On Fri, June 29, 2012 16:25, ravi sharma wrote: (01)
> 1. 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? (02)
No. As John says, definitions aren't TRUE (or, for that matter, FALSE), they
just express how you use a term. (03)
If the question is about psychology instead of math, then we probably could
imprecisely define those terms so that the referred-to majority *would* (not
"will") agree to it as "representing TRUTH", if we also gave a sufficiently
vague definition of "representing TRUTH" before asking. (04)
We could also get the majority of people to agree if we paid them 100 euros
(or equivalent in their own currency). 8)# (05)
> 2. How can we then state 2+2 = 4, except conceptually unless list items
> in point one above are established to be TRUE? (06)
However, if we do define "1", "2", "3", "4", "+", and "=" in a logic, then we
can prove *in that logic* the above statement. If the logic defines TRUE, we
can prove that the above statement is TRUE (in that logic). (07)
-- doug f (08)
> 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.
>> > 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.
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> (Dr. Ravi Sharma)
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