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On 11/9/2024 12:35 PM, joes wrote:And makes the system NECESSARILY less powerful.Am Sat, 09 Nov 2024 11:46:42 -0600 schrieb olcott:On 11/9/2024 11:27 AM, joes wrote:Am Sat, 09 Nov 2024 11:09:02 -0600 schrieb olcott:True is only provable from axioms thus ~Provable(PA, G) == ~True(PA, G)On 11/9/2024 10:04 AM, joes wrote:Where is the difference?Am Sat, 09 Nov 2024 08:45:12 -0600 schrieb olcott:Gödel had a different f-cking basis.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:Gödel showed otherwise.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.The metatheory proves otherwise. If G were not true, ~G would need toThe meta-theory does not and never has proved otherwise.
be provable.
>
People simply stupidly assume that true in the meta-theory
is the same as true in the theory. It is not, that it merely
a stupidly false assumptions.
ZFC is neither incomplete nor inconsistent.>It is not any less powerful than PA in the same f-cking way that ZFCWhen truth is only derived by starting with truth and applying truthNo, unless your system is less powerful than PA.
preserving operations then unprovable in PA becomes untrue in PA.
Untrue means the negation is true, but ~G is also unprovable.
is not less powerful than naive set theory.
Then it is incomplete or inconsistent.
Stipulating that True(L,x) only means Provable(L,x)
from the axioms of L simply gets rid of incompleteness
and undecidability nothing else is changed.
>*This is the Liar Paradox applied to itself*
>>Within my model: Only PA can prove what is true in PA.Yes it is. If MM proves that a sentence is true in PA, thatBut, 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.
sentence is true in PA.
PA can’t prove anything about itself.
>>But MM has exactly the same axioms and rules as PA, so anythingOne single level of indirect reference CHANGES EVERYTHING. PA
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
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"?
>
This sentence is not true: "This sentence is not true" is true.
*This is the Liar Paradox applied to itself*
This sentence is not true: "This sentence is not true" is true.
*This is the Liar Paradox applied to itself*
This sentence is not true: "This sentence is not true" is true.
*This is the Liar Paradox applied to itself*
This sentence is not true: "This sentence is not true" is true.
*This is the Liar Paradox applied to itself*
This sentence is not true: "This sentence is not true" is true.
I told you this many times before and you didn't bother to notice.
I told you this many times before and you didn't bother to notice.
I told you this many times before and you didn't bother to notice.
I told you this many times before and you didn't bother to notice.
I told you this many times before and you didn't bother to notice.
This sentence has words, is true.Are you reading in plaintext?Does your reader not mark quotes?Instead of replying immediately after my comment, skip a line. Leave aCan yo please add a newline so that you comments are no buried in myHow does your newsreader mark quotes?
comments?
freaking blank line inbetween.
>>No it does f-cking not. WTF is it true about?"This sentence is not true" however has a welldefined meaning.https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously isThis sentence is not true: "This sentence is not true" is trueI think you missed some quotation marks there. The outer sentence is
because the inner sentence is nonsense gibberish.
true, but the inner is perfectly wellformed and syntactically
correct.
also syntactically well formed and semantic gibberish.
Itself?
>
This sentence is true. is infinitely recursive thus has no truth value.
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