektas fiŝe / fiŝa. (vision)
La kuko ŝajnas fiŝa. (general perception)
La kuko odoras fiŝon / fiŝe. (smell)

Utter chaos.

I completely concur with your analysis that in these cases the adjectives are predicatives and not adverbials. And without a dictionary I would say "la kuko gustas/sonas/aspektas/ŝajnas/odoras fiŝa" with an adjective in all cases. "La kuko gustas malbone" sounds to me more like "the cake has problems transmitting its taste; it is hardly tasteable (sorry for the neologism). And "La kuko gustas forte fiŝa." looks perfectly logical to me.

But hey, this is the way Esperanto is and how we learned to love it.

And we are back again to the arbitrariness of transitivity: "gusti" is intransitive, but "odori" is transitive, although all we did was change the sense involved.

- - - -

But boli? that can be transitive or intransitive (from the logic of it, speaking as an English-speaker).

There is no rationale behind it. The fact that "boli" means "being in a boiling state" and not "bring something to its boiling point" depends merely on the decision Zamenhof took when he first introduced this word.

nornen:

But boli? that can be transitive or intransitive (from the logic of it, speaking as an English-speaker).

There is no rationale behind it. The fact that "boli" means "being in a boiling state" and not "bring something to its boiling point" depends merely on the decision Zamenhof took when he first introduced this word.

My guess is that he preferred the i-form to show state and have igi-form to show an action leading to that state. Cf. brili → briligi. Otherwise showing the state would have become cumbersome.

Metsis:

nornen:
My guess is that he preferred the i-form to show state and have igi-form to show an action leading to that state. Cf. brili → briligi. Otherwise showing the state would have become cumbersome.

Aha. Very helpful and interesting. I will stay alert to that idea as I study. Many thanks. Even if there are exceptions it seems an interesting rule of thumb.

And some verbs seem to need both variants:

sidi - to sit
sidiĝi - to sit down (become seated)
sidigi - to seat (as ushers sidiĝas guests at a wedding, for example).

En Esperanto oni uzas N-finaĵon (akuzativon) por:

• Rekta objekto; Li skribas leteroN. 
(*)
• Movo al direkto; Ŝi metis krajonon sur la tabloN. Li iras en la ĉambroN.

• Tempo; Mi venos dimanĉoN.
 La kunsido okazos la 3-aN de Majo.
• Mezuro; La rivero estas 50 kilometrojN longa.

Do, kun kelkaj prepozicioj oni povas uzi N-finaĵon (→ movo al direkto).
• Bonvolu legi ĉe La tuta Esperanto la lecionon 7.
+ Legi ankaŭ la 11-an lecionon (§76, §77, §78 kaj §79)

* * *

(*) 100 bazaj verboj de Esperanto

Ĝisdatigita: 2020-05-05

I don't have my Esperanto beginner's book with me right now, but I remember a section where they said that the -n replaces a preposition. Esperanto has all sorts of prepositions to describe relationships precisely, as well as je which is more vague and is often used with dates or times. In theory, we can chain prepositions together if we have to.

* Mi respondis al vi. = I responded to you.
* Mi vizitos kun ŝi je lundo. = I will visit with her in a way that involves Monday.
* Mi legis je viaj libroj. = I was reading in a way that involves your books.
* La ŝtono falis al en la rivero. = The stone fell into the river.
* La rivero estas longa je 50 kilometroj. = The river is long in a way that involves 50 kilometers.

As a convenience, we can replace the first preposition in a phrase with the -n. It tends to happen in places where English just wouldn't bother with a preposition (or with some wordy equivalent to je).

* Mi respondis vin. = I answered you.
* Mi vizitos ŝin lundon. = I will visit her Monday.
* Mi legis viajn librojn. = I was reading your books.
* La ŝtono falis en la riveron. = The stone fell in the river.
* La rivero estas 50 kilometrojn longa. = The river is 50 kilometers long.

It just so happens that the -n is usually replacing al or je, probably because people would be too confused if it always replaced just anything. Like je, the -n mostly just has whatever meaning would be most obvious from the context. If a sentence has too many accusatives so that it would get hard to understand, we can always just replace some of them with prepositions for clarity. The -n can't go on the subject, though, because there's no preposition for that.

Common usage:
* Mi respondis vin. = I answered you.
* Mi vizitos ŝin lunde. = I will visit her Monday.
* Mi legis viajn librojn. = I was reading your books.
* La ŝtono falis en la riveron. = The stone fell in the river.
* La rivero estas 50 kilometrojn longa. = The river is 50 kilometers long.

Mi legis je viaj libroj.
La ŝtono falis al en la rivero.

These two are just wrong.

sergejm:* Mi respondis vin. = I answered you.

Mi respondis al vi la demandon.

La afero repondita en akuzativo kaj la persono, al kiu oni repondas, kun la prepozicio "al".