In the sentence, "He loves to travel," "to travel" is described as a nonfinite clause (source). However, one of the rules regarding clauses is that they must at least contain a subject and a verb. So how can "to travel" be a clause? Or is the subject of "to travel" implied? And, why isn't "to travel" a prepositional phrase?
As you note, a clause is defined as a group of words with a subject and a predicate, but it's argued that infinitives, as in your examples, can function as clauses by taking nonovert subjects. From the Wikipedia article on clauses
"Some modern theories of syntax take many to-infinitives to be constitutive of non-finite clauses. This stance is supported by the clear predicate status of many to-infinitives. It is challenged, however, by the fact that to-infinitives do not take an overt subject, e.g.
She refuses to consider the issue. He attempted to explain his concerns.
The to-infinitives to consider and to explain clearly qualify as predicates (because they can be negated). They do not, however, take overt subjects. The subjects she and he are dependents of the matrix verbs refuses and attempted, respectively, not of the to-infinitives. Data like these are often addressed in terms of control. The matrix predicates refuses and attempted are control verbs; they control the embedded predicates consider and explain, which means they determine which of their arguments serves as the subject argument of the embedded predicate. Some theories of syntax posit the null subject PRO (i.e. pronoun) to help address the facts of control constructions, e.g. She refuses PRO to consider the issue. He attempted PRO to explain his concerns. With the presence of PRO as a null subject, to-infinitives can be construed as complete clauses, since both subject and predicate are present."
Apparently not everyone agrees with this syntactical prestidigitation.
"One must keep in mind, though, that PRO-theory is particular to one tradition in the study of syntax and grammar (Government and Binding Theory, Minimalist Program). Other theories of syntax and grammar (e.g. Head-Driven Phrase Structure Grammar, Construction Grammar, dependency grammar) reject the presence of null elements such as PRO, which means they are likely to reject the stance that to-infinitives constitute clauses."
As you suggest, the logical subject of the verb "travel" is "he". And the fact that "travel" is a verb is one reason why "to travel" cannot be a prepositional phrase. PP have a preposition and a NP (noun phrase).
Since ordinarily only expressions of the same grammatical category can be coordinated with "and", we can construct examples to test whether "to travel" could be a PP with a P and a NP:
*He loves to travel and in the kitchen. (so "to travel" is not a PP) *He loves to travel and the kitchen. (so "travel" is not a NP) *He loves to and in travel. (so "to" is not a P)
By definition,A nonfinite clause cannot stand on its own. It rarely includes a subject, and the verb cannot be inflected for tense or person. A nonfinite clause may serve as a subject or a complement to a verb, a preposition or a noun. Here are some examples:
To speak in class is difficult for some children. (subject)
Speaking in class is what he does best. (subject)
He loves to participate. (verb complement)
He dislikes sitting quietly. (verb complement)
Charlie smiled after answering the question. (prep complement)
Charlie is used to answering questions.
Charlie is interested in hearing the answers.
Prepared students excel in class. (modifier to subject noun)
Students encouraged by their teachers do well. (modifier to subject noun)
Now back to your question:
He loves to travel. ( verb complement)
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