With verbs without the -ig- or -iĝ- infix, how do I know they are transitive?
For example, boli doesn't explicitly say it does not take an object, and you need to know its counterpart (boligi) in order to understand when to use each.
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Unfortunately one has to memorize this. But it is not as hard as it seems. You already have to memorize the precise meaning of a verb and transitivity or intransitivity is part of its meaning. The trouble is when a verb in another language (such as English) is both transitive and intransitive and is given as a translation in the dictionary. "boli" is an example of this being translated to an english verb that is both transitive and intransitive (as are many verbs in English). But the word "morti" is translated as "die" and that is clearly intransitive. The word "mortigi" is "kill", which is transitive.
The idea is that Esperanto is precise, so a verb should only have one specific meaning, unlike in English. And that means in Esperanto it should either be the transitive meaning or the intransitive meaning and that is fixed. In English if you yell "I burn" you could either be a barbarian running around ancient Rome burning it to the ground during one of its sackings, or you could be the Roman, running around being burned by those barbarians. In Esperanto, we would know who you are: The barbarian yells "Mi bruligas" and the Roman yells "Mi brulas".
Other natural languages already distinguish the meanings. For example in Czech, "bruli" is "hořet" and "bruligi" is "pálit". Similarly, "boli" does not have an equivalent in Czech, you have to use the transitive "vařit" with a reflexive pronoun, so "vařit se". So a person studying from the Czech dictionary would not have a problem with transitivity of either bruli or boli. Of course a Czech speaker would have other problem verbs.