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

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.

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.

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"?

--
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.