No. Cogitate is both transitive and intransitive, that is we may cogitate something and cogitate about something. But we do not cogitate that... in the sense of forming an opinion about it.
When it has a subject, verb, punctuation, capitalization, a predicate, and a complete thought. A sentence is a sentence when it is handed down by a judge (or a magistrate).
A sentence is a complete clause with a subject and a finite verb. A sentence fragment is not a complete clause, but is part of a clause (often lacking the verb to make a full sentence). For instance,...