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<div class="moz-cite-prefix">On 2/14/2018 7:19 PM, Newberry wrote:<br>

</div>

<blockquote type="cite" cite="mid:p62n8a$r58$***@dont-email.me">Pete

Olcott wrote:

<br>

<blockquote type="cite">On 2/14/2018 11:27 AM, Newberry wrote:

<br>

<blockquote type="cite">On Wednesday, February 14, 2018 at

8:56:41 AM UTC-8, Pete Olcott wrote:

<br>

<blockquote type="cite">On 2/14/2018 10:48 AM, Newberry wrote:

<br>

<blockquote type="cite">Pete Olcott wrote:

<br>

<blockquote type="cite">On 2/14/2018 1:53 AM, Newberry

wrote:

<br>

<blockquote type="cite">Pete Olcott wrote:

<br>

<blockquote type="cite">On 2/13/2018 11:26 PM,

Newberry wrote:

<br>

<blockquote type="cite">Pete Olcott wrote:

<br>

<blockquote type="cite">On 2/13/2018 8:15 PM,

Newberry wrote:

<br>

<blockquote type="cite">Pete Olcott wrote:

<br>

<blockquote type="cite">On 2/13/2018 12:18 PM,

Jim Burns wrote:

<br>

<blockquote type="cite">On 2/12/2018 9:52

PM, Pete Olcott wrote:

<br>

<blockquote type="cite">On 2/12/2018 12:55

PM, Richard Tobin wrote: <br> <blockquote type="cite">In article <a class="moz-txt-link-rfc2396E" href="mailto:UIGdnZNYXKRiXhzHnZ2dnUU7-***@giganews.com"><UIGdnZNYXKRiXhzHnZ2dnUU7-***@giganews.com></a>,

<br>

Pete Olcott� <a class="moz-txt-link-rfc2396E" href="mailto:***@NoEmail.address"><***@NoEmail.address></a> wrote:

<br>

</blockquote>

</blockquote>

<br>

<blockquote type="cite">

<blockquote type="cite">

<blockquote type="cite">Since an

expression X of language L is not a

statement of

<br>

language L unless and until it is

proven to be True or

<br>

False in L, every statement of

language L can be proved

<br>

or disproved in L.

<br>

</blockquote>

<br>

So your language varies over time?

<br>

</blockquote>

</blockquote>

<br>

<blockquote type="cite">I am not saying

that.

<br>

</blockquote>

<br>

When you say

<br>

"expressions ... do not count ...

until after ... ",

<br>

you are saying that.

<br>

<br>

<blockquote type="cite">I am saying that

expressions of language do not count as

<br>

statements of language until after they

have been proven

<br>

True or False.

<br>

</blockquote>

<br>

For a wide range of theories T, there is a

closed formula

<br>

G_T for which it has been proved

<br>

T |- G_T <->

~Ex:Proof_T(x,[G_T])

<br>

</blockquote>

<br>

All of those proofs are necessarily

semantically incorrect.

<br>

<br>

When-so-ever any closed WFF X of any

language L is evaluated

<br>

for True or False this semantically requires

a formal proof

<br>

from X to expressions T of language L that

have been defined

<br>

to have the semantic property of True.

<br>

<br>

There cannot possibly be a complete

inference chain from an

<br>

expression X of language L that makes

~Provable(L, X) true

<br>

because both True and False are only defined

as provable

<br>

from T.

<br>

</blockquote>

<br>

That is what Gödel's theorem says, that there

is no chain of

<br>

inferences that either prove or disprove G.

Why do you keep

<br>

saying

<br>

you

<br>

refuted it?

<br>

</blockquote>

<br>

To claim that an expression of language is True

or False

<br>

without being

<br>

provably True or False is religion not logic.

<br>

</blockquote>

<br>

Gödel's first theorem does not make any such

claim. It says that

<br>

there

<br>

are unprovable and undisprovable closed WFFs in

the language of PA.

<br>

<br>

</blockquote>

<br>

Yet by definition all closed WFF must evaluate to

True or False

<br>

</blockquote>

<br>

Well, Gödel proved that there are undecidable closed

WFFs in the

<br>

language of PA. You are saying that it would imply

that such WFFs are

<br>

neither true nor false, and that is impossible.

<br>

<br>

So you are making two claims

<br>

1) true = provable

<br>

2) Closed WFF that is neither true nor false cannot

possibly exist

<br>

<br>

So there must be an error in Gödel's proof somewhere,

but you do not

<br>

know where.

<br>

<br>

<br>

</blockquote>

<br>

True is a certain kind of provable.

<br>

Closed WFF that is neither true nor false is wrong.

<br>

</blockquote>

<br>

It may well be wrong. But why do you assert it does not

exist?

<br>

<br>

</blockquote>

<br>

I never asserted that it does not exist. The intersection of

<br>

the set of closed WFF of L that do not evaluate to True or

False

<br>

and the set of WFF that are statements of L is the empty

set.

<br>

<br>

Semantically incorrect finite strings do exist, I never said

that

<br>

they do not.

<br>

</blockquote>

<br>

According to you T/F = provable/refutable. And you are saying

that

<br>

there are closed WFFs that are neither provable nor refutable.

Is that

<br>

correct?

<br>

<br>

</blockquote>

<br>

You said it incorrectly.

<br>

T/F → provable/refutable

<br>

</blockquote>

<br>

T cannot be a proper subset of provable because the system would

be unsound.

<br>

<br>

</blockquote>

<b></b><br>

<b>Provable(L, X) means:</b><b><br>

</b>For expression X of language L, that there exists a formal proof

from <br>

expression X of language L to expression Y of language L. <br>

<br>

<b>True(L, X) means: </b><b><br>

</b>For expression X of language L, that there exists a formal proof

from <br>

expression X of language L to expression Y of language L <font

size="+1"><b><br>

and expression Y of language L is a member of T. </b></font><br>

<br>

<br>

<blockquote type="cite" cite="mid:p62n8a$r58$***@dont-email.me">

<blockquote type="cite">Here is a closed WFF that is not provable

or refutable:

<br>

Liar-Paradox ≡ ~True(Liar-Paradox) // HOL with self-reference

semantics

<br>

</blockquote>

<br>

Gödel's sentence is also a closed WFF that is not provable or

refutable. Why do you have a problem with that?

<br>

<br>

</blockquote>

<br>

To see exactly why Gödel is incorrect only requires understanding <br>

exactly why the Liar Paradox is incorrect and exactly how the Liar <br>

Paradox is analogous to the 1931 GIT. <br>

<br>

Copyright 2018 (and other years) Pete Olcott <br>

<br>

<div class="moz-signature">-- <br>

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<font face="Segoe UI Symbol, sans-serif"><font size="2"><b>

∀X True(X) ↔ ∃Γ ⊆ Axioms Provable(Γ, X) </b></font>

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