[FOM] explicit variables

A. Mani a_mani_sc_gs at yahoo.co.in
Sun May 21 15:23:17 EDT 2006

On Saturday 20 May 2006 20:27, Thomas Forster wrote:
>   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.
There is a lot of literature on 'schema' vs other ways of writing. Generally 
one should say what the intended interpretation is.  The distinctions are 
naturally connected with deep philosophical issues.

See for example : Savellos, E ' On Defining Identity' NDJFL 31, 3, 1990

Or Norman Martin's book on first order logic may be more useful. The 
substitution rules are particularly explicit.

The literature on the topic from philosophical viewpoints is enormous.

A. Mani
Member, Cal. Math. Soc

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