I was just watching a linguistics video in which it was stated that in the sentence "John loves Mary", the verb love requires the direct object Mary, implying that it would be incorrect to say simply "John loves". Now, what if I, a native speaker of English, disagree with this assertion? I think "John loves" is a perfectly good sentence. It means he loves in general.
Similarly, I think the sentence "I am" is complete, without any complement. I've seen this sentence often enough and it means I exist.
Now, I can foresee your responses: sentences such as "I am" and "John loves" are spiritual and poetic. So what if they are? Is the aim of linguistics to ban poetry?
I don't mean to be antagonistic, but I'm having some difficulty penetrating into the linguistic way of thinking.
A side note: I have seen it written in several places that a verb can be "both transitive and intransitive". How can this be? If a transitive verb is a verb that accepts an object, and an intransitive verb is one that does not, then these categories are mutually exclusive.