[CL] Why Don't We Need Free Variables?
Randall R Schulz
rschulz at sonic.net
Tue Aug 2 08:34:06 CDT 2005
On Tuesday 02 August 2005 01:11, you wrote:
> >Why must formulas that do not in themselves express a truth value be
> 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
It seems you've made an excessively limiting assumption that formulas
are to be asserted and nothing else.
More information about the CL