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John - Can we precisely define number '0' or '1' or a 'whole number' so that majority of people who read english language but not necessarily any particular math-logic will agree to it as representing TRUTH?
- How can we then state 2+2 = 4, except conceptually unless list items in point one above are established to be TRUE?
Regards. Ravi
On Fri, Jun 29, 2012 at 12:52 PM, John F Sowa <sowa@xxxxxxxxxxx> wrote:
Ron and Chris,
A major reason for using a formal logic is that the syntactic
conventions help to sort out the metalevels. I have to apologize
for not getting them right in my previous emails. I'll make more
of an effort to get them straight in this one.
RW
> I am still trying figure out how
>
> 'p' is true if and only if p.
>
> changes what I thought I knew before I read that line and the endless
> discussion preceding and following its appearance.
As Chris said, that principle doesn't say anything new. It merely
states the normal convention that everybody uses when they use
the word 'true'.
But there are many issues about the word 'truth' that philosophers
have been debating for centuries. One issue is whether there exists
something real that is called Truth.
Nominalists such as Quine try to eliminate abstract entities such
as whatever the word 'truth' might denote. They would say that
'truth' is an empty noun formed from the adjective 'true', and
the word 'true' is nothing more than a convention defined by
the pattern of that formula above.
In any case, I'd like to comment on the question of metalevels.
Common Logic, as defined by the ISO standard, does not support
metalevel language. But the IKL extensions to CL added a keyword
'that' for expressing metalanguage.
For example, the sentence "Bob knows that two plus two equals four"
would be represented in IKL by a sentence such as the following:
(knows Bob (that (= 4 (+ 2 2 ))))
In this example, the object level statement is (= 4 (+ 2 2)).
The keyword 'that' is a kind of quote that enables metalevel statements
about the nested proposition. The example says Bob knows it.
--
Thanks.
Ravi
(Dr. Ravi Sharma)
313 204 1740 Mobile
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