Is "This statement is false" a proposition?

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wij

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Aug 8, 2022, 8:37:08 AMAug 8
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P= "This statement is false"
Is P a proposition? This question depends largely on how P is interpreted,
because the sentence itself does not have T/F value (it is given by its evaluator).
Now, if the T/F value of the P as shown is defined by an evaluator, a circular
argument is formed. In this regard, the sentence P should be classified as
something like undefined or undecidable. P is not a 'proper' proposition.

bool P() {
return !Evalu_TF(P);
};

This 'undefined' solution extends to several paradoxes like "Achilles and the
tortoise" and Supertask (the given problem does not contain the answer or
confusing). The verdict, including 'circular argument', also applies to a
number of foundamental math proofs. I just mention it. What involved is huge.

wij

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Aug 8, 2022, 9:20:06 AMAug 8
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In current "Halting Problem" atmosphere. I should add:

void P(Arg x) {
if(H(p,x)==0) return;
Infinite_Loop: goto Infinite_loop;
}

Such P is defined (if H is defined).
In reality, all random string (program) are defined to x86 CPU.
Basically, no program is "pathological" to CPU. Similar cases are like in
Godel's incompleteness proof (I did not really read it), such 'P' is defined
and does exist (if H exists).

Richard Damon

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Aug 8, 2022, 8:38:28 PMAug 8
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On 8/8/22 9:20 AM, wij wrote:
> On Monday, 8 August 2022 at 20:37:08 UTC+8, wij wrote:
>> P= "This statement is false"
>> Is P a proposition? This question depends largely on how P is interpreted,
>> because the sentence itself does not have T/F value (it is given by its evaluator).
>> Now, if the T/F value of the P as shown is defined by an evaluator, a circular
>> argument is formed. In this regard, the sentence P should be classified as
>> something like undefined or undecidable. P is not a 'proper' proposition.
>>
>> bool P() {
>> return !Evalu_TF(P);
>> };
>>
>> This 'undefined' solution extends to several paradoxes like "Achilles and the
>> tortoise" and Supertask (the given problem does not contain the answer or
>> confusing). The verdict, including 'circular argument', also applies to a
>> number of foundamental math proofs. I just mention it. What involved is huge.

Right, we can show that P is not a Truth Bearer, and thus doesn't have a
truth value.

>
> In current "Halting Problem" atmosphere. I should add:
>
> void P(Arg x) {
> if(H(p,x)==0) return;
> Infinite_Loop: goto Infinite_loop;
> }
>
> Such P is defined (if H is defined).
> In reality, all random string (program) are defined to x86 CPU.
> Basically, no program is "pathological" to CPU. Similar cases are like in
> Godel's incompleteness proof (I did not really read it), such 'P' is defined
> and does exist (if H exists).

Right, P(P) is a Halting Computation DOES have a truth value for ANY H
that can be defined, thus the Halting Question is a Truth Bearer, and
thus HAS a correct answer, even if H can't give it.


The question, What can H(P,P) return to be correct, is a question that
doesn't have a Truth Value, and thus isn't a Truth Bearer, but it fails
to be a proper question even before that point, as H needs to be a
DEFINED function, and thus H(P,P) has a defined value, which could be
correct or not (in fact, we know it will not). Asking what it could do
if it was something different is an improper question.

We CAN ask, what can H1(P,P) return to be corect, as that question DOES
have an answer (at least if H can be determined to be Halting or proved
to be non-halting). H1(P,P) returns the opposite of whatever H(P,P)
return, if it returns, or non-halting if H(P,P) will be non-halting.

If we can't determine if H(P,P) is Halting or Not, then we don't know
what value to return from H1(P,P), but one of the answers WILL be correct.

Daniel Pehoushek

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Aug 9, 2022, 6:35:58 AMAug 9
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i called the olcott program a cycle detector many years ago
daniel2380++

wij

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Aug 9, 2022, 1:44:15 PMAug 9
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Sorry, would you make you point clearer?

olcott

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Aug 9, 2022, 2:02:13 PMAug 9
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I bought LiarParadox.org to address this issue.
It used to hound a Wordpress site that had all my papers.
Now the papers are on Researchgate.org

Here is my earliest paper on the Liar Paradox:

https://www.researchgate.net/publication/307442489_Formalizing_the_logical_self-reference_error_of_the_Liar_Paradox

Here is the error in C++:

int main()
{
bool LiarPardox = (LiarParadox == true);
}

--
Copyright 2022 Pete Olcott

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

Richard Damon

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Aug 9, 2022, 10:54:34 PMAug 9
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Which in C++ (or C) is UNDEFINED BEHAVIOR, as you are referencing the
value of the variable LiarParadox before it is set.

You have the problem that neither C nor C++ has the capability of
expressing the statement you are trying to represent, as they can only
COMPUTE based on values given, not solve systems of equations.

You need a language which allows the expression of this level of statement.

Note, C and C++ are only Turing Complete languages, which doesn't mean
they are capable of expressing all statements of logic, as logic is more
expressive than simple computations.

wij

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Aug 10, 2022, 11:00:46 AMAug 10
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On Wednesday, 10 August 2022 at 02:02:13 UTC+8, olcott wrote:
> ...
> int main()
> {
> bool LiarPardox = (LiarParadox == true);
> }

Yes, that is the good part of using C/C++ language to express idea.
"This statement is true" is also an 'undefined' statement in this regard.

olcott

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Aug 10, 2022, 1:07:04 PMAug 10
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*What is the proper definition of a truth bearer*?

Expressions of language that can be resolved to a truth value are [truth
bearers]. This includes expressions of language that currently have
unknown truth values.

Expressions of language that cannot possibly be resolved to a truth
value because their type or structure are not [truth bearers].

Expressions of language that contradict their own truth value: "This
sentence is not true." cannot possibly be resolved to a truth value are
not [truth bearers].

There are only two ways that an expression of language can be resolved
to a truth value:
(1) An expression of language is assigned a truth value such as "cats
are animals" is defined to be true.
(2) Truth preserving operations are applied to expressions of language
that are known to be true. {cats are animals} and {animals are living
things} therefore {cats are living things}. Copyright 2021 PL Olcott

Skep Dick

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Aug 10, 2022, 3:55:05 PMAug 10
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On Wednesday, 10 August 2022 at 19:07:04 UTC+2, olcott wrote:
> Expressions of language that can be resolved to a truth value are [truth
> bearers]. This includes expressions of language that currently have
> unknown truth values.

So then the expression 'x = x` is a truth-bearer.

In [1]: expression = 'x == x'

It has an unknown truth-value until evaluated.

It can be resolved to True;

In [2]: x = object()

In [3]: eval(expression)
Out[3]: True

Or it can be resolved to False;

In [4]: x = another_object()

In [5]: eval(expression)
Out[5]: False

Sounds like you don't understand how truth works?

olcott

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Aug 10, 2022, 4:10:01 PMAug 10
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On 8/10/2022 2:55 PM, Skep Dick wrote:
> On Wednesday, 10 August 2022 at 19:07:04 UTC+2, olcott wrote:
>> Expressions of language that can be resolved to a truth value are [truth
>> bearers]. This includes expressions of language that currently have
>> unknown truth values.
>
> So then the expression 'x = x` is a truth-bearer.
>
> In [1]: expression = 'x == x'
>

It is a tautology that a thing <is> itself: 'x == x'
expression = 'x == x'
merely adds one level of indirect reference.

Skep Dick

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Aug 10, 2022, 4:17:26 PMAug 10
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On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
> It is a tautology that a thing <is> itself: 'x == x'
> expression = 'x == x'
> merely adds one level of indirect reference.

"Tautology" means "true in ALL possible models/interpretations".

"x == x" is NOT a tautology. I literally just showed you a model in which it's false.

olcott

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Aug 10, 2022, 5:02:00 PMAug 10
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On 8/10/2022 3:17 PM, Skep Dick wrote:
> On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
>> It is a tautology that a thing <is> itself: 'x == x'
>> expression = 'x == x'
>> merely adds one level of indirect reference.
>
> "Tautology" means "true in ALL possible models/interpretations".
>
> "x == x" is NOT a tautology.

A thing is NOT itself?

Skep Dick

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Aug 10, 2022, 5:09:13 PMAug 10
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On Wednesday, 10 August 2022 at 23:02:00 UTC+2, olcott wrote:
> On 8/10/2022 3:17 PM, Skep Dick wrote:
> > On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
> >> It is a tautology that a thing <is> itself: 'x == x'
> >> expression = 'x == x'
> >> merely adds one level of indirect reference.
> >
> > "Tautology" means "true in ALL possible models/interpretations".
> >
> > "x == x" is NOT a tautology.
> A thing is NOT itself?

What? Why are you interpreting 'x==x' as a statement?
It's a question!

Is x the same as x?

Both answers are perfectly valid in different contexts:
yes - x is the same as x. It remained the same from one moment into the next. Classical logic.
no - x is not the same as x. it changed from one moment into the next. Schrödinger logic.




olcott

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Aug 10, 2022, 5:18:17 PMAug 10
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Yuu cannot correctly cross the boundary from the analytic to the synthetic.

Skep Dick

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Aug 10, 2022, 5:31:20 PMAug 10
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On Wednesday, 10 August 2022 at 23:18:17 UTC+2, olcott wrote:
> On 8/10/2022 4:09 PM, Skep Dick wrote:
> > On Wednesday, 10 August 2022 at 23:02:00 UTC+2, olcott wrote:
> >> On 8/10/2022 3:17 PM, Skep Dick wrote:
> >>> On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
> >>>> It is a tautology that a thing <is> itself: 'x == x'
> >>>> expression = 'x == x'
> >>>> merely adds one level of indirect reference.
> >>>
> >>> "Tautology" means "true in ALL possible models/interpretations".
> >>>
> >>> "x == x" is NOT a tautology.
> >> A thing is NOT itself?
> >
> > What? Why are you interpreting 'x==x' as a statement?
> > It's a question!
> >
> > Is x the same as x?
> >
> > Both answers are perfectly valid in different contexts:
> > yes - x is the same as x. It remained the same from one moment into the next. Classical logic.
> > no - x is not the same as x. it changed from one moment into the next. Schrödinger logic.
> Yuu cannot correctly cross the boundary from the analytic to the synthetic.

What boundary? Everything is synthetic.

Even when you think you are being analytical you are synthesising an analysis.

Richard Damon

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Aug 10, 2022, 8:44:14 PMAug 10
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On 8/10/22 1:06 PM, olcott wrote:
> On 8/10/2022 10:00 AM, wij wrote:
>> On Wednesday, 10 August 2022 at 02:02:13 UTC+8, olcott wrote:
>>>   ...
>>> int main()
>>> {
>>> bool LiarPardox = (LiarParadox == true);
>>> }
>>
>> Yes, that is the good part of using C/C++ language to express idea.
>> "This statement is true" is also an 'undefined' statement in this regard.
>>
>
> *What is the proper definition of a truth bearer*?
>
> Expressions of language that can be resolved to a truth value are [truth
> bearers]. This includes expressions of language that currently have
> unknown truth values.
>
> Expressions of language that cannot possibly be resolved to a truth
> value because their type or structure are not [truth bearers].
>
> Expressions of language that contradict their own truth value: "This
> sentence is not true." cannot possibly be resolved to a truth value are
> not [truth bearers].
>
> There are only two ways that an expression of language can be resolved
> to a truth value:
> (1) An expression of language is assigned a truth value such as "cats
> are animals" is defined to be true.
> (2) Truth preserving operations are applied to expressions of language
> that are known to be true. {cats are animals} and {animals are living
> things} therefore {cats are living things}. Copyright 2021 PL Olcott
>

Or, the Truth of the statement can be EMPIRICALLY demonstrated.

The statement "The Earth is Round" is True, not because we have assigned
the "Round Property" to the name "Earth", or because we have somehow
manipulated know true statements to prove that the Earth must be round,
but because by DIRECT OBSERVATION, we see that it meets the definition
we has assigned to "Round".

Note, that "Cats are Animals" is NOT just a matter of definition, but of
this sort of empirical proof.

First we define what we mean by an "Animal", as a certain classification
of living organisms.

Then we define what we mean by a "Cat", which while it might include a
requirment that these be animals, might not.

We can then (if not forced by the definition) determine if Cats actually
are Animals.

There have been a number of cases where something that was THOUGHT to be
a thing that was part of a category, turned out on better understanding
to not actually be actually in that category, but was something else.

The Truth value of "Halting" is this sort of property. We have a
definition of it, that it relates to a Machine reaching a final state
for a given input, but the "proof" of a given Machine Halting or Not
isn't really proof in the normal sense, but the emperical running of the
machine and seeing if we get it to halt. If it doesn't halt, we might
need to resort to some logic to prove that it won't. But the emperical
fact that if we run the machine and reach the final state says that no
matter what logic you claim to have used to show it won't halt, that
logic is proved incorrect by the emperical fact that it did.

Richard Damon

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Aug 10, 2022, 8:49:23 PMAug 10
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So why does the one x bind in a different context then the other?

Of course, there IS a case where x == x can legitimately return FALSE,
because there do exists some systems with an unusual definition of equality.


If x has the value of not-a-number (NaN) then by the offical definition
of IEEE floating print logic,

x == x needs to return FALSE, and is one way to test a floating point
value to see if it is a NaN.

olcott

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Aug 10, 2022, 8:59:49 PMAug 10
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Yes you are correct. I was only referring to analytic rather than
synthetic truth.

https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction

Richard Damon

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Aug 10, 2022, 9:19:57 PMAug 10
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But then you keep using the wrong term. And use wrong examples.

"Cats are Animals" is NOT actually an Analytic Truth, since the terms
refer to things that actually exist, and so the ACTUAL truth relies on
Reality.

By YOUR logic, we could say "Cats are Plants" to be an analytic truth by
just defining it that way, but such a system is inconsistent with
reality, and thus not accepted.

Note, the term "Truth Beared" is NOT limited to just analytic truth. A
statement can be a truth bearer even if the only way to determine its
truth is emperical.

olcott

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Aug 10, 2022, 9:28:55 PMAug 10
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WRONG

“Analytic” sentences, such as “Pediatricians are doctors,” have
historically been characterized as ones that are true by virtue of the
meanings of their words alone and/or can be known to be so solely by
knowing those meanings.
https://plato.stanford.edu/entries/analytic-synthetic/

Skep Dick

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Aug 10, 2022, 10:27:44 PMAug 10
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The Earth meets your definition of “round”? Why? Earth is not round. We approximate it to be round, or oblate.

But that is just what we say about it colloquially. It isn’t literally true.





Skep Dick

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Aug 10, 2022, 10:38:43 PMAug 10
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On Thursday, 11 August 2022 at 02:49:23 UTC+2, richar...@gmail.com wrote:
> On 8/10/22 5:09 PM, Skep Dick wrote:
> > On Wednesday, 10 August 2022 at 23:02:00 UTC+2, olcott wrote:
> >> On 8/10/2022 3:17 PM, Skep Dick wrote:
> >>> On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
> >>>> It is a tautology that a thing <is> itself: 'x == x'
> >>>> expression = 'x == x'
> >>>> merely adds one level of indirect reference.
> >>>
> >>> "Tautology" means "true in ALL possible models/interpretations".
> >>>
> >>> "x == x" is NOT a tautology.
> >> A thing is NOT itself?
> >
> > What? Why are you interpreting 'x==x' as a statement?
> > It's a question!
> >
> > Is x the same as x?
> >
> > Both answers are perfectly valid in different contexts:
> > yes - x is the same as x. It remained the same from one moment into the next. Classical logic.
> > no - x is not the same as x. it changed from one moment into the next. Schrödinger logic.
> >
> >
> >
> >
> So why does the one x bind in a different context then the other?
It isn’t a different context.

I am binding x to two different objects.

Instances of object are equal to themselves.
Instances of another…object aren’t.


> Of course, there IS a case where x == x can legitimately return FALSE,
> because there do exists some systems with an unusual definition of equality.
>
>
> If x has the value of not-a-number (NaN) then by the offical definition
> of IEEE floating print logic,
>
> x == x needs to return FALSE, and is one way to test a floating point
> value to see if it is a NaN.

None of this matters. The point I am making is that the expression “x == x” has no value by default.
Assigning one to it is a design choice.

The value of “x=x” is a free variable. It can be anything you want it to be.

Richard Damon

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Aug 10, 2022, 10:51:21 PMAug 10
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On 8/10/22 10:38 PM, Skep Dick wrote:
> On Thursday, 11 August 2022 at 02:49:23 UTC+2, richar...@gmail.com wrote:
>> On 8/10/22 5:09 PM, Skep Dick wrote:
>>> On Wednesday, 10 August 2022 at 23:02:00 UTC+2, olcott wrote:
>>>> On 8/10/2022 3:17 PM, Skep Dick wrote:
>>>>> On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
>>>>>> It is a tautology that a thing <is> itself: 'x == x'
>>>>>> expression = 'x == x'
>>>>>> merely adds one level of indirect reference.
>>>>>
>>>>> "Tautology" means "true in ALL possible models/interpretations".
>>>>>
>>>>> "x == x" is NOT a tautology.
>>>> A thing is NOT itself?
>>>
>>> What? Why are you interpreting 'x==x' as a statement?
>>> It's a question!
>>>
>>> Is x the same as x?
>>>
>>> Both answers are perfectly valid in different contexts:
>>> yes - x is the same as x. It remained the same from one moment into the next. Classical logic.
>>> no - x is not the same as x. it changed from one moment into the next. Schrödinger logic.
>>>
>>>
>>>
>>>
>> So why does the one x bind in a different context then the other?
> It isn’t a different context.
>
> I am binding x to two different objects.
>
> Instances of object are equal to themselves.
> Instances of another…object aren’t.
>

And how does your language know which x to bind to which object?

It seems you have an inconsisten system.

>
>> Of course, there IS a case where x == x can legitimately return FALSE,
>> because there do exists some systems with an unusual definition of equality.
>>
>>
>> If x has the value of not-a-number (NaN) then by the offical definition
>> of IEEE floating print logic,
>>
>> x == x needs to return FALSE, and is one way to test a floating point
>> value to see if it is a NaN.
>
> None of this matters. The point I am making is that the expression “x == x” has no value by default.
> Assigning one to it is a design choice.
>
> The value of “x=x” is a free variable. It can be anything you want it to be.
>

Since == is a comparison, and not a binding, nornally, two references to
the same name in a given expression will be bound to the same object.

Or, is you system just randomly changing the binding of a variable in
the middle of operations on a whim?

Richard Damon

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Aug 10, 2022, 10:57:41 PMAug 10
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But the definition of "Pediatrician" is that it is a TYPE of doctor that
....

It specifically defines the label as a subclass.

"Cat" is a different sort of thing, while we conventionaally might use a
"animal" reference in describing it, that is because the sort of thing
we call a "Cat" happens to emperically be an animal.

"Cats" are a classification of a set of entities with certain
properties. It just so happens to turn out that one of them is that they
also fall within the classification we call animals.

This shows the "flaw" of trying to use too sharp of a knife to divide
the types of truth from each other.

olcott

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Aug 10, 2022, 11:09:37 PMAug 10
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Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Carnivora
Suborder: Feliformia
Family: Felidae
Subfamily: Felinae
Genus: Felis
Species: F. catus[1]
https://en.wikipedia.org/wiki/Cat


>
> "Cat" is a different sort of thing, while we conventionaally might use a
> "animal" reference in describing it, that is because the sort of thing
> we call a "Cat" happens to emperically be an animal.
>
> "Cats" are a classification of a set of entities with certain
> properties. It just so happens to turn out that one of them is that they
> also fall within the classification we call animals.
>
> This shows the "flaw" of trying to use too sharp of a knife to divide
> the types of truth from each other.
>


Richard Damon

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Aug 10, 2022, 11:13:08 PMAug 10
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I said "Round" which is an approximate shape, not Spherical.

Also note, that if you shrank the earth to the size of a normal "ball"
of some sort (a conventional one would be a billiard ball) its roundness
is comparable to many things we just take as "a sphere", but not a round
as "precision" spheres.

Skep Dick

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Aug 10, 2022, 11:17:15 PMAug 10
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On Thursday, 11 August 2022 at 04:51:21 UTC+2, richar...@gmail.com wrote:
> And how does your language know which x to bind to which object?
I don't understand your question. The bindings and evaluations are explicit.

What's confusing you?

> It seems you have an inconsisten system.
Even if it were true - why should I care?

A design choice exists: a system can be consistent; or complete but not both.

Which one you choose depends on your use-case for the system.

> Since == is a comparison, and not a binding, nornally, two references to
> the same name in a given expression will be bound to the same object.
>
> Or, is you system just randomly changing the binding of a variable in
> the middle of operations on a whim?
What? I'll annotate it for you...

In [2]: x = object(). # bind x to object()

In [3]: x == x # evaluate x == x
Out[3]: True

In [4]: x = another_object() # now re-bind x to another object

In [5]: x == x # evaluate x == x
Out[5]: False

If that's confusing you I can use different variable names...

In [6]: x = object()

In [7]: y = another_object()

In [8]: x == x
Out[8]: True

In [9]: y == y
Out[9]: False







Richard Damon

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Aug 10, 2022, 11:19:09 PMAug 10
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But that hierarchy is EMPERICAL, not just analytically defined.

Vs, Pediatrician, which is a name for a specific specialization of
Doctor, and innately is a subclass.

Note, the Label Cat existed long before most of those levels of
Hierarchy were invented.

It should be pointed out that some species get reclassified as we
determine that the hierarcies we THOUGHT they belonged to were incorrect.

Analytical Definition, to truely be a pure analitical definition must
not be based on something that can turn out to be untrue.

Skep Dick

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Aug 10, 2022, 11:21:10 PMAug 10
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On Thursday, 11 August 2022 at 05:13:08 UTC+2, richar...@gmail.com wrote:
> I said "Round" which is an approximate shape, not Spherical.
Well, on approximation the Earth is approximately (but not exactly) flat!

I made a coffee table yesterday and I didn't even have to take the curvature into account!

All approximations are good enough for some purpose.

> Also note, that if you shrank the earth to the size of a normal "ball"
> of some sort (a conventional one would be a billiard ball) its roundness
> is comparable to many things we just take as "a sphere", but not a round
> as "precision" spheres.

And if you expanded it to the size of the Universe or something?

You don't get to play the scale transformation game just one way.

olcott

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Aug 10, 2022, 11:37:07 PMAug 10
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An empirical definition requires sense data from the sense organs to
verify. That a {cat} is a {feline} is defined to be true, thus does not
depend on sense data from the sense organs.



>
>>>
>>> "Cat" is a different sort of thing, while we conventionaally might
>>> use a "animal" reference in describing it, that is because the sort
>>> of thing we call a "Cat" happens to emperically be an animal.
>>>
>>> "Cats" are a classification of a set of entities with certain
>>> properties. It just so happens to turn out that one of them is that
>>> they also fall within the classification we call animals.
>>>
>>> This shows the "flaw" of trying to use too sharp of a knife to divide
>>> the types of truth from each other.
>>>
>>
>>
>


dklei...@gmail.com

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Aug 11, 2022, 12:13:08 AMAug 11
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If we define the meaning of a word as a set of attributes then we will
have the meaning of "pediatrician" to be a superset of "doctor". That
is "if A means some subset of B then a B is an A". Are there any other
analytic expressions?

Richard Damon

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Aug 11, 2022, 8:01:24 AMAug 11
to

On 8/10/22 11:17 PM, Skep Dick wrote:
> On Thursday, 11 August 2022 at 04:51:21 UTC+2, richar...@gmail.com wrote:
>> And how does your language know which x to bind to which object?
> I don't understand your question. The bindings and evaluations are explicit.
>
> What's confusing you?
>
>> It seems you have an inconsisten system.
> Even if it were true - why should I care?
>
> A design choice exists: a system can be consistent; or complete but not both.
>
> Which one you choose depends on your use-case for the system.
>
>> Since == is a comparison, and not a binding, nornally, two references to
>> the same name in a given expression will be bound to the same object.
>>
>> Or, is you system just randomly changing the binding of a variable in
>> the middle of operations on a whim?
> What? I'll annotate it for you...
>
> In [2]: x = object(). # bind x to object()
>
> In [3]: x == x # evaluate x == x
> Out[3]: True
>
> In [4]: x = another_object() # now re-bind x to another object
>
> In [5]: x == x # evaluate x == x
> Out[5]: False

WHy? both x's refer to the same new object?

>
> If that's confusing you I can use different variable names...
>
> In [6]: x = object()
>
> In [7]: y = another_object()
>
> In [8]: x == x
> Out[8]: True
>
> In [9]: y == y
> Out[9]: False
>

so why does y not equal to y?

I thought you claim was every object was equal to itself.

You clearly aren't explaining what you mean by your notation, and thus
being intentionally deceptive, in other words, being a liar.

Note, I showed an EXPLICIT case that show that the assumptions that an
object is equal to itself, because the non-a-number value is defined
that way.

You are just working with some generic object, claiming that objects are
always equal to themselves, but then saying some other object isn't
equal to itself, so you have a contradiction in you logic, or an
intentional deception.

Richard Damon

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Aug 11, 2022, 8:05:22 AMAug 11
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It still is closer to a perfect sphere as a relative deviation (which is
how spherisity is measured) than many things we do consider to be a sphere.

Skep Dick

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Aug 11, 2022, 8:13:07 AMAug 11
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On Thursday, 11 August 2022 at 14:05:22 UTC+2, richar...@gmail.com wrote:
> It still is closer to a perfect sphere as a relative deviation (which is
> how spherisity is measured) than many things we do consider to be a sphere.
Uhuh. And how do you measure "closeness" ?

You really want to have your cake and eat it too, don't you?

On the one hand you get to exercise your own judgment.
On the other hand you want strict adherence to defintiions.
And on a third hand you turn a blind eye when your own examples don't satisfy your own definitions.

It's a stupid game! The only winning move is to not play.



Skep Dick

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Aug 11, 2022, 8:22:29 AMAug 11
to
On Thursday, 11 August 2022 at 14:01:24 UTC+2, richar...@gmail.com wrote:
> so why does y not equal to y?
What a stupid question?

Why does x = x? Because it's an axiom!
Why does y != y? Because it's an axiom!

To accept or reject axioms is subject to individual preference.

> I thought you claim was every object was equal to itself.
I didn't make any such claim, but lets pretend that I did.

Every object is equal to itself.
y is not equal to itself => y is not an object

Can you logic or...?

> You clearly aren't explaining what you mean by your notation, and thus
> being intentionally deceptive, in other words, being a liar.
Bullshit.

What do you mean by x=x in the standard notation? You mean "True"
That is the value which you have assigned to the expression!

What do I mean by y=y in my notation? I mean "False".
That is the value which I have assigned to the expression.

> Note, I showed an EXPLICIT case that show that the assumptions that an
> object is equal to itself, because the non-a-number value is defined
> that way.
and y != y is also defined that way.

What's your point?

> You are just working with some generic object, claiming that objects are
> always equal to themselves
I have never made that claim.

I have stated (over and over) that x=x ↔ True is an arbitrary axiom.
And I am pointing that y=y ↔ False is just an arbitrary an axiom.

But the point is that you can CHOOSE the truth-value of your axiom!

> but then saying some other object isn't
> equal to itself, so you have a contradiction in you logic
Good thing I have never said anything like that!

What I am saying is that some objects may be equal to themselves; and some object may not be equal to themselves.

And I can derrive some logic/computation out of that.

I can also say things like...

All objects are the same. Except for their differences.
All objects are different. Except for their similarities.

And I can derrive some logic/computation out of that too.




Richard Damon

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Aug 11, 2022, 11:10:24 PMAug 11
to
On 8/11/22 8:22 AM, Skep Dick wrote:
> On Thursday, 11 August 2022 at 14:01:24 UTC+2, richar...@gmail.com wrote:
>> so why does y not equal to y?
> What a stupid question?
>
> Why does x = x? Because it's an axiom!
> Why does y != y? Because it's an axiom!

But axioms are supposed to be evident.

Just saying "because' means that your system has no logical reasoning
behind it.

>
> To accept or reject axioms is subject to individual preference.

Not really, unless you are creating private systems/fields of study.

>
>> I thought you claim was every object was equal to itself.
> I didn't make any such claim, but lets pretend that I did.
>
> Every object is equal to itself.
> y is not equal to itself => y is not an object
>
> Can you logic or...?

But you said that the things you are manipulating are objects.

>
>> You clearly aren't explaining what you mean by your notation, and thus
>> being intentionally deceptive, in other words, being a liar.
> Bullshit.
>
> What do you mean by x=x in the standard notation? You mean "True"
> That is the value which you have assigned to the expression!
>
> What do I mean by y=y in my notation? I mean "False".
> That is the value which I have assigned to the expression.

So, you are defining a system based on non-sense and illogic.

Sounds about right for you.

Richard Damon

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Aug 11, 2022, 11:13:12 PMAug 11
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It may require sense data to VERIFY, but not to have an actual truth value.

There is an empirical value for the number of Humans that were on the
Earth at a precise point in time.

That number is exact, and the asserting that the value is that value
would be true, and that that value is any other value is false.

THe fact that no one actually sensed that value is irrelvent.

Richard Damon

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Aug 11, 2022, 11:22:19 PMAug 11
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So you don't understand non-binary properties?

Things like "Roundness" have a scale.

A pyramid is almost completely NOT "Round".

A regular dodecahedron is sort of round, but also has noticable deviations.

An "American" football has some aspects of roundness, but is highly
distored in other aspects.

A pancake if often somewhat round on one plane.

A soccor ball is fairly round, with some definite deviations.

The Earth is highly round.

A machined ball bearing is even rounder.


Yes, language can get messy, The Earth is "Round" because it match the
gradient propert of Roundness to a high enough degree that it is
considered to have that property.

Arguing over that sort of fine detail shows you aren't actually
interested in an honest discussion.

Skep Dick

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Aug 12, 2022, 4:55:40 PMAug 12
to
On Friday, 12 August 2022 at 05:10:24 UTC+2, richar...@gmail.com wrote:
> On 8/11/22 8:22 AM, Skep Dick wrote:
> > On Thursday, 11 August 2022 at 14:01:24 UTC+2, richar...@gmail.com wrote:
> >> so why does y not equal to y?
> > What a stupid question?
> >
> > Why does x = x? Because it's an axiom!
> > Why does y != y? Because it's an axiom!
> But axioms are supposed to be evident.
There is great irony in the fact that just a few days ago you were accusing me of being "unable" to think abstractly without concretizing everything.

Now look at you! Grasphing for concrete/evident axioms.

Mathematics is just made up rules! It's a bycicle for your mind.

> Just saying "because' means that your system has no logical reasoning
> behind it.
I don't know in what way I need to (if it's even possible) to explain to you that Logic, Computation and Mathematics are one and the same thing looked at from different perspectives.

Rules. Made up rules.

> Not really, unless you are creating private systems/fields of study.
Every mainstream field of study was once a "private system". And then it wasn't.

> But you said that the things you are manipulating are objects.
Yes. And? I do manipulate objects. I also manipulate non-objects.

> So, you are defining a system based on non-sense and illogic.
Holy shit, cowboy! Which part of this is eluding you?!?

(x == x) ⇔ True
(y == y) ⇔ False

Do you even know what the logical symbol ⇔ means ?!?

> Sounds about right for you.
An uncharitable ignoramus. Sounds about right for you.



Skep Dick

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Aug 12, 2022, 5:03:39 PMAug 12
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On Friday, 12 August 2022 at 05:22:19 UTC+2, richar...@gmail.com wrote:
> So you don't understand non-binary properties?
> Things like "Roundness" have a scale.
So you don't actually understand scale invariance?

https://en.wikipedia.org/wiki/Scale_invariance

> A pyramid is almost completely NOT "Round".
Precisely! No matter the scale (small or large) - a pyramid is never round.

> A regular dodecahedron is sort of round, but also has noticable deviations.
Lol. Yes. That is the lie they told you in calculus. That you can fill a circle with a many-sided polygons and then it magically becomes a circle.

> An "American" football has some aspects of roundness, but is highly
> distored in other aspects.
It sure has curvature. I have no idea what "roundness" is.

> A ancake if often somewhat round on one plane.
> A soccor ball is fairly round, with some definite deviations.
> The Earth is highly round.
> A machined ball bearing is even rounder.

Approximately speaking a triangle is also round!
It fills up a circle exactly like a dodecagon doesn't fill up a circle either.


> Yes, language can get messy, The Earth is "Round" because it match the
> gradient propert of Roundness to a high enough degree that it is
> considered to have that property.
Oooh! "High enough degree"

> Arguing over that sort of fine detail shows you aren't actually
> interested in an honest discussion.
So you have decided to climb upon a (dead) moral high horse, now that you've run out of precision?


Richard Damon

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Aug 12, 2022, 5:48:38 PMAug 12
to
Right, and without further explanation of the apparent insanity, your
system is shown to be useless.

>
>> Sounds about right for you.
> An uncharitable ignoramus. Sounds about right for you.
>
>
>

And like your system, so is most of what you say.

Since you won't define your system, we can take ANYTHING you mean to
mean whatever we want to, after all, you have declared that people don't
need to be mind-readers, so we don't need to follow your intent in your
statments, and anything that hasn't been explicitly defined, can be
assuemd to be whatever we want it to be.

Done to the meaning of the words you use, maybe you actually mean by
"define" what most of us mean "guess". After all, you reject the concept
that conventions hold.

Skep Dick

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Aug 12, 2022, 6:08:01 PMAug 12
to
On Friday, 12 August 2022 at 23:48:38 UTC+2, richar...@gmail.com wrote:
> Right, and without further explanation of the apparent insanity, your
> system is shown to be useless.
Oh. So now you started caring about pragmatics?

I thought you can just do abstraction without having to concretize everything.

> Since you won't define your system, we can take ANYTHING you mean to
> mean whatever we want to, after all, you have declared that people don't
> need to be mind-readers, so we don't need to follow your intent in your
> statments, and anything that hasn't been explicitly defined, can be
> assuemd to be whatever we want it to be.
You can do that. But at least be honest why you are doing it.

It's because you are grumpy old fart who doesn't like to be challenged by somebody half his age.

You are just being dismissive and far too lazy to even open the Wikipedia page on *R.

> Done to the meaning of the words you use, maybe you actually mean by
> "define" what most of us mean "guess". After all, you reject the concept
> that conventions hold.
Yes - I reject conventions. But YOU don't. You LOVE conventions.

So what's the conventional definition of "definition" ?
What's the conventional meaning of "meaning"?





Richard Damon

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Aug 12, 2022, 6:37:19 PMAug 12
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Maybe you are starting to come into the light.

There is a reason some definitions are accepted by convention, because
without those base axiometic definitions, we have nothing to use to
define anything.

Ultimately, at the core, you reach concepts that can't be just defined
by words, as you don't have any words to use to define them.

This is the core of the conventions.

Remove the conventions, and you need to start from NOTHING, and you
can't make that first step, and those first steps are the messy one.

Just like most of us just take the numbers like 0, 1, 2, 3, 4, ... for
granted, as the actual logic to bootstrap to that point is more
complicated than most of us want to have to deal with.

So we just import that definition into our system from the established
conventions.

Normally we use the system, of

0 is just defined
1 = succ(0)
2 - succ(1)
...
n+1 - succ(n)


but there is also the following number system out of game theory:
(There is actually meaning to the notation, finding it is an exercise to
the reader).

0 = {|}
1 = {0|}
2 = {1|}
3 = {2|}

which also allows us to define some rationals as

1/2 = {0|1}

This system has some interesting properties when you start to add a few
new definitions into it, that are actauly fairly simple that gets us
into surreal numbers and beyond.

Skep Dick

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Aug 12, 2022, 6:41:45 PMAug 12
to
Do you actually understand that the set-theoretic treatment of the numbers, and the Peano axiomatisation are developments in the last 150 years.

What is it that you think humans did for the 2500 years before that? We hadn’t defined the numbers! Oh nooooo! Can’t use them undefined.


Richard Damon

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Aug 12, 2022, 6:48:41 PMAug 12
to
We took them as undefined common conventions.

Since you reject the concept of these conventions, you don't have that
base to stand on.

The conventions allow us to agree with "meta-rules" the basic rules that
build the system.

But if you reject the conventions, you don't have thosse meta-rules to
stand on.

Skep Dick

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Aug 13, 2022, 5:09:34 AMAug 13
to
On Saturday, 13 August 2022 at 00:48:41 UTC+2, richar...@gmail.com wrote:
> We took them as undefined common conventions.
You don't even understand what defined and undefined means in context of Mathematics!

x/0 is undefined in all systems.
∞ - ∞ is undefined in the standard system

You don't even understand the implications of undefined behavior.

https://en.wikipedia.org/wiki/Undefined_behavior

> Since you reject the concept of these conventions, you don't have that
> base to stand on.
I don't need a base to stand on. I am not a foundationalist. I am an anti-foundationalist.

Mathematics has no foundation. At best Mathematics has foundations (plural) - infinitely many foundations.
No single foundation can ever account for every possible use-case.
Every single foundation necessarily has drawbacks/trade-offs.

This is common sense to all programmers. Every programming paradigm has drawbacks!

Which is why we are multi-paradigm thinkers.

> The conventions allow us to agree with "meta-rules" the basic rules that
> build the system.
There is no such thing as THE rules!

The rules are after the fact! The rules are just design choices.

The Design (of the system) comes first. Not the rules.

Mathematics is invented, not discovered.

> But if you reject the conventions, you don't have thosse meta-rules to
> stand on.
Precisely! I don't need any meta-rules to "stand on" - I am not a foundationalist.

You are still stuck in the rut of thinking in terms of rules. What a good computer you are!

Perhaps you should consider an altrernative perspective? Not the rules of logic, but the logic of rules.

https://nguyentito.eu/locus-solum-mscs.pdf



Mr Flibble

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Aug 13, 2022, 7:47:37 AMAug 13
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On Mon, 8 Aug 2022 05:37:07 -0700 (PDT)
wij <wyni...@gmail.com> wrote:

> P= "This statement is false"
> Is P a proposition? This question depends largely on how P is
> interpreted, because the sentence itself does not have T/F value (it
> is given by its evaluator). Now, if the T/F value of the P as shown
> is defined by an evaluator, a circular argument is formed. In this
> regard, the sentence P should be classified as something like
> undefined or undecidable. P is not a 'proper' proposition.
>
> bool P() {
> return !Evalu_TF(P);
> };
>
> This 'undefined' solution extends to several paradoxes like "Achilles
> and the tortoise" and Supertask (the given problem does not contain
> the answer or confusing). The verdict, including 'circular argument',
> also applies to a number of foundamental math proofs. I just mention
> it. What involved is huge.

It is a category error.

/Flibble

Richard Damon

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Aug 13, 2022, 9:22:24 AMAug 13
to

On 8/13/22 5:09 AM, Skep Dick wrote:
> On Saturday, 13 August 2022 at 00:48:41 UTC+2, richar...@gmail.com wrote:
>> We took them as undefined common conventions.
> You don't even understand what defined and undefined means in context of Mathematics!
>
> x/0 is undefined in all systems.
> ∞ - ∞ is undefined in the standard system
>
> You don't even understand the implications of undefined behavior.
>
> https://en.wikipedia.org/wiki/Undefined_behavior
>
>> Since you reject the concept of these conventions, you don't have that
>> base to stand on.
> I don't need a base to stand on. I am not a foundationalist. I am an anti-foundationalist.

And anti-social

>
> Mathematics has no foundation. At best Mathematics has foundations (plural) - infinitely many foundations.
> No single foundation can ever account for every possible use-case.
> Every single foundation necessarily has drawbacks/trade-offs.
>
> This is common sense to all programmers. Every programming paradigm has drawbacks!
>
> Which is why we are multi-paradigm thinkers.

Which is why you need to SPECIFY which foundation you are using as
statements mean different things in different foundations.

Because that gets clumsy, we assign a "default" foundation that is assumed.

Since you won't stand on a foundation, your "work" just colapses.

>
>> The conventions allow us to agree with "meta-rules" the basic rules that
>> build the system.
> There is no such thing as THE rules!
>
> The rules are after the fact! The rules are just design choices.
>
> The Design (of the system) comes first. Not the rules.
>
> Mathematics is invented, not discovered.

Not quite. There are core foundations of logic that have been discovered
if ignored lead to logic that can't support itself.

>
>> But if you reject the conventions, you don't have thosse meta-rules to
>> stand on.
> Precisely! I don't need any meta-rules to "stand on" - I am not a foundationalist.

Then you can't build anything. What is your FIRST principle, and what
does it stand on.

>
> You are still stuck in the rut of thinking in terms of rules. What a good computer you are!
>
> Perhaps you should consider an altrernative perspective? Not the rules of logic, but the logic of rules.
>
> https://nguyentito.eu/locus-solum-mscs.pdf
>
>
>

I will need a bit of time to absorb that thought, but the key is that it
appears that this logic of rules can only come about once you HAVE a set
of rules of logic to build it on.

The "Logic of Rules" will still need the "Rules of Logic" for it to work.

This seems to be a common problem with many of the "grand thinkers",
that they fail to see the assumptions they have built into their system
bacause they have just accepted them as pre-existing.

THey are using a foundation they refuse to see, and thus don't build
fully on it and the structure can colapse.

dklei...@gmail.com

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Aug 13, 2022, 3:59:39 PMAug 13
to
On Saturday, August 13, 2022 at 2:09:34 AM UTC-7, Skep Dick wrote:
>
> Perhaps you should consider an altrernative perspective? Not the rules of logic, but the logic of rules.
>
> https://nguyentito.eu/locus-solum-mscs.pdf
>
Thank You for th reference to something that is new to me.

I will have to make significant effort to understand it. At first glance
the prognosis is not promising. It sounds too much like high power
nuttery. But I should not jump to a dismissal.

Skep Dick

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Aug 13, 2022, 5:16:43 PMAug 13
to
If I may make a suggestion that may spare you a significant amount of time.

I would NEVER recommend reading such a dense paper with zero context - you are going to end up nowhere. Especialy if you don't know that Girard lost the plot a little bit around that time of his career so it's difficult to pry apart the novelty from the quackery.

Despite his explicit hatred for game semantics, he landed up exactly there anyway - game theory. Dialogical logic.
So it's entirely possible that you already have some intuition for the implication of his work, but you may have arrived at those intuitions/implications via a different field.

First start with the background/history of DIalogical Logic (https://plato.stanford.edu/entries/logic-dialogical/) and if any of the fields/authors sound familiar to you and you already have intuitions in constructive mathematics, type theory or game theory - rather follow the most recent developments in that area.

Girard is a genius. But he's also a crank/lone wolf and he hasn't had much of a community to help him develop his work or make it more accessible to outsiders.





Skep Dick

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Aug 13, 2022, 5:34:48 PMAug 13
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On Saturday, 13 August 2022 at 15:22:24 UTC+2, richar...@gmail.com wrote:
> And anti-social
Looks like we have ourselves a society of anti-socialites.

> Which is why you need to SPECIFY which foundation you are using as
> statements mean different things in different foundations.
I don't know how else to explain it to you... I don't use any particular foundations.

I start with theorems (conclusions!) and I figure out axioms (premises!) as I go along.

> Because that gets clumsy, we assign a "default" foundation that is assumed.
There is no default foundation.

There is your default (if you even have one)
There is my default (if I even have one)

> Since you won't stand on a foundation, your "work" just colapses.
No it doesn't. The lack of foundation IS my foundation.

My work stands on its own head.

> Not quite. There are core foundations of logic that have been discovered
> if ignored lead to logic that can't support itself.
Which logic? There are so many logics to choose from!

Classical, intuitionistic, dialectic, temporal, linear, symbolic, modal.

Logic, like mathematics, is invented.

As long as you understand the invention/creation process you don't need any foundations.

> Then you can't build anything. What is your FIRST principle, and what
> does it stand on.
My FIRST principle is that there are NO first principles!

It stands on its own head! Like any recursive function does!

> I will need a bit of time to absorb that thought, but the key is that it
> appears that this logic of rules can only come about once you HAVE a set
> of rules of logic to build it on.
No! This logic is about the process of CONSTRUCTING (inventing) the rules!

Protocol synthesis.

> The "Logic of Rules" will still need the "Rules of Logic" for it to work.
This logic is precisely about defining what "working" means!

> This seems to be a common problem with many of the "grand thinkers",
> that they fail to see the assumptions they have built into their system
> bacause they have just accepted them as pre-existing.
The assumptions they have built into their system are after the fact.

They are outputs of the Design process!

> THey are using a foundation they refuse to see, and thus don't build
> fully on it and the structure can colapse.
What could possibly make it collapse? We have already figured out that ANY set of axioms we develop fail to produce contradictions. Platonism died a few centuries ago.

This way we got Bolyai, Lobachevsky, and Riemann geometries.


Richard Damon

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Aug 13, 2022, 6:08:38 PMAug 13
to
On 8/13/22 5:34 PM, Skep Dick wrote:
> On Saturday, 13 August 2022 at 15:22:24 UTC+2, richar...@gmail.com wrote:
>> And anti-social
> Looks like we have ourselves a society of anti-socialites.
>
>> Which is why you need to SPECIFY which foundation you are using as
>> statements mean different things in different foundations.
> I don't know how else to explain it to you... I don't use any particular foundations.

Then you have no foundations, so your work is build on sand and colapses.

>
> I start with theorems (conclusions!) and I figure out axioms (premises!) as I go along.

But those theorems come from something. If you don't know the rules used
to make them, you can't actually use them, as you don't know there
actual meaning.

So, starting with theorems contradicts your previous statement that you
don't use foundations. What it appears is that you don't know what
foundations you are building on, or even if you are working on a
consistent set of foundations.

That makes your work worthless, as you don't know under what conditions
it holds.

>
>> Because that gets clumsy, we assign a "default" foundation that is assumed.
> There is no default foundation.

But there are, every effective group defines its defaults, or finds it
has nothing to work with.

>
> There is your default (if you even have one)
> There is my default (if I even have one)


And that attutide means you are anti-social and can't actually work with
others.

>
>> Since you won't stand on a foundation, your "work" just colapses.
> No it doesn't. The lack of foundation IS my foundation.
>
> My work stands on its own head.

Maybe it stands on its own head because it has nothing to stand on.
>
>> Not quite. There are core foundations of logic that have been discovered
>> if ignored lead to logic that can't support itself.
> Which logic? There are so many logics to choose from!
>
> Classical, intuitionistic, dialectic, temporal, linear, symbolic, modal.
>
> Logic, like mathematics, is invented.
>
> As long as you understand the invention/creation process you don't need any foundations.
>
>> Then you can't build anything. What is your FIRST principle, and what
>> does it stand on.
> My FIRST principle is that there are NO first principles!

Then you have nothing. Or you think you are God.

Or you are just stupid and don't understand what you first princliples
are, or if they actaully even work.

>
> It stands on its own head! Like any recursive function does!
>
>> I will need a bit of time to absorb that thought, but the key is that it
>> appears that this logic of rules can only come about once you HAVE a set
>> of rules of logic to build it on.
> No! This logic is about the process of CONSTRUCTING (inventing) the rules!
>
> Protocol synthesis.

And where does it get the material to synthesis those protocols?

>
>> The "Logic of Rules" will still need the "Rules of Logic" for it to work.
> This logic is precisely about defining what "working" means!
>
>> This seems to be a common problem with many of the "grand thinkers",
>> that they fail to see the assumptions they have built into their system
>> bacause they have just accepted them as pre-existing.
> The assumptions they have built into their system are after the fact.
>
> They are outputs of the Design process!
>
>> THey are using a foundation they refuse to see, and thus don't build
>> fully on it and the structure can colapse.
> What could possibly make it collapse? We have already figured out that ANY set of axioms we develop fail to produce contradictions. Platonism died a few centuries ago.
>

So, you have deluded yourself to ignore failed logic systems, that
almost suredly says your logic system is actually failed.

We know of MANY system that have colasped because they were found to be
self-inconsistent, because they produce contradictions.

So, you statement that ANY set of axioms we develop will fail to produce
contradictions is proven to be false.

Skep Dick

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Aug 13, 2022, 6:52:16 PMAug 13
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On Sunday, 14 August 2022 at 00:08:38 UTC+2, richar...@gmail.com wrote:
> Then you have no foundations, so your work is build on sand and colapses.
^^^ This criterion is built on sand and colapses.

Upon what foundation do you base the assertion that systems need to have foundations?

> But those theorems come from something.
Yes. They come from me sucking my thumb.

>If you don't know the rules used to make them, you can't actually use them, as you don't know there
> actual meaning.
Says who? Engineers don't care about denotational semantics.

We care about what stuff DOES, not what it MEANS. My programs don't mean anything - they do stuff.

> So, starting with theorems contradicts your previous statement that you
> don't use foundations.
So what? Non-contradiction is just an axiom. You can choose to accept it, or reject it, or consider it on case-by-case basis.

Each design choice a different logical system makes.

Where is the "fondation"?

>What it appears is that you don't know what
> foundations you are building on, or even if you are working on a
> consistent set of foundations.
I thought you said you reason from first principles?

Consistency is one possible semantic property of the system.

You may or may not be interested in it. It's just a design choice.

> That makes your work worthless, as you don't know under what conditions
> it holds.
Only if you are an uncharitable wanker who thinks I am too stupid to do risk analysis based on my use-case.

> >> Because that gets clumsy, we assign a "default" foundation that is assumed.
> > There is no default foundation.
> But there are, every effective group defines its defaults, or finds it
> has nothing to work with.
When you set it up like a tautology - no shit!

Any foundation is a default foundation.
Even the lack of a foundation is still a default foundation!

Foundations can be chosen on case-by-case basis!
Depending on whatever is relevant at the time!

> And that attutide means you are anti-social and can't actually work with
> others.
OK, I'll let my colleagues know.

> Maybe it stands on its own head because it has nothing to stand on.
Precisely! But it still stands.

> Then you have nothing. Or you think you are God.
If I have nothing then I still have something!

> Or you are just stupid and don't understand what you first princliples
> are, or if they actaully even work.
I told you what my first principles is!

The first principle is that there are NO first principles.
My first principle is the rejection of ALL axioms. Including the non-contradiction axiom.

What is it that you don't understand?

> And where does it get the material to synthesis those protocols?
From wherever we get any of the materials to conceptualise stuff.


> So, you have deluded yourself to ignore failed logic systems, that
> almost suredly says your logic system is actually failed.
What is it that you don't understand when I say that the notion of a "failed logical system" is NOT a logical notion.

Our criteria for success and failure are NOT logical.

> We know of MANY system that have colasped because they were found to be
> self-inconsistent, because they produce contradictions.
So what? On what foundation do you base the assertion that logic should contain no contradictions?

> So, you statement that ANY set of axioms we develop will fail to produce
> contradictions is proven to be false.
Wow! Idiot. ANY powerful language left unrestricted produces contradictions!
That's a feature not a bug!

For all we know ZFC is inconsistent. That doesn't even matter. It's useful!
If we happen to find a contradiction in it - it won't undo any of the utility the system has had for the past 100+ years.

Your religion is Logicism and your God is the non-contradiction axiom...

I am with Walt Whitman on this one... Do I contradict myself? Very well then, I contradict myself. I am large - I contain multitudes.


Richard Damon

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Aug 13, 2022, 7:30:41 PMAug 13
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On 8/13/22 6:52 PM, Skep Dick wrote:
> On Sunday, 14 August 2022 at 00:08:38 UTC+2, richar...@gmail.com wrote:
>> Then you have no foundations, so your work is build on sand and colapses.
> ^^^ This criterion is built on sand and colapses.

No, it is a firm foundation. Can you show otherwise?

>
> Upon what foundation do you base the assertion that systems need to have foundations?

First principles.

If you have no first principle, you have no principles, so nothing proven.

>
>> But those theorems come from something.
> Yes. They come from me sucking my thumb.

A if you want to try to persuade people that this is a good basis to
accept your ideas, go ahead.

>
>> If you don't know the rules used to make them, you can't actually use them, as you don't know there
>> actual meaning.
> Says who? Engineers don't care about denotational semantics.

We sure do. In fact, if something doesn't make sense, you can't actually
safely use it.

>
> We care about what stuff DOES, not what it MEANS. My programs don't mean anything - they do stuff.



>
>> So, starting with theorems contradicts your previous statement that you
>> don't use foundations.
> So what? Non-contradiction is just an axiom. You can choose to accept it, or reject it, or consider it on case-by-case basis.
>
> Each design choice a different logical system makes.
>
> Where is the "fondation"?

So, you have just effectively said that there is no way to tell if a
system is useful or not. I guess that shows where you systems are going
to end on that spectrum.

You don't know what your system means, or if it yields results that are
actually usable, but the look pretty (I guess, depend on pretty).

>
>> What it appears is that you don't know what
>> foundations you are building on, or even if you are working on a
>> consistent set of foundations.
> I thought you said you reason from first principles?
>
> Consistency is one possible semantic property of the system.
>
> You may or may not be interested in it. It's just a design choice.

Nope, because a fundamental property is that a system that allows
contradictions, if it allows deriving other properties from existing
properties, will tend to allow more contradictions to be derived, until
the system doesn't provide the ability to know if anything actually
means anything.

>
>> That makes your work worthless, as you don't know under what conditions
>> it holds.
> Only if you are an uncharitable wanker who thinks I am too stupid to do risk analysis based on my use-case.

You have defined that you don't have the data to DO a risk anaylsis. You
have symbols without meaning. You don't know under what conditions that
statement are actually defined under, you don't have the data to DO a
risk analysis.

That or you have just been lying about not having the foundations of the
theorems you are taking.

>
>>>> Because that gets clumsy, we assign a "default" foundation that is assumed.
>>> There is no default foundation.
>> But there are, every effective group defines its defaults, or finds it
>> has nothing to work with.
> When you set it up like a tautology - no shit!
>
> Any foundation is a default foundation.
> Even the lack of a foundation is still a default foundation!
>
> Foundations can be chosen on case-by-case basis!
> Depending on whatever is relevant at the time!
>
>> And that attutide means you are anti-social and can't actually work with
>> others.
> OK, I'll let my colleagues know.

But I bet you have an agreed upon set of defaults with them, or you
speciiy your system each time to them.

>
>> Maybe it stands on its own head because it has nothing to stand on.
> Precisely! But it still stands.

Try to stand on your own head!

Not stand with you head to the floor, but STAND ON YOU HEAD as your
foundation.

>
>> Then you have nothing. Or you think you are God.
> If I have nothing then I still have something!

Nope, Nothing is not a something. You have Nothing, not even the empty
set, as that is a something.

You can't talk of the "set of knowledge" because you don't have the
foundation of a set theory, you have NOTHING.

>
>> Or you are just stupid and don't understand what you first princliples
>> are, or if they actaully even work.
> I told you what my first principles is!
>
> The first principle is that there are NO first principles.
> My first principle is the rejection of ALL axioms. Including the non-contradiction axiom.

Then you have nothing to work with, and are beleiving in a false world.

>
> What is it that you don't understand?
>
>> And where does it get the material to synthesis those protocols?
> From wherever we get any of the materials to conceptualise stuff.

Which are the first principles, which you don't have.

>
>
>> So, you have deluded yourself to ignore failed logic systems, that
>> almost suredly says your logic system is actually failed.
> What is it that you don't understand when I say that the notion of a "failed logical system" is NOT a logical notion.
>
> Our criteria for success and failure are NOT logical.

So, you are saying your criteria for success are ILLOGICAL?

>
>> We know of MANY system that have colasped because they were found to be
>> self-inconsistent, because they produce contradictions.
> So what? On what foundation do you base the assertion that logic should contain no contradictions?

The emperical first principle that contradictions lead to valueless
systems.

>
>> So, you statement that ANY set of axioms we develop will fail to produce
>> contradictions is proven to be false.
> Wow! Idiot. ANY powerful language left unrestricted produces contradictions!
> That's a feature not a bug!

"Left Unrestricted", that is why we need rules, and we need to be smart
about our rules.

>
> For all we know ZFC is inconsistent. That doesn't even matter. It's useful!
> If we happen to find a contradiction in it - it won't undo any of the utility the system has had for the past 100+ years.
>
> Your religion is Logicism and your God is the non-contradiction axiom...
>
> I am with Walt Whitman on this one... Do I contradict myself? Very well then, I contradict myself. I am large - I contain multitudes.
>
>

Yes, we might find that ZFC is actually inconsistent, and then we would
need to find what we need to remove from it to keep most of what it
generated and get it back to be consistent.

Just like what happened when it was found that Naive Set Theory broke
things and allowed contradictions, so we need to adjust how we did set
theory to close that hole.

That's the good thing of having a good foundation, when you find a
problem, there is normally a good way to fix it. While we can't know for
certain that the full foundation is without cracks, we do know that it
seems at least generally sound, and any actual cracks are apt to be in
some corner. Switch to a less well tested foundation, and you have less
certainty on that, but you mght be able to make a risk analysts.

Not knowing what you foundation is and how good it is, says you can't do
that risk analysis, as you don't have the needed factors to analyize.


Skep Dick

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Aug 13, 2022, 8:29:03 PMAug 13
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On Sunday, 14 August 2022 at 01:30:41 UTC+2, richar...@gmail.com wrote:
> On 8/13/22 6:52 PM, Skep Dick wrote:
> > On Sunday, 14 August 2022 at 00:08:38 UTC+2, richar...@gmail.com wrote:
> >> Then you have no foundations, so your work is build on sand and colapses.
> > ^^^ This criterion is built on sand and colapses.
> No, it is a firm foundation. Can you show otherwise?
Uhh. Burden of proof?

If your foundation is "firm" prove its firmness.

> If you have no first principle, you have no principles, so nothing proven.
Well, what kind of scam do you have going on there? What proves YOUR first principle?

> >> But those theorems come from something.
> > Yes. They come from me sucking my thumb.
> A if you want to try to persuade people that this is a good basis to
> accept your ideas, go ahead.
Well, what makes your thumb-sucking better than my thumb-sucking?

> We sure do. In fact, if something doesn't make sense, you can't actually
> safely use it.
Uhm.... You do understand that proving the safety properties of systems IS part&parcel of model-checking, right?

https://en.wikipedia.org/wiki/Safety_property

When last did you prove the safety property of your stove?
I bet you just used good enough heuristics, like most humans!


> So, you have just effectively said that there is no way to tell if a
> system is useful or not.
What? Of course I have a way to tell if it's useful.

Does it do what I expect it to do?
Does it NOT do what I don't expect it to do?

That's not logic - that's expectations.

>I guess that shows where you systems are going to end on that spectrum.
I bet you guessed wrong which end of the spectrum my systems end up on.

> You don't know what your system means, or if it yields results that are
> actually usable, but the look pretty (I guess, depend on pretty).
Of course I know whether the systems are useful! How do I know? Because people are actually USING them.
But I have no fucking idea what my systems mean.

What does Google mean?
What does AWS mean?
What does Twitter mean?

> Nope, because a fundamental property is that a system that allows
> contradictions, if it allows deriving other properties from existing
> properties, will tend to allow more contradictions to be derived, until
> the system doesn't provide the ability to know if anything actually
> means anything.
Which is PRECISELY how it is! Nobody gives a shit what a system MEANS.

People care about what systems DOES.

What does an airplane mean? It doesn't mean anything! It flies! It enables faster travel!

> You have defined that you don't have the data to DO a risk anaylsis. You
> have symbols without meaning.
You are super confused. The symbol 10 means the number 10. You know how to count, right?

What that number REPRESENTS is an entirely non-Mathematical question.
It's a question of HOW are you using the symbols?
WHAT are you using the symbols for?


>You don't know under what conditions that statement are actually defined under, you don't have the data to DO a
> risk analysis.
Then how am I doing risk analysis?

> That or you have just been lying about not having the foundations of the
> theorems you are taking.
I don't have foundations. Everything is ad-hoc - depending on my use-case.

I know a bunch of design patterns.

> But I bet you have an agreed upon set of defaults with them, or you
> speciiy your system each time to them.
Which system are you even talking about? We are systems engineers!

We have systems, systems of systems and systems of systems of systems.
They all have different configuration parameters or "defaults".

We have a few shared languages - English, Mathematics, a metric fuckton of metaphors and jargon which has been culturaly evolved.

But ultimately, we create/negotiate meaning in real time.

> >> Maybe it stands on its own head because it has nothing to stand on.
> > Precisely! But it still stands.
> Try to stand on your own head!
> Not stand with you head to the floor, but STAND ON YOU HEAD as your
> foundation.
Not so good with metaphors, anlogies and abstract thought, eh?

With this level of pedantry, nitpicking and inability to communicate, I wonder whether YOU are capable of team work...

> Nope, Nothing is not a something. You have Nothing, not even the empty
> set, as that is a something.
If nothing wasn't something then you wouldn't be able to conceptualise it.
Let alone encode it in language.

> You can't talk of the "set of knowledge" because you don't have the
> foundation of a set theory, you have NOTHING.
I can't talk about the thing that I am talking about "because I don't have the foundations"

Who's going to stop me from talking about the "set of knowledge" despite my lack of foundations?

You?

> Then you have nothing to work with, and are beleiving in a false world.
And yet I am working with it.

The world doesn't give a shit what you think or say about it.
True or false. It's the exact same world.

> >> And where does it get the material to synthesis those protocols?
> > From wherever we get any of the materials to conceptualise stuff.
> Which are the first principles, which you don't have.
Uhhh. ANd where did you get the material to synthesize your first principles?
And where did you get the material to synthesize the material?

Recursion - you don't grok it.


> So, you are saying your criteria for success are ILLOGICAL?
No, I am not. I am saying that our criteria for success or failure are neither logical nor illogical.

Our criteria have nothing to do with logic.
Logic is just a tool with a narrow domain of applicability.

> The emperical first principle that contradictions lead to valueless
> systems.
So English is valueless to you? OK...

> "Left Unrestricted", that is why we need rules, and we need to be smart
> about our rules.
You think it's "smart" to restrict the expressive power of recursive languages?

No wonder you can't communicate effectively in English!

> Yes, we might find that ZFC is actually inconsistent, and then we would
> need to find what we need to remove from it to keep most of what it
> generated and get it back to be consistent.
Why wait until then? Just take out everything that doesn't work already!

> Just like what happened when it was found that Naive Set Theory broke
> things and allowed contradictions, so we need to adjust how we did set
> theory to close that hole.
Yeah. You closed that hole, alright! By restricting comprehension.

Own goal.

> That's the good thing of having a good foundation, when you find a
> problem, there is normally a good way to fix it.
You still haven't address the foundational issue here...

What makes ANYTHING a "problem"?!?

> While we can't know for
> certain that the full foundation is without cracks, we do know that it
> seems at least generally sound, and any actual cracks are apt to be in
> some corner. Switch to a less well tested foundation, and you have less
> certainty on that, but you mght be able to make a risk analysts.
As a risk analyst - I can tell you that Logicians are utter idiots.

Who builds a system that doesn't tolerate ANY failure !?!
Who builds a system which EXPLODES on failure ?!?!

> Not knowing what you foundation is and how good it is, says you can't do
> that risk analysis, as you don't have the needed factors to analyize.
I just did it...

By abandoning the "law" of non-contradiction I have reduced the risk of my system exploding.

Richard Damon

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Aug 13, 2022, 9:27:25 PMAug 13
to
On 8/13/22 8:29 PM, Skep Dick wrote:
> On Sunday, 14 August 2022 at 01:30:41 UTC+2, richar...@gmail.com wrote:
>> On 8/13/22 6:52 PM, Skep Dick wrote:
>>> On Sunday, 14 August 2022 at 00:08:38 UTC+2, richar...@gmail.com wrote:
>>>> Then you have no foundations, so your work is build on sand and colapses.
>>> ^^^ This criterion is built on sand and colapses.
>> No, it is a firm foundation. Can you show otherwise?
> Uhh. Burden of proof?

Burden of proof is on the one promposing change. First Principles are
the establish system, so the burden of proof is on YOUR side.

First Principle are those fundamentals that we find SO fundamental and
obvious that we accept them "universally" as Axioms, without proof,
because without them we have nothing to base a proof on. These are the
principles that have stood the test of time and conditions, and have
been found to be UNIVERSALLY true in any system that actually turned out
to be useful.

You reject First Principles, therefore you have no accepted universal
axioms to base any of your proof on, so you can't actually "prove"
anything to be actually true, only that it seems to fit within your
system. You have to "hope" that the things you "arbitrarily" chose as
your basis (since you don't have a first principle to guide what you can
choose) to actually work together and be useful.

>
> If your foundation is "firm" prove its firmness.

I will go with the Millenniums of testing as its proof.

>
>> If you have no first principle, you have no principles, so nothing proven.
> Well, what kind of scam do you have going on there? What proves YOUR first principle?

The experiance of the ages.

>
>>>> But those theorems come from something.
>>> Yes. They come from me sucking my thumb.
>> A if you want to try to persuade people that this is a good basis to
>> accept your ideas, go ahead.
> Well, what makes your thumb-sucking better than my thumb-sucking?

Because it is based on the testing of ages.

>
>> We sure do. In fact, if something doesn't make sense, you can't actually
>> safely use it.
> Uhm.... You do understand that proving the safety properties of systems IS part&parcel of model-checking, right?

And how do you actually test that if you don't have a foundation to
provide any data that is meaningful.

You are defining that your system is just symbolic, but "bad" is
semantic, so you need to know meaning to determine if something "bad"
will happen.

You lost you definitions of things when you stripped the Theorems from
the foundations and put them on a new experimental one. You have no
actual basis to even define safety.

>
> https://en.wikipedia.org/wiki/Safety_property
>
> When last did you prove the safety property of your stove?
> I bet you just used good enough heuristics, like most humans!

I trust that UL testing is good enough,

Note also, that definition isn't actualy correct, as there is NEVER
"absolute" safety in any "Real" system, as there are always dangers
beyound our ability to predict or mitigate. We can perhaps in limited
system show that as long as they are operated withing their
specifications, there are no hazards created by the system.

In general, we accept relative safety, if the predictable dangers are
sufficiently small compared to the uncontrollable dangers, then it is
acceptable. Sometimes we even accept measurable dangers if the cost to
mitigate is too hi