On Tuesday, 6 December 2022 at 07:48:42 UTC+2, richar...@gmail.com wrote:
> On 12/5/22 2:17 PM, Skep Dick wrote:
> > On Monday, 5 December 2022 at 15:16:36 UTC+2, richar...@gmail.com wrote:
> >> Except that adding the axiom that negates the tautology doesn't
> >> invalidate the logic that proved the tautology, it only makes the new
> >> system with the added axiom inconsistent.
> > You are confused about the whole thing. Tautology means true in ALL possible interpretations.
> Then nothing is a tautology, as you can also totally reinterprete the
> meaning of all the symbols used in the statement.
Precisely! Nothing **IS** a tautology. The empty type is inhabited ( https://en.wikipedia.org/wiki/Empty_type )

Which is exactly the principle of explosion. There's your first principle!

From falsehood anything follows. Which is precisely where axioms follow from! NOTHING.

> Even 1 = 1 can't be tautology as = could be defined as being compose of
> exactly the same atoms in the same place, and the two 1's are written in
> different physical locations and thus not equal.
Congratulations. Now you understand the problem!

Is comparing 1 to 1 a binary; or a unary operation?

The answer to that question literally determines the truth or falsify of the "=" operator!
If you are comparing one thing (to itself) - then 1 = 1 is true.
If you are comparing two things (to each other) - then 1 = 1 is false.

How many things are you comparing when you compare 1 = 1?

> Which is about axioms, and not tautologies, so you have gone off track.
Axioms are defined as tautologies. Which is precisely the game of "pretend" and self-deception you are playing with yourself when you put yourself IN a system.

You pretend THAT your axioms (e.g excluded middle) are tautologies knowing full-well there exist other systems in which it's not the case.
So in order to call it a "tautology" you have to pretend your logic-system is the ONLY system.

Just like any religion...

On 2022-12-05 15:19:57 +0000, olcott said:

> On 12/5/2022 8:29 AM, Mikko wrote:
>> On 2022-12-04 15:20:27 +0000, olcott said:
>>
>>> On 12/4/2022 3:31 AM, Mikko wrote:
>>>> On 2022-12-03 17:34:55 +0000, olcott said:
>>>>
>>>>> If simulating halt decider H correctly simulates its input D until H
>>>>> correctly determines that its simulated D would never stop running
>>>>> unless aborted then H can abort its simulation of D and correctly
>>>>> report that D specifies a non-halting sequence of configurations.
>>>>>
>>>>> Once the above is verified to be a tautology then it can be accepted as
>>>>> an axiom for Simulating halt deciders.
>>>>
>>>> Once that is verified to be a tautology then it can (and should) be removed
>>>> from the set of axioms for Simulating halt deciders (and other axiom sets).
>>>> It is regarded as a bad style to use redundant axioms, and tautologies are
>>>> theorems of logic, thus redundant as axioms of a theory.
>>>>
>>>> Mikko
>>>>
>>>
>>> All axioms are tautologies. The only way to correctly determine that a
>>> brand new axiom has been discovered is to verify that it is a tautology.
>>
>> Not necessarily, as Richard Damon already pointed out. Of course, if you
>> wish, you can call the rest "postulates" instead of axioms. What exactly
>> is the difference between an axiom and a postulate is a matter of opinion,
>> but the most common opinion is that there is no difference, or at least
>> no important difference, and the words "axiom" and "postulate" are
>> synonymes.
>>
>> Mikko
>>
>
> With axioms and tautologies both are necessarily true thus impossibly
> false. We can know that a herd of cows is not a pile of bricks on the
> basis of the meaning of the words. These meanings are expressed as
> stipulated relations between finite strings.

There are several kinds of statements that need not be proven but can be
used in a proof anyway. Logically they are all axioms. You may choose to
call them by different words depending on how you justify them but that
is not necessary and makes no difference for logic.

Mikko

On Monday, 5 December 2022 at 17:11:56 UTC+2, olcott wrote:
> The axiom/tautology must be verified as true entirely on the basis of
> its meaning.
For as long as you keep thinking in terms of "true" and "false" any axiom you consider "true" I will happily consider "false"

> That is mere nonsense.
To demonstrate...

> When we define that a herd of cows is a pile of bricks we are wrong.
When we define that a herd of cows is a pile of bricks we are right.

Because there's no such thing as "right" or "wrong" definitions.

> When we ignore the law of non-contradiction we are wrong.
When we ignore the law of non-contradiction we are right.

Because there's no such thing as "right" or "wrong" laws of logic.

https://plato.stanford.edu/entries/dialetheism/

On Monday, 5 December 2022 at 17:25:19 UTC+2, olcott wrote:
> I am unifying (thus broadening) these concepts across formal systems and
> natural language to derive the most basic foundation of the notion of
> analytical truth.
The truth is that there is no truth.

Formal logic is synthetic, not analytic.

On 12/6/2022 5:21 AM, Mikko wrote:
> On 2022-12-05 15:19:57 +0000, olcott said:
>
>> On 12/5/2022 8:29 AM, Mikko wrote:
>>> On 2022-12-04 15:20:27 +0000, olcott said:
>>>
>>>> On 12/4/2022 3:31 AM, Mikko wrote:
>>>>> On 2022-12-03 17:34:55 +0000, olcott said:
>>>>>
>>>>>> If simulating halt decider H correctly simulates its input D until
>>>>>> H correctly determines that its simulated D would never stop
>>>>>> running unless aborted then H can abort its simulation of D and
>>>>>> correctly report that D specifies a non-halting sequence of
>>>>>> configurations.
>>>>>>
>>>>>> Once the above is verified to be a tautology then it can be
>>>>>> accepted as an axiom for Simulating halt deciders.
>>>>>
>>>>> Once that is verified to be a tautology then it can (and should) be
>>>>> removed
>>>>> from the set of axioms for Simulating halt deciders (and other
>>>>> axiom sets).
>>>>> It is regarded as a bad style to use redundant axioms, and
>>>>> tautologies are
>>>>> theorems of logic, thus redundant as axioms of a theory.
>>>>>
>>>>> Mikko
>>>>>
>>>>
>>>> All axioms are tautologies. The only way to correctly determine that a
>>>> brand new axiom has been discovered is to verify that it is a
>>>> tautology.
>>>
>>> Not necessarily, as Richard Damon already pointed out. Of course, if you
>>> wish, you can call the rest "postulates" instead of axioms. What exactly
>>> is the difference between an axiom and a postulate is a matter of
>>> opinion,
>>> but the most common opinion is that there is no difference, or at least
>>> no important difference, and the words "axiom" and "postulate" are
>>> synonymes.
>>>
>>> Mikko
>>>
>>
>> With axioms and tautologies both are necessarily true thus impossibly
>> false. We can know that a herd of cows is not a pile of bricks on the
>> basis of the meaning of the words. These meanings are expressed as
>> stipulated relations between finite strings.
>
> There are several kinds of statements that need not be proven but can be
> used in a proof anyway. Logically they are all axioms. You may choose to
> call them by different words depending on how you justify them but that
> is not necessary and makes no difference for logic.
>
> Mikko
>

An axiom is typically an expression of language that is simply assumed
to be true as the basis for a proof. When creating a brand new
axiomatic system that overturns the results of other systems simply
assuming that an axiom of this system is true is not enough.

When this brand new axiom is be proven true entirely on the basis of its
meaning thenn (then and only then) can it be accepted to overturn prior
results. The above *axiom of simulating halt deciders* is proven to be
true on the basis of its meaning.

Proving that the premise of the above axiom is fulfilled by H and D
requires treating C/x86 as a formal system having its own axioms that
are proven to be true on the basis of their meaning:

(a) A correct simulation of N steps of x86 code is any simulation that
derives the line-by-line execution trace specified by its x86 source-
code for N steps of execution.

(b) Non-terminating behavior is recognized by matching any
non-terminating behavior pattern after N steps of execution.
*Details of these two are provided in the original post*

When the simlating halt decider axiom and corresponding x86 axioms are
understood to be necessarily true then when H reports that D specifies a
non-halting sequence of configurations, H is understood to be
necessarily correct.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/6/2022 6:52 AM, Skep Dick wrote:
> On Monday, 5 December 2022 at 17:11:56 UTC+2, olcott wrote:
>> The axiom/tautology must be verified as true entirely on the basis of
>> its meaning.
> For as long as you keep thinking in terms of "true" and "false" any axiom you consider "true" I will happily consider "false"
>
>> That is mere nonsense.
> To demonstrate...
>
>> When we define that a herd of cows is a pile of bricks we are wrong.
> When we define that a herd of cows is a pile of bricks we are right.
>
> Because there's no such thing as "right" or "wrong" definitions.
>

Incoherence proves that a definition is wrong:
A cup is the same as 16 tablespoons
is the same as 48 teaspoons
is the same as three cups.

Contradiction between two definitions proves
that at least one of them is wrong.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/6/2022 6:55 AM, Skep Dick wrote:
> On Monday, 5 December 2022 at 17:25:19 UTC+2, olcott wrote:
>> I am unifying (thus broadening) these concepts across formal systems and
>> natural language to derive the most basic foundation of the notion of
>> analytical truth.
> The truth is that there is no truth.

negating itself thus proving that there is truth.

>
> Formal logic is synthetic, not analytic.

You are utterly clueless about the analytic synthetic distinction.
Any expression of language that can be proven to be true (or false)
entirely on the basis of its meaning without the need for any sense data
from the sense organs is analytic.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Tuesday, 6 December 2022 at 16:36:11 UTC+2, olcott wrote:
> Incoherence proves that a definition is wrong:
> A cup is the same as 16 tablespoons
> is the same as 48 teaspoons
> is the same as three cups.
>
> Contradiction between two definitions proves
> that at least one of them is wrong.
No, it just proves that they are mutually exclusive.

That doesn't mean "wrong". Wrongness is a moral judgment - logic doesn't deal with moral judgments.

On Tuesday, 6 December 2022 at 16:41:28 UTC+2, olcott wrote:
> On 12/6/2022 6:55 AM, Skep Dick wrote:
> > On Monday, 5 December 2022 at 17:25:19 UTC+2, olcott wrote:
> >> I am unifying (thus broadening) these concepts across formal systems and
> >> natural language to derive the most basic foundation of the notion of
> >> analytical truth.
> > The truth is that there is no truth.
> negating itself thus proving that there is truth.
No. Thus demonstrating that despite the inherent undecidability of the meaning of the sentence - you are going to to interpret it whichever way you want.
Because the interpretation of undecidable expressions is dependent on arbitrary choice.

> You are utterly clueless about the analytic synthetic distinction.
What distinction? Everything is in logic and language is synthetic.

Maths is invented. Logic is invented. Language is invented.

> Any expression of language that can be proven to be true (or false)
> entirely on the basis of its meaning without the need for any sense data
> from the sense organs is analytic.
But linguistic meaning is invented. Thus it's synthetic, not analytic.

On 12/6/2022 9:05 AM, Skep Dick wrote:
> On Tuesday, 6 December 2022 at 16:36:11 UTC+2, olcott wrote:
>> Incoherence proves that a definition is wrong:
>> A cup is the same as 16 tablespoons
>> is the same as 48 teaspoons
>> is the same as three cups.
>>
>> Contradiction between two definitions proves
>> that at least one of them is wrong.
> No, it just proves that they are mutually exclusive.
>
> That doesn't mean "wrong". Wrongness is a moral judgment - logic doesn't deal with moral judgments.
>
>

Wrong meaning incorrect.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/6/2022 9:10 AM, Skep Dick wrote:
> On Tuesday, 6 December 2022 at 16:41:28 UTC+2, olcott wrote:
>> On 12/6/2022 6:55 AM, Skep Dick wrote:
>>> On Monday, 5 December 2022 at 17:25:19 UTC+2, olcott wrote:
>>>> I am unifying (thus broadening) these concepts across formal systems and
>>>> natural language to derive the most basic foundation of the notion of
>>>> analytical truth.
>>> The truth is that there is no truth.
>> negating itself thus proving that there is truth.
> No. Thus demonstrating that despite the inherent undecidability of the meaning of the sentence - you are going to to interpret it whichever way you want.
> Because the interpretation of undecidable expressions is dependent on arbitrary choice.
>
>> You are utterly clueless about the analytic synthetic distinction.
> What distinction? Everything is in logic and language is synthetic.
>
> Maths is invented. Logic is invented. Language is invented.
>
>> Any expression of language that can be proven to be true (or false)
>> entirely on the basis of its meaning without the need for any sense data
>> from the sense organs is analytic.
> But linguistic meaning is invented. Thus it's synthetic, not analytic.
>

That is not what is meant by the analytic/synthetic distinction.
You are using the incorrect sense meaning of the terms.

Synthetic of the analytic/synthetic distinction is an idiomatic meaning
having nothing to do with synthesis.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Tuesday, 6 December 2022 at 17:27:39 UTC+2, olcott wrote:
> Wrong meaning incorrect.
Doesn't matter which word you use. Structurally correct doesn't mean behaviourally correct.

"Beware of bugs in the above code; I have only proved it correct, not tried it." --Donald Knuth

On Tuesday, 6 December 2022 at 17:32:16 UTC+2, olcott wrote:
> That is not what is meant by the analytic/synthetic distinction.
> You are using the incorrect sense meaning of the terms.
No, I am not. I am using precisely the sense I want to be using and there's nothing wrong; or incorrect about it.

> Synthetic of the analytic/synthetic distinction is an idiomatic meaning
> having nothing to do with synthesis.
I don't care what it has to do with. I reject your distinction.

On 12/6/22 10:34 AM, Skep Dick wrote:
> On Tuesday, 6 December 2022 at 17:32:16 UTC+2, olcott wrote:
>> That is not what is meant by the analytic/synthetic distinction.
>> You are using the incorrect sense meaning of the terms.
> No, I am not. I am using precisely the sense I want to be using and there's nothing wrong; or incorrect about it.

Which is precisely your logical flaw.

It doesn't matter what YOU think something means, it matters what the
agreed meaning is.

>
>> Synthetic of the analytic/synthetic distinction is an idiomatic meaning
>> having nothing to do with synthesis.
> I don't care what it has to do with. I reject your distinction.

So you reject that basis of logic.

On 12/5/22 1:50 AM, Skep Dick wrote:
> On Tuesday, 6 December 2022 at 07:48:42 UTC+2, richar...@gmail.com wrote:
>> On 12/5/22 2:17 PM, Skep Dick wrote:
>>> On Monday, 5 December 2022 at 15:16:36 UTC+2, richar...@gmail.com wrote:
>>>> Except that adding the axiom that negates the tautology doesn't
>>>> invalidate the logic that proved the tautology, it only makes the new
>>>> system with the added axiom inconsistent.
>>> You are confused about the whole thing. Tautology means true in ALL possible interpretations.
>> Then nothing is a tautology, as you can also totally reinterprete the
>> meaning of all the symbols used in the statement.
> Precisely! Nothing **IS** a tautology. The empty type is inhabited ( https://en.wikipedia.org/wiki/Empty_type )
>
> Which is exactly the principle of explosion. There's your first principle!
>
> From falsehood anything follows. Which is precisely where axioms follow from! NOTHING.

So since you start from nothing, you can get nothing,

You don't even have the empty type, as that is something

>
>> Even 1 = 1 can't be tautology as = could be defined as being compose of
>> exactly the same atoms in the same place, and the two 1's are written in
>> different physical locations and thus not equal.
> Congratulations. Now you understand the problem!
>
> Is comparing 1 to 1 a binary; or a unary operation?

Depends on Context.

>
> The answer to that question literally determines the truth or falsify of the "=" operator!
> If you are comparing one thing (to itself) - then 1 = 1 is true.
> If you are comparing two things (to each other) - then 1 = 1 is false.

Right, so Context matters.

>
> How many things are you comparing when you compare 1 = 1?
>
>> Which is about axioms, and not tautologies, so you have gone off track.
> Axioms are defined as tautologies. Which is precisely the game of "pretend" and self-deception you are playing with yourself when you put yourself IN a system.
>
> You pretend THAT your axioms (e.g excluded middle) are tautologies knowing full-well there exist other systems in which it's not the case.
> So in order to call it a "tautology" you have to pretend your logic-system is the ONLY system.
>
> Just like any religion...

ALL Knowledge comes from "religion", as Religion is really just your
picking of the First Principles you are going to work with.

And you don't need to assum your logic-system is the ONLY system, just
the system you are talking in. It is quite possible to acknoledge the
existance of other systems but still define that you are talking within
your given one.

This all seems beyond your understanding.

On 12/5/22 1:20 AM, Skep Dick wrote:
> On Tuesday, 6 December 2022 at 07:55:15 UTC+2, richar...@gmail.com wrote:
>> No, axioms are assumed true, and generally "self-evident".
>>
>> Tautologies are statements provably true by the nature of the statement
>> and not needing emperical knowledge. It is true in ALL embodyments of
>> the basic system.
> Distinction without a difference.
>
> The "law" of excluded middle is formalised as. ~p ∨ p ⇔ ⊤
> In English that spells out "~p ∨ p" is materially equivalent to a tautology.

Which only applies to a logic system that contains the law of the
excluded middle, so not all systems.

>
>> "Jack is twelve" is NOT a tautology, even if Jack happens to be twelve.
> But '"Jack is twelve" is true' is a tautology.

No, because Jack might actually be 11.

>
>> "If Jack was eleven a year ago, he now is twelve" would be a tautology
>> under the assumption that we are dealing with system with a normal
>> passage of time.
> That's most definitely not a tautology. It's a conditional.
>
> You know, because ⊤ means "unconditionally true".

So, what is the condition that the statments "If Jack as eleven a year
ago, he now is twelve" is not true?

The STATEMENT is unconditionally true, in ALL models (instances of
reality) in the system assumed.

We could even likely strengthen the statement to "ONLY if Jack wa eleven
a year ago, will he now be twelve."

On 12/6/22 9:27 AM, olcott wrote:
> On 12/6/2022 5:21 AM, Mikko wrote:
>> On 2022-12-05 15:19:57 +0000, olcott said:
>>
>>> On 12/5/2022 8:29 AM, Mikko wrote:
>>>> On 2022-12-04 15:20:27 +0000, olcott said:
>>>>
>>>>> On 12/4/2022 3:31 AM, Mikko wrote:
>>>>>> On 2022-12-03 17:34:55 +0000, olcott said:
>>>>>>
>>>>>>> If simulating halt decider H correctly simulates its input D
>>>>>>> until H correctly determines that its simulated D would never
>>>>>>> stop running unless aborted then H can abort its simulation of D
>>>>>>> and correctly report that D specifies a non-halting sequence of
>>>>>>> configurations.
>>>>>>>
>>>>>>> Once the above is verified to be a tautology then it can be
>>>>>>> accepted as an axiom for Simulating halt deciders.
>>>>>>
>>>>>> Once that is verified to be a tautology then it can (and should)
>>>>>> be removed
>>>>>> from the set of axioms for Simulating halt deciders (and other
>>>>>> axiom sets).
>>>>>> It is regarded as a bad style to use redundant axioms, and
>>>>>> tautologies are
>>>>>> theorems of logic, thus redundant as axioms of a theory.
>>>>>>
>>>>>> Mikko
>>>>>>
>>>>>
>>>>> All axioms are tautologies. The only way to correctly determine that a
>>>>> brand new axiom has been discovered is to verify that it is a
>>>>> tautology.
>>>>
>>>> Not necessarily, as Richard Damon already pointed out. Of course, if
>>>> you
>>>> wish, you can call the rest "postulates" instead of axioms. What
>>>> exactly
>>>> is the difference between an axiom and a postulate is a matter of
>>>> opinion,
>>>> but the most common opinion is that there is no difference, or at least
>>>> no important difference, and the words "axiom" and "postulate" are
>>>> synonymes.
>>>>
>>>> Mikko
>>>>
>>>
>>> With axioms and tautologies both are necessarily true thus impossibly
>>> false. We can know that a herd of cows is not a pile of bricks on the
>>> basis of the meaning of the words. These meanings are expressed as
>>> stipulated relations between finite strings.
>>
>> There are several kinds of statements that need not be proven but can be
>> used in a proof anyway. Logically they are all axioms. You may choose to
>> call them by different words depending on how you justify them but that
>> is not necessary and makes no difference for logic.
>>
>> Mikko
>>
>
> An axiom is typically an expression of language that is simply assumed
> to be true as the basis for a proof. When  creating a brand new
> axiomatic system that overturns the results of other systems simply
> assuming that an axiom of this system is true is not enough.

So if that is what yo are attempting, you need to admit that you aren't
working in the original system.

You prove yourself to be a liar.

>
> When this brand new axiom is be proven true entirely on the basis of its
> meaning thenn (then and only then) can it be accepted to overturn prior
> results. The above *axiom of simulating halt deciders* is proven to be
> true on the basis of its meaning.

Statements that can be proven true entierly on the basis of its meaning
do not NEED To be taken as axioms,

>
> Proving that the premise of the above axiom is fulfilled by H and D
> requires treating C/x86 as a formal system having its own axioms that
> are proven to be true on the basis of their meaning:

Nope, the program does NOT prove your claim.

You are shown to be a bad programmer that can't recognize your own bugs.

>
> (a) A correct simulation of N steps of x86 code is any simulation that
> derives the line-by-line execution trace specified by its x86 source-
> code for N steps of execution.

Which, since different than the definition of correct used in the
definition of a UTM, you have lost the ability to say that the correct
simulaiton of the input represents that actual behavior of the macnine
that input represents.

>
> (b) Non-terminating behavior is recognized by matching any
> non-terminating behavior pattern after N steps of execution.
> *Details of these two are provided in the original post*

Except you never prove non-terminal behavior of the actual execution of
the input, since you use the wrong definition of correct simulation.

You logic FAILS.

>
> When the simlating halt decider axiom and corresponding x86 axioms are
> understood to be necessarily true then when H reports that D specifies a
> non-halting sequence of configurations, H is understood to be
> necessarily correct.
>

Nope, You are just creting a new INCONSITANT logic system that accepts
as non-halitng inputs that actually do halt.

On Tue, 06 Dec 2022 09:11:47 -0800, Richard Damon wrote:

> On 12/5/22 1:50 AM, Skep Dick wrote:
>> On Tuesday, 6 December 2022 at 07:48:42 UTC+2, richar...@gmail.com
>> wrote:
>>> On 12/5/22 2:17 PM, Skep Dick wrote:
>>>> On Monday, 5 December 2022 at 15:16:36 UTC+2, richar...@gmail.com
>>>> wrote:
>>>>> Except that adding the axiom that negates the tautology doesn't
>>>>> invalidate the logic that proved the tautology, it only makes the
>>>>> new system with the added axiom inconsistent.
>>>> You are confused about the whole thing. Tautology means true in ALL
>>>> possible interpretations.
>>> Then nothing is a tautology, as you can also totally reinterprete the
>>> meaning of all the symbols used in the statement.
>> Precisely! Nothing **IS** a tautology. The empty type is inhabited (
>> https://en.wikipedia.org/wiki/Empty_type )
>>
>> Which is exactly the principle of explosion. There's your first
>> principle!
>>
>> From falsehood anything follows. Which is precisely where axioms
>> follow from! NOTHING.
>
> So since you start from nothing, you can get nothing,
>
> You don't even have the empty type, as that is something
>
>
>>> Even 1 = 1 can't be tautology as = could be defined as being compose
>>> of exactly the same atoms in the same place, and the two 1's are
>>> written in different physical locations and thus not equal.
>> Congratulations. Now you understand the problem!
>>
>> Is comparing 1 to 1 a binary; or a unary operation?
>
> Depends on Context.
>
>
>> The answer to that question literally determines the truth or falsify
>> of the "=" operator!
>> If you are comparing one thing (to itself) - then 1 = 1 is true.
>> If you are comparing two things (to each other) - then 1 = 1 is false.
>
> Right, so Context matters.
>
>
>> How many things are you comparing when you compare 1 = 1?
>>
>>> Which is about axioms, and not tautologies, so you have gone off
>>> track.
>> Axioms are defined as tautologies. Which is precisely the game of
>> "pretend" and self-deception you are playing with yourself when you put
>> yourself IN a system.
>>
>> You pretend THAT your axioms (e.g excluded middle) are tautologies
>> knowing full-well there exist other systems in which it's not the case.
>> So in order to call it a "tautology" you have to pretend your
>> logic-system is the ONLY system.
>>
>> Just like any religion...
>
> ALL Knowledge comes from "religion", as Religion is really just your
> picking of the First Principles you are going to work with.
>
> And you don't need to assum your logic-system is the ONLY system, just
> the system you are talking in. It is quite possible to acknoledge the
> existance of other systems but still define that you are talking within
> your given one.
>
> This all seems beyond your understanding.

Will you two idiots get a room and save us the fucking drama?

/Flibble

On Tuesday, 6 December 2022 at 19:24:01 UTC+2, richar...@gmail.com wrote:
> On 12/5/22 1:20 AM, Skep Dick wrote:
> > On Tuesday, 6 December 2022 at 07:55:15 UTC+2, richar...@gmail.com wrote:
> >> No, axioms are assumed true, and generally "self-evident".
> >>
> >> Tautologies are statements provably true by the nature of the statement
> >> and not needing emperical knowledge. It is true in ALL embodyments of
> >> the basic system.
> > Distinction without a difference.
> >
> > The "law" of excluded middle is formalised as. ~p ∨ p ⇔ ⊤
> > In English that spells out "~p ∨ p" is materially equivalent to a tautology.
> Which only applies to a logic system that contains the law of the
> excluded middle, so not all systems.
Obviously. In those logic systems it's not a tautology.

Hence the part where you have to play amnesiac and forget that a tautology has to be true in all models.

It was a misnomer all along.

> >> "Jack is twelve" is NOT a tautology, even if Jack happens to be twelve..
> > But '"Jack is twelve" is true' is a tautology.
> No, because Jack might actually be 11.
Then '"Jack is 11" is true' is a tautology.

> So, what is the condition that the statments "If Jack as eleven a year
> ago, he now is twelve" is not true?
The part after the "IF". If Jack wasn't 11 a year ago then he's not 12.

> The STATEMENT is unconditionally true, in ALL models (instances of
> reality) in the system assumed.
It's literally false in every instance of reality where Jack wasn't 11 a year ago!

> We could even likely strengthen the statement to "ONLY if Jack wa eleven
> a year ago, will he now be twelve."
Strengthen it all you want. It's a conditional - therefore not a tautology.

On Tue, 06 Dec 2022 10:16:56 -0800, Skep Dick wrote:

> On Tuesday, 6 December 2022 at 19:24:01 UTC+2, richar...@gmail.com
> wrote:
>> On 12/5/22 1:20 AM, Skep Dick wrote:
>> > On Tuesday, 6 December 2022 at 07:55:15 UTC+2, richar...@gmail.com
>> > wrote:
>> >> No, axioms are assumed true, and generally "self-evident".
>> >>
>> >> Tautologies are statements provably true by the nature of the
>> >> statement and not needing emperical knowledge. It is true in ALL
>> >> embodyments of the basic system.
>> > Distinction without a difference.
>> >
>> > The "law" of excluded middle is formalised as. ~p ∨ p ⇔ ⊤
>> > In English that spells out "~p ∨ p" is materially equivalent to a
>> > tautology.
>> Which only applies to a logic system that contains the law of the
>> excluded middle, so not all systems.
> Obviously. In those logic systems it's not a tautology.
>
> Hence the part where you have to play amnesiac and forget that a
> tautology has to be true in all models.
>
> It was a misnomer all along.
>
>> >> "Jack is twelve" is NOT a tautology, even if Jack happens to be
>> >> twelve.
>> > But '"Jack is twelve" is true' is a tautology.
>> No, because Jack might actually be 11.
> Then '"Jack is 11" is true' is a tautology.
>
>> So, what is the condition that the statments "If Jack as eleven a year
>> ago, he now is twelve" is not true?
> The part after the "IF". If Jack wasn't 11 a year ago then he's not 12.
>
>> The STATEMENT is unconditionally true, in ALL models (instances of
>> reality) in the system assumed.
> It's literally false in every instance of reality where Jack wasn't 11 a
> year ago!
>
>> We could even likely strengthen the statement to "ONLY if Jack wa
>> eleven a year ago, will he now be twelve."
> Strengthen it all you want. It's a conditional - therefore not a
> tautology.

Get a fucking room already.

/Flibble

On 12/6/22 1:16 PM, Skep Dick wrote:
> On Tuesday, 6 December 2022 at 19:24:01 UTC+2, richar...@gmail.com wrote:
>> On 12/5/22 1:20 AM, Skep Dick wrote:
>>> On Tuesday, 6 December 2022 at 07:55:15 UTC+2, richar...@gmail.com wrote:
>>>> No, axioms are assumed true, and generally "self-evident".
>>>>
>>>> Tautologies are statements provably true by the nature of the statement
>>>> and not needing emperical knowledge. It is true in ALL embodyments of
>>>> the basic system.
>>> Distinction without a difference.
>>>
>>> The "law" of excluded middle is formalised as. ~p ∨ p ⇔ ⊤
>>> In English that spells out "~p ∨ p" is materially equivalent to a tautology.
>> Which only applies to a logic system that contains the law of the
>> excluded middle, so not all systems.
> Obviously. In those logic systems it's not a tautology.

Right, "Tautology" is a lable that applies to a statement in the systems
it applies to.

>
> Hence the part where you have to play amnesiac and forget that a tautology has to be true in all models.

All Models, not all systems.

You don't seem to understand the difference.

>
> It was a misnomer all along.

Seems to be a misunderstanding of your part.

>
>>>> "Jack is twelve" is NOT a tautology, even if Jack happens to be twelve.
>>> But '"Jack is twelve" is true' is a tautology.
>> No, because Jack might actually be 11.
> Then '"Jack is 11" is true' is a tautology.
>
>> So, what is the condition that the statments "If Jack as eleven a year
>> ago, he now is twelve" is not true?
> The part after the "IF". If Jack wasn't 11 a year ago then he's not 12.
>
>> The STATEMENT is unconditionally true, in ALL models (instances of
>> reality) in the system assumed.
> It's literally false in every instance of reality where Jack wasn't 11 a year ago!

Nope. You don't understand the meaning of the statement then.

>
>> We could even likely strengthen the statement to "ONLY if Jack wa eleven
>> a year ago, will he now be twelve."
> Strengthen it all you want. It's a conditional - therefore not a tautology.

Nope, you don't seem to understand the stateent.

Seems normal for you.

On 12/6/2022 11:30 AM, Richard Damon wrote:
> On 12/6/22 9:27 AM, olcott wrote:
>> On 12/6/2022 5:21 AM, Mikko wrote:
>>> On 2022-12-05 15:19:57 +0000, olcott said:
>>>
>>>> On 12/5/2022 8:29 AM, Mikko wrote:
>>>>> On 2022-12-04 15:20:27 +0000, olcott said:
>>>>>
>>>>>> On 12/4/2022 3:31 AM, Mikko wrote:
>>>>>>> On 2022-12-03 17:34:55 +0000, olcott said:
>>>>>>>
>>>>>>>> If simulating halt decider H correctly simulates its input D
>>>>>>>> until H correctly determines that its simulated D would never
>>>>>>>> stop running unless aborted then H can abort its simulation of D
>>>>>>>> and correctly report that D specifies a non-halting sequence of
>>>>>>>> configurations.
>>>>>>>>
>>>>>>>> Once the above is verified to be a tautology then it can be
>>>>>>>> accepted as an axiom for Simulating halt deciders.
>>>>>>>
>>>>>>> Once that is verified to be a tautology then it can (and should)
>>>>>>> be removed
>>>>>>> from the set of axioms for Simulating halt deciders (and other
>>>>>>> axiom sets).
>>>>>>> It is regarded as a bad style to use redundant axioms, and
>>>>>>> tautologies are
>>>>>>> theorems of logic, thus redundant as axioms of a theory.
>>>>>>>
>>>>>>> Mikko
>>>>>>>
>>>>>>
>>>>>> All axioms are tautologies. The only way to correctly determine
>>>>>> that a
>>>>>> brand new axiom has been discovered is to verify that it is a
>>>>>> tautology.
>>>>>
>>>>> Not necessarily, as Richard Damon already pointed out. Of course,
>>>>> if you
>>>>> wish, you can call the rest "postulates" instead of axioms. What
>>>>> exactly
>>>>> is the difference between an axiom and a postulate is a matter of
>>>>> opinion,
>>>>> but the most common opinion is that there is no difference, or at
>>>>> least
>>>>> no important difference, and the words "axiom" and "postulate" are
>>>>> synonymes.
>>>>>
>>>>> Mikko
>>>>>
>>>>
>>>> With axioms and tautologies both are necessarily true thus
>>>> impossibly false. We can know that a herd of cows is not a pile of
>>>> bricks on the basis of the meaning of the words. These meanings are
>>>> expressed as stipulated relations between finite strings.
>>>
>>> There are several kinds of statements that need not be proven but can be
>>> used in a proof anyway. Logically they are all axioms. You may choose to
>>> call them by different words depending on how you justify them but that
>>> is not necessary and makes no difference for logic.
>>>
>>> Mikko
>>>
>>
>> An axiom is typically an expression of language that is simply assumed
>> to be true as the basis for a proof. When  creating a brand new
>> axiomatic system that overturns the results of other systems simply
>> assuming that an axiom of this system is true is not enough.
>
> So if that is what yo are attempting, you need to admit that you aren't
> working in the original system.
>
> You prove yourself to be a liar.
>
>>
>> When this brand new axiom is be proven true entirely on the basis of its
>> meaning thenn (then and only then) can it be accepted to overturn prior
>> results. The above *axiom of simulating halt deciders* is proven to be
>> true on the basis of its meaning.
>
> Statements that can be proven true entierly on the basis of its meaning
> do not NEED To be taken as axioms,
>

If they are to be used as the basis of a proof that overturns
conventional wisdom then they are being used as axioms.

Mentioning that it is true on the basis of its meaning causes people
that are interested in truth to verify that it is true on this basis,
otherwise they would not bother and thus be unaware of its truth.

>>
>> Proving that the premise of the above axiom is fulfilled by H and D
>> requires treating C/x86 as a formal system having its own axioms that
>> are proven to be true on the basis of their meaning:
>
> Nope, the program does NOT prove your claim.
>
> You are shown to be a bad programmer that can't recognize your own bugs.
>
>>
>> (a) A correct simulation of N steps of x86 code is any simulation that
>> derives the line-by-line execution trace specified by its x86 source-
>> code for N steps of execution.
>
> Which, since different than the definition of correct used in the
> definition of a UTM, you have lost the ability to say that the correct
> simulaiton of the input represents that actual behavior of the macnine
> that input represents.

It is generally the case that when the line-by-line execution trace of a
simulation of a machine description exactly matches the line-by-line
steps specified by this machine description that this simulation is
proved to be correct.

The exact same non-terminating behavior pattern specified by the
correctly simulated D of H(D,D) is precisely matched by the Peter Linz
correctly simulated Ĥ of embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩. (page 4)

*Simulating Halt Decider Applied to the Halting Theorem*
https://www.researchgate.net/publication/364657019_Simulating_Halt_Decider_Applied_to_the_Halting_Theorem

>>
>> (b) Non-terminating behavior is recognized by matching any
>> non-terminating behavior pattern after N steps of execution.
>> *Details of these two are provided in the original post*
>
> Except you never prove non-terminal behavior of the actual execution of
> the input, since you use the wrong definition of correct simulation.
>
> You logic FAILS.
>
>>
>> When the simlating halt decider axiom and corresponding x86 axioms are
>> understood to be necessarily true then when H reports that D specifies a
>> non-halting sequence of configurations, H is understood to be
>> necessarily correct.
>>
>
> Nope, You are just creting a new INCONSITANT logic system that accepts
> as non-halitng inputs that actually do halt.
>

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/6/22 2:33 PM, olcott wrote:
> On 12/6/2022 11:30 AM, Richard Damon wrote:
>> On 12/6/22 9:27 AM, olcott wrote:
>>> On 12/6/2022 5:21 AM, Mikko wrote:
>>>> On 2022-12-05 15:19:57 +0000, olcott said:
>>>>
>>>>> On 12/5/2022 8:29 AM, Mikko wrote:
>>>>>> On 2022-12-04 15:20:27 +0000, olcott said:
>>>>>>
>>>>>>> On 12/4/2022 3:31 AM, Mikko wrote:
>>>>>>>> On 2022-12-03 17:34:55 +0000, olcott said:
>>>>>>>>
>>>>>>>>> If simulating halt decider H correctly simulates its input D
>>>>>>>>> until H correctly determines that its simulated D would never
>>>>>>>>> stop running unless aborted then H can abort its simulation of
>>>>>>>>> D and correctly report that D specifies a non-halting sequence
>>>>>>>>> of configurations.
>>>>>>>>>
>>>>>>>>> Once the above is verified to be a tautology then it can be
>>>>>>>>> accepted as an axiom for Simulating halt deciders.
>>>>>>>>
>>>>>>>> Once that is verified to be a tautology then it can (and should)
>>>>>>>> be removed
>>>>>>>> from the set of axioms for Simulating halt deciders (and other
>>>>>>>> axiom sets).
>>>>>>>> It is regarded as a bad style to use redundant axioms, and
>>>>>>>> tautologies are
>>>>>>>> theorems of logic, thus redundant as axioms of a theory.
>>>>>>>>
>>>>>>>> Mikko
>>>>>>>>
>>>>>>>
>>>>>>> All axioms are tautologies. The only way to correctly determine
>>>>>>> that a
>>>>>>> brand new axiom has been discovered is to verify that it is a
>>>>>>> tautology.
>>>>>>
>>>>>> Not necessarily, as Richard Damon already pointed out. Of course,
>>>>>> if you
>>>>>> wish, you can call the rest "postulates" instead of axioms. What
>>>>>> exactly
>>>>>> is the difference between an axiom and a postulate is a matter of
>>>>>> opinion,
>>>>>> but the most common opinion is that there is no difference, or at
>>>>>> least
>>>>>> no important difference, and the words "axiom" and "postulate" are
>>>>>> synonymes.
>>>>>>
>>>>>> Mikko
>>>>>>
>>>>>
>>>>> With axioms and tautologies both are necessarily true thus
>>>>> impossibly false. We can know that a herd of cows is not a pile of
>>>>> bricks on the basis of the meaning of the words. These meanings are
>>>>> expressed as stipulated relations between finite strings.
>>>>
>>>> There are several kinds of statements that need not be proven but
>>>> can be
>>>> used in a proof anyway. Logically they are all axioms. You may
>>>> choose to
>>>> call them by different words depending on how you justify them but that
>>>> is not necessary and makes no difference for logic.
>>>>
>>>> Mikko
>>>>
>>>
>>> An axiom is typically an expression of language that is simply assumed
>>> to be true as the basis for a proof. When  creating a brand new
>>> axiomatic system that overturns the results of other systems simply
>>> assuming that an axiom of this system is true is not enough.
>>
>> So if that is what yo are attempting, you need to admit that you
>> aren't working in the original system.
>>
>> You prove yourself to be a liar.
>>
>>>
>>> When this brand new axiom is be proven true entirely on the basis of its
>>> meaning thenn (then and only then) can it be accepted to overturn prior
>>> results. The above *axiom of simulating halt deciders* is proven to
>>> be true on the basis of its meaning.
>>
>> Statements that can be proven true entierly on the basis of its
>> meaning do not NEED To be taken as axioms,
>>
>
> If they are to be used as the basis of a proof that overturns
> conventional wisdom then they are being used as axioms.

Then you aren't working in the original field, as fields are defined by
the axiom that they are built on.

>
> Mentioning that it is true on the basis of its meaning causes people
> that are interested in truth to verify that it is true on this basis,
> otherwise they would not bother and thus be unaware of its truth.
>

No, your claim that it it is from the meaning of the words is just an
attempt to cover the fact that you can't actually PROVE them from the
actual meaning of the words.

As I pointed out, you are using two different, and incompatible,
meanings of correct simulation to bridge fr0m what H does and what a UTM
shows.

This makes your logic invalid.

>>>
>>> Proving that the premise of the above axiom is fulfilled by H and D
>>> requires treating C/x86 as a formal system having its own axioms that
>>> are proven to be true on the basis of their meaning:
>>
>> Nope, the program does NOT prove your claim.
>>
>> You are shown to be a bad programmer that can't recognize your own bugs.
>>
>>>
>>> (a) A correct simulation of N steps of x86 code is any simulation that
>>> derives the line-by-line execution trace specified by its x86 source-
>>> code for N steps of execution.
>>
>> Which, since different than the definition of correct used in the
>> definition of a UTM, you have lost the ability to say that the correct
>> simulaiton of the input represents that actual behavior of the macnine
>> that input represents.
>
> It is generally the case that when the line-by-line execution trace of a
> simulation of a machine description exactly matches the line-by-line
> steps specified by this machine description that this simulation is
> proved to be correct.

No. That is a correct PARTIAL simulation.

The definiton you want to use to show simulation matchs to the direct
behavior requires COMPLETE correct simulation.

That is like saying you have correctly assembled a jig saw puzzle
because you have correctly put together a couple of the pieces of the set.

>
> The exact same non-terminating behavior pattern specified by the
> correctly simulated D of H(D,D) is precisely matched by the Peter Linz
> correctly simulated Ĥ of embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩. (page 4)

Nope. You "claimed" non-terminating behavior pattern is NOT correct, and
you have never even attempted to prove that it is.

YOU FAIL.

>
> *Simulating Halt Decider Applied to the Halting Theorem*
> https://www.researchgate.net/publication/364657019_Simulating_Halt_Decider_Applied_to_the_Halting_Theorem

A bunchn of garbage.

YOU FAIL.

You show that you don't understand the basics of logic or proof.

>
>
>>>
>>> (b) Non-terminating behavior is recognized by matching any
>>> non-terminating behavior pattern after N steps of execution.
>>> *Details of these two are provided in the original post*
>>
>> Except you never prove non-terminal behavior of the actual execution
>> of the input, since you use the wrong definition of correct simulation.
>>
>> You logic FAILS.
>>
>>>
>>> When the simlating halt decider axiom and corresponding x86 axioms are
>>> understood to be necessarily true then when H reports that D specifies a
>>> non-halting sequence of configurations, H is understood to be
>>> necessarily correct.
>>>
>>
>> Nope, You are just creting a new INCONSITANT logic system that accepts
>> as non-halitng inputs that actually do halt.
>>
>

On Tuesday, 6 December 2022 at 20:58:56 UTC+2, richar...@gmail.com wrote:
> Right, "Tautology" is a lable that applies to a statement in the systems
> it applies to.
Precisely! So it can't be true in ALL interpretations/systems/models.

Because it's a statement made in the internal language of the system!

> > Hence the part where you have to play amnesiac and forget that a tautology has to be true in all models.
> All Models, not all systems.
Yes, they are. There's logic. And then there are models/systems of logic.

Classical logic is a model/system of logic.
Intuitionistic is a model/system of logic.
Modal logic is a model/system of logic.
Temporal logic is a model/system of logic.

> You don't seem to understand the difference.
I understand how synonyms work just fine.

> > It was a misnomer all along.
> Seems to be a misunderstanding of your part.
You keep projecting your misunderstanding onto me.

> > It's literally false in every instance of reality where Jack wasn't 11 a year ago!
> Nope. You don't understand the meaning of the statement then.
Q.E.D. Projection.

> >> We could even likely strengthen the statement to "ONLY if Jack wa eleven
> >> a year ago, will he now be twelve."
> > Strengthen it all you want. It's a conditional - therefore not a tautology.
> Nope, you don't seem to understand the stateent.
Q.E.D. Projection.

> Seems normal for you.
Q.E.D. Projection.

On 12/7/2022 2:20 AM, Skep Dick wrote:
> On Tuesday, 6 December 2022 at 20:58:56 UTC+2, richar...@gmail.com wrote:
>> Right, "Tautology" is a lable that applies to a statement in the systems
>> it applies to.
> Precisely! So it can't be true in ALL interpretations/systems/models.
>
> Because it's a statement made in the internal language of the system!
>
>>> Hence the part where you have to play amnesiac and forget that a tautology has to be true in all models.
>> All Models, not all systems.
> Yes, they are. There's logic. And then there are models/systems of logic.
>
> Classical logic is a model/system of logic.
> Intuitionistic is a model/system of logic.
> Modal logic is a model/system of logic.
> Temporal logic is a model/system of logic.
>

The higher level logic of correct reasoning subsumes all of the
differently logics of formal and natural logic into a single system of
correct reasoning.

(1) Some finite strings are stipulated to have the semantic property of
Boolean true. Such as Haskell Curry elementary theorems
https://www.liarparadox.org/Haskell_Curry_45.pdf
or basic facts specified in natural language: cats ⊂ animals.

(2) Some finite strings are derived by applying truth preserving
operations operations to (1) and/or the result of (2).

Any system of reasoning that diverges from this model diverges from
correct reasoning.

>> You don't seem to understand the difference.
> I understand how synonyms work just fine.
>
>>> It was a misnomer all along.
>> Seems to be a misunderstanding of your part.
> You keep projecting your misunderstanding onto me.
>
>>> It's literally false in every instance of reality where Jack wasn't 11 a year ago!
>> Nope. You don't understand the meaning of the statement then.
> Q.E.D. Projection.
>
>>>> We could even likely strengthen the statement to "ONLY if Jack wa eleven
>>>> a year ago, will he now be twelve."
>>> Strengthen it all you want. It's a conditional - therefore not a tautology.
>> Nope, you don't seem to understand the stateent.
> Q.E.D. Projection.
>
>> Seems normal for you.
> Q.E.D. Projection.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer