[FOM] explicit variables

[Thomas Forster]

Dear Colleagues,

   One of my CS colleagues was asking me today about a notational point,
and the brief literature search i have just done on the books on my
shelves has not turned up an answer: it occurs to me that this is the sort
of thing list members might know about.

  The question was: is there a literature about the possible significance
of making explicit in a letter which stands for a formula in predicate
logic the variables which are free in the formula?  I mean: sometimes we
write `F(x)' to indicate that the formula that the named string will stand
for (or which will be substituted for it) has the variable `x' free in it.  
In other settings we don't make the free variables explicit in this way.

I thought that this is the kind of thing Quine would have written about, 
if anyone did.  I've just looked in my copies of Mathematical Logic, 
Methods of Logic and Elementary Logic but drawn a blank. 

   Does anyone know of useful discussions on this point..?

            tf
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