Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct

Am Sat, 09 Nov 2024 08:45:12 -0600 schrieb olcott:

On 11/9/2024 5:01 AM, joes wrote:

Am Fri, 08 Nov 2024 18:39:34 -0600 schrieb olcott:

On 11/8/2024 6:33 PM, Richard Damon wrote:

On 11/8/24 6:36 PM, olcott wrote:

On 11/8/2024 3:59 PM, Richard Damon wrote:

On 11/8/24 4:17 PM, olcott wrote:

On 11/8/2024 12:31 PM, Richard Damon wrote:

On 11/8/24 1:08 PM, olcott wrote:

On 11/8/2024 12:02 PM, Richard Damon wrote:

On 11/8/24 12:25 PM, olcott wrote:
>

That formal systems that only apply truth preserving
operations to expressions of their formal language that have
been stipulated to be true cannot possibly be undecidable is
proven to be over-your-head on the basis that you have no
actual reasoning as a rebuttal.

Gödel showed otherwise.

That is counter-factual within my precise specification.

What Gödel did is a fact.

When truth is only derived by starting with truth and applying truth
preserving operations then unprovable in PA becomes untrue in PA.

No, unless your system is less powerful than PA.
Untrue means the negation is true, but ~G is also unprovable.

No, all you have done is shown that you don't undertstand what
you are talking about.
Godel PROVED that the FORMAL SYSTEM that his proof started in,
is unable to PROVE that the statement G, being "that no Natural
Number g, that satifies a particularly designed Primitive
Recursive Relationship" is true, but also shows (using the
Meta- Mathematics that derived the PRR for the original Formal
System) that no such number can exist.

The equivocation of switching formal systems from PA to
meta-math.

There’s no such thing happening. They are very clearly separated.

No, it just shows you don't understand how meta-systems work.

IT SHOWS THAT I KNOW IT IS STUPID TO CONSTRUE TRUE IN META-MATH AS
TRUE IN PA.

MM doesn’t even contain the same sentences as PA.

But, as I pointed out, the way Meta-Math is derived from PA,

Meta-math <IS NOT> PA.
True in meta-math <IS NOT> True in PA.

Yes it is. If MM proves that a sentence is true in PA, that sentence is
true in PA.

Within my model: Only PA can prove what is true in PA.

PA can’t prove anything about itself.

This sentence is not true: "This sentence is not true"
is only true because the inner sentence is bullshit gibberish.

It’s a perfectly wellformed sentence.

But MM has exactly the same axioms and rules as PA, so anything
established by that set of axioms and rules in MM is established in
PA too.
There are additional axioms in MM, but the rules are built
specifically

One single level of indirect reference CHANGES EVERYTHING.
PA speaks PA. Meta-math speaks ABOUT PA.
The liar paradox is nonsense gibberish except when applied to itself,
then it becomes true.

What is "the liar paradox applied to itself"?

Can yo please add a newline so that you comments are no buried in my
comments?

How does your newsreader mark quotes?

This sentence is not true: "This sentence is not true" is true because
the inner sentence is nonsense gibberish.

I think you missed some quotation marks there. The outer sentence is true,
but the inner is perfectly wellformed and syntactically correct. Anyway,
Gödels sentence isn’t exactly this, because formal systems don’t speak.
It is just a number that happens to encode itself.

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.