I can run faster than _. (1) him (2) he?
Which is correct?
You know more about this than me.
You know more about this than I.
The second sounds unnatural, but I think it is correct because a trailing know is implied.
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My guess is both are correct. The first than is used as a preposition while the second one is used as a conjunction.
Note however, to me, the first sentence means you know more about this than you know about me while the second one means you know more about this than I know about this.
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The second sentence is, indeed, the correct one. If in doubt, always try to fill in the missing words - just as you did.
If you don't, your sentences might get misinterpreted. Consider this example
The first uses than as a preposition having me as its complement. The second uses than as a conjunction to introduce the elliptical clause I (do). ‘The Cambridge Guide to English Usage’ reports that:
No one need hesitate to say You know more about this than me.