Have you ever wondered what's up with the weird word "methinks"? I mean, why isn't it just "I think"? The answer is weirder than you may think!
Old English used to have two distinct verbs, þencan 'to think' and þyncan 'to seem, appear'. They ultimately come from the same root, which explains the similarity.
(By the way, the 'þ' character is called a thorn, and it represents a "th" sound.)
In Middle English these two verbs merged together in form, so they both became "thinken", but the senses stayed mostly distinct.
The one that meant 'seem' could be used in a way that's very foreign to modern English speakers—it could appear with an object and no subject.
Specifically, it was a dative object, which was usually used for things like indirect objects and objects of some prepositions. (We don't have a distinct dative case anymore.)
So the "me" in "methinks" isn't a subject—it's a dative object. The unstated subject is "it". Taken together, it means 'it seems to me'.
German still has a lot of constructions like this—you say "mir ist kalt" to mean 'I'm cold', but literally it means 'it's cold to me'.
The Spanish verb "gustar" works the same way. "Me gusta" means 'I like' but more literally translates to '(it) is pleasing to me'.
So to make a long story short, "methinks" is not just an Olde Timey way to say "I think"—it's a rather archaic way to say "seems to me".
In practice, there's not much of a difference between "The lady doth protest too much, I think" and "The lady doth protest too much, seems to me."
But this means you can also stick other object pronouns in there, like "himthinks" and "usthinks". Methinks we should bring this back. /fin
