FOM: 2nd-order logic

[Vann McGee]

George Boolos told me about a result about second-order logic which was 
apparently known in the literature, though not know to me. I have, 
unfortunately, lost the reference, and my memory is sketchy, but it went 
something like this: There is an exotic form of quantification with the 
following property: for any second-order sentence, one can find a logically 
equivalent sentence that uses the exotic quantifier as well as the logical 
operations from first-order logic, but doesn't use any second-order 
variables. George reported to me that Quine regarded this result as 
answering his principal objections to second-order logic.

I am hoping that someone in the fom group will know what I'm talking about 
and can give me a citation. I would be very grateful.

Yours,
Vann McGee