[FOM] explicit variables

[Jim Hardy]

I don't know of a literature that asks the question in the way that you do,
as significance of marking the free variable or not, but there is a
literature on the semantic significance of free variables.  In that light,
free variables are often taken as somewhat akin to pronouns in natural
language.  The theories regarding their semantic significance are quite
disparate ranging from claiming that they have no significance of themselves
all the way to claims that free variables refer to variable or arbitrary
objects.  If this literature would be helpful, I'd be happy to list some
references or provide a précis.

Jim Hardy

Thomas Forster asked:


  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.