“This looks like him” or “This looks like he”? [duplicate]

Question

This question already has an answer here:

• “like I” or “like me”? 5 answers

Another, easier case question:

Obviously, of the two variants

This looks like him

and

This looks like he

the first seems more naturally idiomatic. However, is it grammatically correct?

I think the not-necessarily-separable questions at work here are:

• Whether "to look like" is a linking verb in English ("This looks [~to be] he") (likely it is);

• Whether "to look like" is an idiographic construction following its own rules, or rather an ellipticization or reduction of, say "This looks like [it is] he" or "This looks like he [looks (/does)]."

...The only doubt in my mind about whether "This looks like he" is correct is the Columbia Guide citation here, which argues:

Than is both a subordinating conjunction, as in She is wiser than I am, and a preposition, as in She is wiser than me. As subject of the clause introduced by the conjunction than, the pronoun must be nominative, and as object of the preposition than, the following pronoun must be in the objective case. Since the following verb am is often dropped or “understood,” we regularly hear than I and than me.

Is there a linguistic basis for the Columbia Guide's assertion, as there clearly is for the alternative? Or is this simply an argument between prescriptivism, realism, and second-wave prescriptivism?

Cf. "He plays like I" "I do it better than she"

Answer 1

As 'like' is a preposition here, the pronoun after it must be 'him'.

See an example from Merriam-Webster's Dictionary:

like  preposition

:typical of

// was like him to do that

According to Cambridge Dictionary:

LIKE preposition

Like means ‘similar to’.

We often use it with verbs of the senses such as look, sound, feel, taste, seem:

My sister is like my mother. (My sister and my mother are similar)