From Newsgroup: comp.lang.prolog

Well-founded proof theoretic semantics where True(L, x)
is anchored in provability from the axioms of formal
system L seems to eliminate the undecidability that
model theoretic semantics encounters when truth is
measured from outside of the formal system in a separate
model.

This is the *FORMAL* epistemology of:
"true on the basis of meaning expressed in language"
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
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From Newsgroup: comp.lang.prolog

On 1/22/26 12:40 PM, olcott wrote:

Well-founded proof theoretic semantics where True(L, x)
is anchored in provability from the axioms of formal
system L seems to eliminate the undecidability that
model theoretic semantics encounters when truth is
measured from outside of the formal system in a separate
model.

But GOdel's proof wasn't based on a truth outside the system.

The proof was based outside the system, but only about things actually
in the system.

Your problem is you don't seem to understand the rule of context, and
ignore what is actually being said.

There *IS* no number g that satisfies that relationship that he build IN
PA. There is also no proof in PA of this fact.

THere is also no proof in PA that you can't prove the fact.

THus, your "proof theoretic semanrtics" just don't know what to do about
the statement, it is outside their ability to process, and thus make the system just incomplete in its own reasoning. They can't even say it is
outside its ability, as it just can't show that either.

This is the *FORMAL* epistemology of:
"true on the basis of meaning expressed in language"

Which just can't handle mathematics, as you STILL can't explain how you
get from the meaning of the words:

The sum of the squares of the length of the two sides of a right triange
is equal to the square of the length of the hypotenuse.


So, I guess you aren't talking about the problems people actually want
to handle.


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From Newsgroup: comp.lang.prolog

On 1/22/2026 6:09 PM, Richard Damon wrote:

On 1/22/26 12:40 PM, olcott wrote:

Well-founded proof theoretic semantics where True(L, x)
is anchored in provability from the axioms of formal
system L seems to eliminate the undecidability that
model theoretic semantics encounters when truth is
measured from outside of the formal system in a separate
model.

But GOdel's proof wasn't based on a truth outside the system.

The proof was based outside the system,

Hence requiring provability in the system has
always been totally wrong-headed.
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.lang.prolog

On 1/22/26 7:15 PM, olcott wrote:

On 1/22/2026 6:09 PM, Richard Damon wrote:

On 1/22/26 12:40 PM, olcott wrote:

Well-founded proof theoretic semantics where True(L, x)
is anchored in provability from the axioms of formal
system L seems to eliminate the undecidability that
model theoretic semantics encounters when truth is
measured from outside of the formal system in a separate
model.

But GOdel's proof wasn't based on a truth outside the system.

The proof was based outside the system,

Hence requiring provability in the system has
always been totally wrong-headed.

Nope, when in the system, that is all you know.

I guess you are just admitting that proof-theoretic semantics aren't
viable to use, as you think you need to allow looking at proofs outside
the system.

and, since there is an infinite number of possible meta-systems
derivable from a given system, to talk about the non-existence of such a
proof is an unanswerable question, it means the only reliable way to
show there isn't a proof of a statement, is to show the proof of its
negation, or that the statement itself is a contradiction.

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From Newsgroup: comp.lang.prolog

On 1/24/2026 11:17 AM, Richard Damon wrote:

On 1/22/26 7:15 PM, olcott wrote:

On 1/22/2026 6:09 PM, Richard Damon wrote:

On 1/22/26 12:40 PM, olcott wrote:

Well-founded proof theoretic semantics where True(L, x)
is anchored in provability from the axioms of formal
system L seems to eliminate the undecidability that
model theoretic semantics encounters when truth is
measured from outside of the formal system in a separate
model.

But GOdel's proof wasn't based on a truth outside the system.

The proof was based outside the system,

Hence requiring provability in the system has
always been totally wrong-headed.

Nope, when in the system, that is all you know.

So you think that inside and outside are the same thing?
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.lang.prolog

On 1/24/26 12:56 PM, olcott wrote:

On 1/24/2026 11:17 AM, Richard Damon wrote:

On 1/22/26 7:15 PM, olcott wrote:

On 1/22/2026 6:09 PM, Richard Damon wrote:

On 1/22/26 12:40 PM, olcott wrote:

Well-founded proof theoretic semantics where True(L, x)
is anchored in provability from the axioms of formal
system L seems to eliminate the undecidability that
model theoretic semantics encounters when truth is
measured from outside of the formal system in a separate
model.

But GOdel's proof wasn't based on a truth outside the system.

The proof was based outside the system,

Hence requiring provability in the system has
always been totally wrong-headed.

Nope, when in the system, that is all you know.

So you think that inside and outside are the same thing?

No, but the outside can know everything about the inside, and make
things that work on the inside.

Note, in particular, the "Mathematics" of Peano Arithmatic hold in both
the bases system and the meta-math, so any property of mathematics in
the mase system is also a property in the meta-math.

Thus, the Primitive Recursive Relationship derived in the meta-math will
have exactly the same numbers satisfy it in the base system as in the meta-math.

The only really difference is that in the base system, it is just math
on numbers, but in the meta-math, the numbers are encodings of
statements, and the math is equivalent to logical operations that he
shows to actually be equivalent.
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From Newsgroup: comp.lang.prolog

On 1/24/2026 1:23 PM, Richard Damon wrote:

On 1/24/26 12:56 PM, olcott wrote:

On 1/24/2026 11:17 AM, Richard Damon wrote:

On 1/22/26 7:15 PM, olcott wrote:

On 1/22/2026 6:09 PM, Richard Damon wrote:

On 1/22/26 12:40 PM, olcott wrote:

Well-founded proof theoretic semantics where True(L, x)
is anchored in provability from the axioms of formal
system L seems to eliminate the undecidability that
model theoretic semantics encounters when truth is
measured from outside of the formal system in a separate
model.

But GOdel's proof wasn't based on a truth outside the system.

The proof was based outside the system,

Hence requiring provability in the system has
always been totally wrong-headed.

Nope, when in the system, that is all you know.

So you think that inside and outside are the same thing?

No, but the outside can know everything about the inside, and make
things that work on the inside.

Only because outside you have meta-math to
look at these things and inside you only have PA.
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.lang.prolog

On 1/24/26 2:28 PM, olcott wrote:

On 1/24/2026 1:23 PM, Richard Damon wrote:

On 1/24/26 12:56 PM, olcott wrote:

On 1/24/2026 11:17 AM, Richard Damon wrote:

On 1/22/26 7:15 PM, olcott wrote:

On 1/22/2026 6:09 PM, Richard Damon wrote:

On 1/22/26 12:40 PM, olcott wrote:

Well-founded proof theoretic semantics where True(L, x)
is anchored in provability from the axioms of formal
system L seems to eliminate the undecidability that
model theoretic semantics encounters when truth is
measured from outside of the formal system in a separate
model.

But GOdel's proof wasn't based on a truth outside the system.

The proof was based outside the system,

Hence requiring provability in the system has
always been totally wrong-headed.

Nope, when in the system, that is all you know.

So you think that inside and outside are the same thing?

No, but the outside can know everything about the inside, and make
things that work on the inside.

Only because outside you have meta-math to
look at these things and inside you only have PA.

WHich has the Natural Numbers, and thus the relationship, which is
satisfied or not.

PA HAS MATH, but apparently you do not.

I guess you are admitting that 1 + 1 = 2 is too much for your logic system.
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