Consider the sentence "I can run faster than 15 miles per hour." Its meaning is clear and to my eyes obviously grammatically correct. Now let me present some variations that have given me trouble for a long time.
I am faster than 15 miles per hour. – To me this is clearly incorrect. Directly comparing me to a speed doesn't seem right. We need to compare my speed to a speed, or me to another person.
I can run faster than him. – Compared to the base sentence, there is a distinct shift in meaning of the comparison. While before I named a speed faster than which I can run, now I am naming a person. It doesn't seem quite right. I realize the parts of speech can change, but my initial objection is that "him" is not a speed.
I can run faster than he. – This seems most correct to me, but still somehow feels objectionable. Is this in fact the correct way to say it? And if so, is it proper as is or need I say "... faster than he can" or even "... faster than he can run?"
I am faster than him. – With "am" instead of "can run" it now seems slightly more correct. But is it?
I am faster than he. – I'm in doubt here. It doesn't seem wrong to me to say, "I am faster than he is" or even "I am faster than he is fast." (Though I suppose that is a given since I could hardly properly compare to some other category as in "I am faster than he is smart.")
My speed is faster than his. – Hmm. This seems more proper as "my speed is greater than his."
So which of these constructions is correct and which is incorrect? Is there a general rule that I can follow?
UPDATE
The scholarly article Syntactic isomorphism and non-isomorphism under ellipsis may be of great interest to some readers!
Once we accept that the elided constituent and its antecedent can differ in form, it becomes reasonable to ask how large this difference can be. The answer in Rooth (1992), Fiengo and May (1994), Chung et al. (1995) and subsequent work is that the wiggle room is actually quite small: the elided constituent and its antecedent are allowed to differ only in the realization of inflectional morphology. Other than that, both constituents have to be syntactically and lexically isomorphic.
Answer
You find both accusative pronouns (me/him/her/them) and nominative pronouns (I/he/she/they) in this syntactic position in standard English. The forms with the nominal genitive pronouns (mine/yours/hers etc.) are a red herring because they stand for something possessed rather than the person themself.
The traditional rule for comparison with a person is that you must use nominative. However, according to my research, accusative is more common.
I searched the Corpus of Contemporary American English for this syntactic structure, followed by a comma or a period to ensure we are not looking for cases like faster than he is, with a verb following the pronoun, in which case nominative is obligatory.
There were 1046 results for the accusative pronouns and 450 for nominative pronouns, more than 2 to 1 in favor of accusative pronouns—the “traditionally wrong” form. Both forms are standard, so my advice to a writer choosing between these forms is to consider that the “traditionally correct” form is unimpeachably correct but a bit formal. Choose the form that best matches tone and formality level of your writing.
For the curious, the queries looked like this:
[jjr*] than me|him|her|us|them .|,
[jjr*] than I|he|she|we|they .|,
where[jjr*] means any comparative adjective.
Update 2011-05-23
Using the new Google Book Corpus search, I was able to construct a Google ngrams-like graph comparing these usages over time, using these two queries: accusative, nominative:
As you can see, until the late 1980s, the formal usage was more common than the informal usage. Since then, however, accusative has very rapidly eclipsed nominative, even in this corpus, which represents professionally published works.
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