🚀 go-pugleaf

On May 4, 7:47 pm, Newberry <newberr...@gmail.com> wrote:
> We will utilize the following three definitions.
>
> Definition 1: A sentence is meaningful if and only if it is a picture
> of a possible state of affairs.
>
Irrelevant as far as logic is concerned.
>
> Definition 2: A sentence is true if and only if it corresponds to an
> actual state of affairs.
>
No. Truth *ought to be" formal provability as far as logic is
concerned. The only logic that correctly implements this idea is NAFL.
Here is the NAFL truth definition:

A sentence is true w.r. to a consistent NAFL theory T if and only if
it is a theorem of a consistent NAFL theory T*, which is the
"interpretation" of a theory T. Here T* must necessarily prove all the
axioms of T, but could possibly prove sentences undecidable in T. The
warrant for "truth" here is that both T* and T are held in the human
mind. When the human mind realizes that a particular sentence P is not
either provable or refutable (i.e., is undecidable) in the theory T,
it could possibly add P (or ~P) as an axiom to T to obtain the
interpretation T*  This is the only "actual state of affairs" that is
needed in logic.

Why is "truth" as defined above important in logic? Consider sentences
like P->Q ("If P, then Q"). What does "If P...." mean? I assert that
"If P...." is basically an axiomatic assertion of P by the human
being, which already has a theory T in mind. So if P is undecidable in
T, the human mind has created the interpretation T*, in which P is a
theorem (i..e, T*=T+P).

Thus "If P, then Q" basically asserts that Q is a theorem of T*,
assuming P is undecidable in T.

If P is provable in T, then T* must necessarily prove P and "If P,
then Q" assserts that Q is a theorem of T* (and T).

Finally, if P is refutable in T (i.e., ~P is provable in T) then "If,
P, then Q" is a theorem of T as long as P and Q are legitimate
formulas in the language of T. Here the truth of "If P, then Q" may be
interpreted as the provability of ~PvQ in T (and hence T*), which is
trivial because of the provablity of ~P in T.
>
> Definition 3: A sentence is false if its negation corresponds to an
> actual state of affairs.
>
No. A sentence P in the language of a NAFL theory T is false if its
negation satisfies the NAFL truth definition given above (i.e., ~P
must be provable in T*). This could happen via ~P being provable in T,
but that is not required.

Note that different human beings could have different interpretations
of a theory T in which either P or ~P is provable. So truth is w.r.to
a theory T and also could be w.r.to a specific human mind if P is
undecidable in T. Truth is also temporal and could change w.r.to a
given human mind, which could change the interpretation T* according
to its free will at any given time (rather than look for some "actual"
state of affairs, which is not definable w.r.to T; no matter what we
decide as "actual". Any such "reality" is simply axiomatic w.r.to T if
P is undecidable in T, and could be negated).

As long as NAFL is not acknowledged by the academic community, all
discussions of "truth" are farcical. Dishonest wheeler-dealers do not
even have the right to even utter the word "truth" and their dishonest
and irrelelvant musings on this subject as best ignored.

Regards, RS