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

[Pat Hayes]

>Pat,
>
>On Monday 01 August 2005 22:56, Pat Hayes wrote:
>>  >...
>>  >
>>  >In any event, there are valid circumstances in which an open formula
>>  > is what's needed and intended.
>>
>>  I do not know of any that cannot be described as conventions for
>>  using names or quantifiers, both of which are provided in CL.
>
>This is an odd suggestion, given that you rejected using lexical
>patterns to distinguish variables from other named entities.

I didn't reject it. In fact, I said explicitly that it was OK for a 
dialect to do exactly that.

>And it makes no sense to use a quantifier to introduce a free variable,
>does it?

I have no idea what you mean. By definition, a free variable is one 
that is not bound by a quantifier, right?

>  > >...
>>
>>  I think it would be a serious logical mistake to allow [open formulas]
>>  in, if they really are a third category of binding. But let me
>>  suggest: if you feel that open formulas are meaningful and useful, and
>>  represent a kind of logical content, that you provide an extension to
>>  the CL model theory to explain what their truth conditions are.
>
>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??

Pat
-- 
---------------------------------------------------------------------
IHMC		(850)434 8903 or (650)494 3973   home
40 South Alcaniz St.	(850)202 4416   office
Pensacola			(850)202 4440   fax
FL 32502			(850)291 0667    cell
phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes