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

On 11/9/2024 11:27 AM, joes wrote:

Am Sat, 09 Nov 2024 11:09:02 -0600 schrieb olcott:

On 11/9/2024 10:04 AM, joes wrote:

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.

Gödel had a different f-cking basis.

Where is the difference?
 

True is only provable from axioms
thus ~Provable(PA, G) == ~True(PA, G)

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.

It is not any less powerful than PA in the same f-cking way that ZFC is
not less powerful than naive set theory.

Then it is incomplete or inconsistent.
 

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.

 ^
 

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"?

 Open question.
 

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

How does your newsreader mark quotes?

Instead of replying immediately after my comment, skip a line. Leave a
freaking blank line inbetween.

Does your reader not 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.

https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously is
also syntactically well formed and semantic gibberish.

"This sentence is true" however has a welldefined meaning.
 

No it does f-cking not. WTF is it true about?

Gödels sentence isn’t exactly this, because formal systems don’t speak.
It is just a number that happens to encode itself.

Richard Montague's formal system speaks complete English.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer