[CL] Why Don't We Need Free Variables?

[Randall R Schulz]

Pat,

On Tuesday 02 August 2005 01:11, you wrote:
> >...
>
> >Why must formulas that do not in themselves express a truth value be
> >excluded?
>
> Because they are not sentences. What does it mean to assert such a
> formula? What does it entail? Suppose I send you a text with an open
> sentence in it, say (P ?x). What have I conveyed to you? What
> conclusions can you draw from it? Can you infer (P a)? Or (exists
> (?y) (P ?y))? Or what??

There. That's just it. There are things to do with formulas other than 
assert them. Logicians sometimes work with open formulas. If I want to 
create software that caters to such legitimate uses and use CL to 
record and exchange such content, what am I to do?

Surely you can see that the exchange of CL content may be accompanied by 
an explicit indication that "these are facts to be asserted" and "this 
open formula is to be used as ...".

Let the software exchanging such formulas supply a dispensation for such 
formulas (I avoid the term "interpretation," which has a technical 
meaning in logic). If they're used in a context where that is 
unsuitable, then it's one error among many that the software will have 
to be able to recognize and in some way deal with without 
malfunctioning.

It seems you've made an excessively limiting assumption that formulas 
are to be asserted and nothing else.


> Pat


Randy