On 2023-07-07 15:14, olcott wrote:
> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>> On 2023-07-07 12:00, olcott wrote:
>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>> On 2023-07-07 10:40, olcott wrote:
>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>
>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't a
>>>>>>>>>> Tautology (unless you have restricted your univerese of
>>>>>>>>>> systems to make the DEFINITION of "Human" include that is is a
>>>>>>>>>> "Mammal"
>>>>>>>>>
>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>
>>>>>>>> Right, and I gave an example of a set of properties that can
>>>>>>>> define "Human" that means that not all "Humans" might be Mammals.
>>>>>>>>
>>>>>>>
>>>>>>> The way that tautologies work is that humans <are> mammals is
>>>>>>> stipulated
>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>> rejected as
>>>>>>> counter-factual.
>>>>>>
>>>>>> No. That's not the way tautologies work.
>>>>>>
>>>>>> A tautology is a statement which is true in every model. Put
>>>>>> slightly differently, a tautology is a statement whose truth stems
>>>>>> entirely from the meaning *of the logical connectives*.
>>>>>>
>>>>>> André
>>>>>>
>>>>>
>>>>> Welcome back, you are one of very few reviewers that I consider
>>>>> very competent.
>>>>>
>>>>> tautology, in logic, a statement so framed that it cannot be denied
>>>>> without inconsistency. Thus, “All humans are mammals” is held to
>>>>> assert
>>>>> with regard to anything whatsoever that either it is not a human or it
>>>>> is a mammal. But that universal “truth” follows not from any facts
>>>>> noted
>>>>> about real humans but only from the actual use of human and mammal and
>>>>> is thus purely a matter of definition.
>>>>> https://www.britannica.com/topic/tautology
>>>>>
>>>>> I used to refer to the above as a {semantic tautology} until I found
>>>>> this reference that already incorporates that meaning.
>>>>
>>>> That example is terrible. If you want to learn about logic (or any
>>>> other technical subject), Encyclopaedia Britannica is *not* a
>>>> reliable source of information.
>>>>
>>>>> You understand that expressions of natural language that can be
>>>>> verified
>>>>> as completely true entirely on the basis of their semantic meaning are
>>>>> also: statements "that it cannot be denied without inconsistency",
>>>>> don't you?
>>>>>
>>>>> "Baby kittens are not any type of ten story office building." is an
>>>>> example of this broader scoped tautology.
>>
>> 'baby kittens' as opposed to 'adult kittens'.
>>
>>>> That's not a tautology either.
>>>>
>>>
>>> Can you deny it without inconsistency ?
>>
>> Of course I can. Do you understand what 'inconsistency' means? hint:
>> it doesn't mean something which fails to match the real world; it
>> means something in which a given proposition X is both true and false.
>>
>> Consider a model in which there are exactly two entities, fluffy and
>> mittens, and exactly two predicates: Kitten() and OfficeBuilding().
>>
>> What is inconsistent about the following assignment?
>>
>> Kitten = {fluffy, mittens}
>> OfficeBuilding = {fluffy}
>>
>>> That it does not match the definition of tautology that you are
>>> accustomed to does not mean that it does not match the more broadly
>>> defined term of {semantic tautology} that I and Britannica refer to.
>>
>> Britannica's definition is fine. It is their example which is terrible.
>>
>>> Any expression of natural or formal language cannot be denied without
>>> inconsistency is a semantic tautology.
>>>
>>>>> My use of the term {tautology} is simply broader than the typical
>>>>> use of
>>>>> the term within formal logic. That does not mean that I am
>>>>> incorrect. My
>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>
>>>> If you use it in a way that doesn't conform to standard usage then yes,
>>>
>>> In the field of the philosophy of logic we must deal with things such as
>>> the analytic/synthetic distinction. Formal logic doesn't care about such
>>> things and is limited to only going by the book.
>>
>> The analytic/synthetic distinction is part of the philosophy of
>> *language*, not the philosophy of logic. And it is unrelated to the
>> notion of a tautology.
>>
>
> I am stipulating that anything that pertains to the nature of truth
> pertains to the philosophy of logic.

And I am stipulating that anything pertaining to elephants pertains to
the philosophy of logic. Of course, this stipulation has absolutely no
effect on how the term is actually used.

>> An analytic sentence is a sentence which is true based on the meanings
>> of the words involved. This is not a particularly useful concept and
>> always applied to a very small, uninteresting subset of sentences.
>>
>
>    "Analytic propositions are true or not true solely by virtue of
>    their meaning..."
>    https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>
> I am stipulating that this includes meanings specified in the formal
> languages of formal systems.

And again your stipulation has no bearing on how the terms are actually
used. If you want to be understood you need to use terms as they are
conventionally used.

You seem to think that 'stipulating' is some sort of magical incantation.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

On 7/7/23 8:33 PM, olcott wrote:

> PURE REASONING WILL CONFIRM:
> Within the semantic meanings that I stipulated a notion of formal
> system can be defined such that incompleteness is impossible and a
> consistent and correct True(L,x) can always be defined.
>
> It this system that I defined unprovable simply mean untrue, yet
> not necessarily false.
>
> In cases where the elements of the set of analytic truth are outside
> of the set of analytic knowledge (such as the Goldbach conjecture)
> the semantic connection may require an infinite number of steps.
>
>

In other words, you are ignoring the definition of standard logic and
making up your own.

Since you disagree on the "Definiton of Truth", nothing you say has
meaning for classical logic.

Thus NOTHING you say has any import on what classical logic says and shows.

Remember, if you presume to be able to change the rules and try to make
that apply to standard logic, anyone else has the right to change YOUR
rules and apply it to yours.

You have just effectively admitting that you have wasted your life
chasing a LIE.

YOU HAVE FAILED, and have just admitted it.

On 7/7/2023 8:33 PM, André G. Isaak wrote:
> On 2023-07-07 15:14, olcott wrote:
>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>> On 2023-07-07 12:00, olcott wrote:
>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>
>>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't a
>>>>>>>>>>> Tautology (unless you have restricted your univerese of
>>>>>>>>>>> systems to make the DEFINITION of "Human" include that is is
>>>>>>>>>>> a "Mammal"
>>>>>>>>>>
>>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>
>>>>>>>>> Right, and I gave an example of a set of properties that can
>>>>>>>>> define "Human" that means that not all "Humans" might be Mammals.
>>>>>>>>>
>>>>>>>>
>>>>>>>> The way that tautologies work is that humans <are> mammals is
>>>>>>>> stipulated
>>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>>> rejected as
>>>>>>>> counter-factual.
>>>>>>>
>>>>>>> No. That's not the way tautologies work.
>>>>>>>
>>>>>>> A tautology is a statement which is true in every model. Put
>>>>>>> slightly differently, a tautology is a statement whose truth
>>>>>>> stems entirely from the meaning *of the logical connectives*.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> Welcome back, you are one of very few reviewers that I consider
>>>>>> very competent.
>>>>>>
>>>>>> tautology, in logic, a statement so framed that it cannot be denied
>>>>>> without inconsistency. Thus, “All humans are mammals” is held to
>>>>>> assert
>>>>>> with regard to anything whatsoever that either it is not a human
>>>>>> or it
>>>>>> is a mammal. But that universal “truth” follows not from any facts
>>>>>> noted
>>>>>> about real humans but only from the actual use of human and mammal
>>>>>> and
>>>>>> is thus purely a matter of definition.
>>>>>> https://www.britannica.com/topic/tautology
>>>>>>
>>>>>> I used to refer to the above as a {semantic tautology} until I found
>>>>>> this reference that already incorporates that meaning.
>>>>>
>>>>> That example is terrible. If you want to learn about logic (or any
>>>>> other technical subject), Encyclopaedia Britannica is *not* a
>>>>> reliable source of information.
>>>>>
>>>>>> You understand that expressions of natural language that can be
>>>>>> verified
>>>>>> as completely true entirely on the basis of their semantic meaning
>>>>>> are
>>>>>> also: statements "that it cannot be denied without inconsistency",
>>>>>> don't you?
>>>>>>
>>>>>> "Baby kittens are not any type of ten story office building." is an
>>>>>> example of this broader scoped tautology.
>>>
>>> 'baby kittens' as opposed to 'adult kittens'.
>>>
>>>>> That's not a tautology either.
>>>>>
>>>>
>>>> Can you deny it without inconsistency ?
>>>
>>> Of course I can. Do you understand what 'inconsistency' means? hint:
>>> it doesn't mean something which fails to match the real world; it
>>> means something in which a given proposition X is both true and false.
>>>
>>> Consider a model in which there are exactly two entities, fluffy and
>>> mittens, and exactly two predicates: Kitten() and OfficeBuilding().
>>>
>>> What is inconsistent about the following assignment?
>>>
>>> Kitten = {fluffy, mittens}
>>> OfficeBuilding = {fluffy}
>>>
>>>> That it does not match the definition of tautology that you are
>>>> accustomed to does not mean that it does not match the more broadly
>>>> defined term of {semantic tautology} that I and Britannica refer to.
>>>
>>> Britannica's definition is fine. It is their example which is terrible.
>>>
>>>> Any expression of natural or formal language cannot be denied without
>>>> inconsistency is a semantic tautology.
>>>>
>>>>>> My use of the term {tautology} is simply broader than the typical
>>>>>> use of
>>>>>> the term within formal logic. That does not mean that I am
>>>>>> incorrect. My
>>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>>
>>>>> If you use it in a way that doesn't conform to standard usage then
>>>>> yes,
>>>>
>>>> In the field of the philosophy of logic we must deal with things
>>>> such as
>>>> the analytic/synthetic distinction. Formal logic doesn't care about
>>>> such
>>>> things and is limited to only going by the book.
>>>
>>> The analytic/synthetic distinction is part of the philosophy of
>>> *language*, not the philosophy of logic. And it is unrelated to the
>>> notion of a tautology.
>>>
>>
>> I am stipulating that anything that pertains to the nature of truth
>> pertains to the philosophy of logic.
>
> And I am stipulating that anything pertaining to elephants pertains to
> the philosophy of logic. Of course, this stipulation has absolutely no
> effect on how the term is actually used.
>
>>> An analytic sentence is a sentence which is true based on the
>>> meanings of the words involved. This is not a particularly useful
>>> concept and always applied to a very small, uninteresting subset of
>>> sentences.
>>>
>>
>>     "Analytic propositions are true or not true solely by virtue of
>>     their meaning..."
>>     https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>
>> I am stipulating that this includes meanings specified in the formal
>> languages of formal systems.
>
> And again your stipulation has no bearing on how the terms are actually
> used. If you want to be understood you need to use terms as they are
> conventionally used.
>
> You seem to think that 'stipulating' is some sort of magical incantation.
>
> André
>

*I must use a stipulative definitions because there are no*
*conventional terms for the meanings that I must refer to*

A stipulative definition is a type of definition in which a new or
currently existing term is given a new specific meaning for the purposes
of argument or discussion in a given context...

a stipulative definition cannot be "correct" or "incorrect"; it can only
differ from other definitions, but it can be useful for its intended
purpose. https://en.wikipedia.org/wiki/Stipulative_definition

Analytic propositions(olcott)
"Analytic propositions are true or not true solely by virtue of
their meaning..."
https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction

I am stipulating that this includes meanings specified in the formal
languages of formal systems.

semantic tautology(olcott)
I am stipulating that a {semantic tautology} includes every expression
of formal or natural language that can be verified as completely true
entirely on the basis of its semantic meaning.

On 7/7/2023 8:53 PM, Richard Damon wrote:
> On 7/7/23 8:33 PM, olcott wrote:
>
>> PURE REASONING WILL CONFIRM:
>> Within the semantic meanings that I stipulated a notion of formal
>> system can be defined such that incompleteness is impossible and a
>> consistent and correct True(L,x) can always be defined.
>>
>> It this system that I defined unprovable simply mean untrue, yet
>> not necessarily false.
>>
>> In cases where the elements of the set of analytic truth are outside
>> of the set of analytic knowledge (such as the Goldbach conjecture)
>> the semantic connection may require an infinite number of steps.
>>
>>
>
>
>
> In other words, you are ignoring the definition of standard logic and
> making up your own.
>

*I must use a stipulative definitions because there are no*
*conventional terms for the meanings that I must refer to*

A stipulative definition is a type of definition in which a new or
currently existing term is given a new specific meaning for the purposes
of argument or discussion in a given context...

a stipulative definition cannot be "correct" or "incorrect"; it can only
differ from other definitions, but it can be useful for its intended
purpose. https://en.wikipedia.org/wiki/Stipulative_definition

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 7/7/23 10:15 PM, olcott wrote:
> On 7/7/2023 8:53 PM, Richard Damon wrote:
>> On 7/7/23 8:33 PM, olcott wrote:
>>
>>> PURE REASONING WILL CONFIRM:
>>> Within the semantic meanings that I stipulated a notion of formal
>>> system can be defined such that incompleteness is impossible and a
>>> consistent and correct True(L,x) can always be defined.
>>>
>>> It this system that I defined unprovable simply mean untrue, yet
>>> not necessarily false.
>>>
>>> In cases where the elements of the set of analytic truth are outside
>>> of the set of analytic knowledge (such as the Goldbach conjecture)
>>> the semantic connection may require an infinite number of steps.
>>>
>>>
>>
>>
>>
>> In other words, you are ignoring the definition of standard logic and
>> making up your own.
>>
>
> *I must use a stipulative definitions because there are no*
> *conventional terms for the meanings that I must refer to*

And since your stipulation don't match the actual definitions, it means
all your work is WORTHLESS when you try to relate it to the classical works.

>
>
> A stipulative definition is a type of definition in which a new or
> currently existing term is given a new specific meaning for the purposes
> of argument or discussion in a given context...

But, when you make the definition contrary makes your arguement
inapplicable to the actual thing.

Note, the comment at the end:

When a stipulative definition is confused with a lexical definition
within an argument there is a risk of equivocation.

Your whole arguement is based on such an equivocation.

>
> a stipulative definition cannot be "correct" or "incorrect"; it can only
> differ from other definitions, but it can be useful for its intended
> purpose.  https://en.wikipedia.org/wiki/Stipulative_definition
>

When the definition differs from the normal definition of the word, it
makes that statement not applicable to anything that uses that normal
definition.

Since you are stipulating a definition which is incorrect for the actual
word, nothing you say after that can be applied to the original.

PERIOD.

Otherwise you are accepting that by stipulating that my cat is a dog,
dog meows, since my cat meows.

You just don't understand what you are doing, which is typical of
Pathological Liars, as by negating the power and meaning of "Truth" the
can think and claim their statements are not lies.

Note, "Stipulating" that the sunlight is dark, doesn't make it hard to see.

On 7/7/23 10:14 PM, olcott wrote:
> On 7/7/2023 8:33 PM, André G. Isaak wrote:
>> On 2023-07-07 15:14, olcott wrote:
>>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>>> On 2023-07-07 12:00, olcott wrote:
>>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>>
>>>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't a
>>>>>>>>>>>> Tautology (unless you have restricted your univerese of
>>>>>>>>>>>> systems to make the DEFINITION of "Human" include that is is
>>>>>>>>>>>> a "Mammal"
>>>>>>>>>>>
>>>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>>
>>>>>>>>>> Right, and I gave an example of a set of properties that can
>>>>>>>>>> define "Human" that means that not all "Humans" might be Mammals.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The way that tautologies work is that humans <are> mammals is
>>>>>>>>> stipulated
>>>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>>>> rejected as
>>>>>>>>> counter-factual.
>>>>>>>>
>>>>>>>> No. That's not the way tautologies work.
>>>>>>>>
>>>>>>>> A tautology is a statement which is true in every model. Put
>>>>>>>> slightly differently, a tautology is a statement whose truth
>>>>>>>> stems entirely from the meaning *of the logical connectives*.
>>>>>>>>
>>>>>>>> André
>>>>>>>>
>>>>>>>
>>>>>>> Welcome back, you are one of very few reviewers that I consider
>>>>>>> very competent.
>>>>>>>
>>>>>>> tautology, in logic, a statement so framed that it cannot be denied
>>>>>>> without inconsistency. Thus, “All humans are mammals” is held to
>>>>>>> assert
>>>>>>> with regard to anything whatsoever that either it is not a human
>>>>>>> or it
>>>>>>> is a mammal. But that universal “truth” follows not from any
>>>>>>> facts noted
>>>>>>> about real humans but only from the actual use of human and
>>>>>>> mammal and
>>>>>>> is thus purely a matter of definition.
>>>>>>> https://www.britannica.com/topic/tautology
>>>>>>>
>>>>>>> I used to refer to the above as a {semantic tautology} until I found
>>>>>>> this reference that already incorporates that meaning.
>>>>>>
>>>>>> That example is terrible. If you want to learn about logic (or any
>>>>>> other technical subject), Encyclopaedia Britannica is *not* a
>>>>>> reliable source of information.
>>>>>>
>>>>>>> You understand that expressions of natural language that can be
>>>>>>> verified
>>>>>>> as completely true entirely on the basis of their semantic
>>>>>>> meaning are
>>>>>>> also: statements "that it cannot be denied without inconsistency",
>>>>>>> don't you?
>>>>>>>
>>>>>>> "Baby kittens are not any type of ten story office building." is an
>>>>>>> example of this broader scoped tautology.
>>>>
>>>> 'baby kittens' as opposed to 'adult kittens'.
>>>>
>>>>>> That's not a tautology either.
>>>>>>
>>>>>
>>>>> Can you deny it without inconsistency ?
>>>>
>>>> Of course I can. Do you understand what 'inconsistency' means? hint:
>>>> it doesn't mean something which fails to match the real world; it
>>>> means something in which a given proposition X is both true and false.
>>>>
>>>> Consider a model in which there are exactly two entities, fluffy and
>>>> mittens, and exactly two predicates: Kitten() and OfficeBuilding().
>>>>
>>>> What is inconsistent about the following assignment?
>>>>
>>>> Kitten = {fluffy, mittens}
>>>> OfficeBuilding = {fluffy}
>>>>
>>>>> That it does not match the definition of tautology that you are
>>>>> accustomed to does not mean that it does not match the more broadly
>>>>> defined term of {semantic tautology} that I and Britannica refer to.
>>>>
>>>> Britannica's definition is fine. It is their example which is terrible.
>>>>
>>>>> Any expression of natural or formal language cannot be denied without
>>>>> inconsistency is a semantic tautology.
>>>>>
>>>>>>> My use of the term {tautology} is simply broader than the typical
>>>>>>> use of
>>>>>>> the term within formal logic. That does not mean that I am
>>>>>>> incorrect. My
>>>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>>>
>>>>>> If you use it in a way that doesn't conform to standard usage then
>>>>>> yes,
>>>>>
>>>>> In the field of the philosophy of logic we must deal with things
>>>>> such as
>>>>> the analytic/synthetic distinction. Formal logic doesn't care about
>>>>> such
>>>>> things and is limited to only going by the book.
>>>>
>>>> The analytic/synthetic distinction is part of the philosophy of
>>>> *language*, not the philosophy of logic. And it is unrelated to the
>>>> notion of a tautology.
>>>>
>>>
>>> I am stipulating that anything that pertains to the nature of truth
>>> pertains to the philosophy of logic.
>>
>> And I am stipulating that anything pertaining to elephants pertains to
>> the philosophy of logic. Of course, this stipulation has absolutely no
>> effect on how the term is actually used.
>>
>>>> An analytic sentence is a sentence which is true based on the
>>>> meanings of the words involved. This is not a particularly useful
>>>> concept and always applied to a very small, uninteresting subset of
>>>> sentences.
>>>>
>>>
>>>     "Analytic propositions are true or not true solely by virtue of
>>>     their meaning..."
>>>     https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>
>>> I am stipulating that this includes meanings specified in the formal
>>> languages of formal systems.
>>
>> And again your stipulation has no bearing on how the terms are
>> actually used. If you want to be understood you need to use terms as
>> they are conventionally used.
>>
>> You seem to think that 'stipulating' is some sort of magical incantation.
>>
>> André
>>
>
> *I must use a stipulative definitions because there are no*
> *conventional terms for the meanings that I must refer to*
>
>
> A stipulative definition is a type of definition in which a new or
> currently existing term is given a new specific meaning for the purposes
> of argument or discussion in a given context...
>
> a stipulative definition cannot be "correct" or "incorrect"; it can only
> differ from other definitions, but it can be useful for its intended
> purpose.  https://en.wikipedia.org/wiki/Stipulative_definition
>
>
> Analytic propositions(olcott)
> "Analytic propositions are true or not true solely by virtue of
> their meaning..."
> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>
> I am stipulating that this includes meanings specified in the formal
> languages of formal systems.
>
> semantic tautology(olcott)
> I am stipulating that a {semantic tautology} includes every expression
> of formal or natural language that can be verified as completely true
> entirely on the basis of its semantic meaning.
>
>
> *PURE REASONING WILL CONFIRM*
> When the body of analytic truth is construed as being entirely
> comprised of elements of semantic_tautology(olcott) then True(L,x)
> is (always and only) established on the basis of semantic connections
> between elements.
>
> True(L,x) always requires this semantic connection thus there cannot
> be a case of True(L,x) that does not include establishing this semantic
> connection through Provable(L,x).
>
> *As Richard pointed out*
> In cases where the elements of the set of analytic truth are outside
> of the set of analytic knowledge (such as the Goldbach conjecture)
> the semantic connection may require an infinite number of steps.
>
> Within the semantic meanings that I stipulated a notion of formal
> system can be defined such that incompleteness is impossible and a
> consistent and correct True(L,x) can always be defined.
>
> It this system that I defined unprovable simply mean untrue, yet
> not necessarily false.
>
>
>

On 7/7/2023 9:37 PM, Richard Damon wrote:
> On 7/7/23 10:15 PM, olcott wrote:
>> On 7/7/2023 8:53 PM, Richard Damon wrote:
>>> On 7/7/23 8:33 PM, olcott wrote:
>>>
>>>> PURE REASONING WILL CONFIRM:
>>>> Within the semantic meanings that I stipulated a notion of formal
>>>> system can be defined such that incompleteness is impossible and a
>>>> consistent and correct True(L,x) can always be defined.
>>>>
>>>> It this system that I defined unprovable simply mean untrue, yet
>>>> not necessarily false.
>>>>
>>>> In cases where the elements of the set of analytic truth are outside
>>>> of the set of analytic knowledge (such as the Goldbach conjecture)
>>>> the semantic connection may require an infinite number of steps.
>>>>
>>>>
>>>
>>>
>>>
>>> In other words, you are ignoring the definition of standard logic and
>>> making up your own.
>>>
>>
>> *I must use a stipulative definitions because there are no*
>> *conventional terms for the meanings that I must refer to*
>
> And since your stipulation don't match the actual definitions, it means
> all your work is WORTHLESS when you try to relate it to the classical
> works.
Not at all. When you apply my new ideas specified by these stipulative
definitions you derive a notion of a formal system with the same
capabilities as the conventional notions, yet incompleteness and
undefinability are eliminated.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 7/7/2023 9:39 PM, Richard Damon wrote:
> On 7/7/23 10:14 PM, olcott wrote:
>> On 7/7/2023 8:33 PM, André G. Isaak wrote:
>>> On 2023-07-07 15:14, olcott wrote:
>>>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>>>> On 2023-07-07 12:00, olcott wrote:
>>>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>>>
>>>>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't a
>>>>>>>>>>>>> Tautology (unless you have restricted your univerese of
>>>>>>>>>>>>> systems to make the DEFINITION of "Human" include that is
>>>>>>>>>>>>> is a "Mammal"
>>>>>>>>>>>>
>>>>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>>>
>>>>>>>>>>> Right, and I gave an example of a set of properties that can
>>>>>>>>>>> define "Human" that means that not all "Humans" might be
>>>>>>>>>>> Mammals.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> The way that tautologies work is that humans <are> mammals is
>>>>>>>>>> stipulated
>>>>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>>>>> rejected as
>>>>>>>>>> counter-factual.
>>>>>>>>>
>>>>>>>>> No. That's not the way tautologies work.
>>>>>>>>>
>>>>>>>>> A tautology is a statement which is true in every model. Put
>>>>>>>>> slightly differently, a tautology is a statement whose truth
>>>>>>>>> stems entirely from the meaning *of the logical connectives*.
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>>
>>>>>>>>
>>>>>>>> Welcome back, you are one of very few reviewers that I consider
>>>>>>>> very competent.
>>>>>>>>
>>>>>>>> tautology, in logic, a statement so framed that it cannot be denied
>>>>>>>> without inconsistency. Thus, “All humans are mammals” is held to
>>>>>>>> assert
>>>>>>>> with regard to anything whatsoever that either it is not a human
>>>>>>>> or it
>>>>>>>> is a mammal. But that universal “truth” follows not from any
>>>>>>>> facts noted
>>>>>>>> about real humans but only from the actual use of human and
>>>>>>>> mammal and
>>>>>>>> is thus purely a matter of definition.
>>>>>>>> https://www.britannica.com/topic/tautology
>>>>>>>>
>>>>>>>> I used to refer to the above as a {semantic tautology} until I
>>>>>>>> found
>>>>>>>> this reference that already incorporates that meaning.
>>>>>>>
>>>>>>> That example is terrible. If you want to learn about logic (or
>>>>>>> any other technical subject), Encyclopaedia Britannica is *not* a
>>>>>>> reliable source of information.
>>>>>>>
>>>>>>>> You understand that expressions of natural language that can be
>>>>>>>> verified
>>>>>>>> as completely true entirely on the basis of their semantic
>>>>>>>> meaning are
>>>>>>>> also: statements "that it cannot be denied without inconsistency",
>>>>>>>> don't you?
>>>>>>>>
>>>>>>>> "Baby kittens are not any type of ten story office building." is an
>>>>>>>> example of this broader scoped tautology.
>>>>>
>>>>> 'baby kittens' as opposed to 'adult kittens'.
>>>>>
>>>>>>> That's not a tautology either.
>>>>>>>
>>>>>>
>>>>>> Can you deny it without inconsistency ?
>>>>>
>>>>> Of course I can. Do you understand what 'inconsistency' means?
>>>>> hint: it doesn't mean something which fails to match the real
>>>>> world; it means something in which a given proposition X is both
>>>>> true and false.
>>>>>
>>>>> Consider a model in which there are exactly two entities, fluffy
>>>>> and mittens, and exactly two predicates: Kitten() and
>>>>> OfficeBuilding().
>>>>>
>>>>> What is inconsistent about the following assignment?
>>>>>
>>>>> Kitten = {fluffy, mittens}
>>>>> OfficeBuilding = {fluffy}
>>>>>
>>>>>> That it does not match the definition of tautology that you are
>>>>>> accustomed to does not mean that it does not match the more broadly
>>>>>> defined term of {semantic tautology} that I and Britannica refer to.
>>>>>
>>>>> Britannica's definition is fine. It is their example which is
>>>>> terrible.
>>>>>
>>>>>> Any expression of natural or formal language cannot be denied without
>>>>>> inconsistency is a semantic tautology.
>>>>>>
>>>>>>>> My use of the term {tautology} is simply broader than the
>>>>>>>> typical use of
>>>>>>>> the term within formal logic. That does not mean that I am
>>>>>>>> incorrect. My
>>>>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>>>>
>>>>>>> If you use it in a way that doesn't conform to standard usage
>>>>>>> then yes,
>>>>>>
>>>>>> In the field of the philosophy of logic we must deal with things
>>>>>> such as
>>>>>> the analytic/synthetic distinction. Formal logic doesn't care
>>>>>> about such
>>>>>> things and is limited to only going by the book.
>>>>>
>>>>> The analytic/synthetic distinction is part of the philosophy of
>>>>> *language*, not the philosophy of logic. And it is unrelated to the
>>>>> notion of a tautology.
>>>>>
>>>>
>>>> I am stipulating that anything that pertains to the nature of truth
>>>> pertains to the philosophy of logic.
>>>
>>> And I am stipulating that anything pertaining to elephants pertains
>>> to the philosophy of logic. Of course, this stipulation has
>>> absolutely no effect on how the term is actually used.
>>>
>>>>> An analytic sentence is a sentence which is true based on the
>>>>> meanings of the words involved. This is not a particularly useful
>>>>> concept and always applied to a very small, uninteresting subset of
>>>>> sentences.
>>>>>
>>>>
>>>>     "Analytic propositions are true or not true solely by virtue of
>>>>     their meaning..."
>>>>
>>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>>
>>>> I am stipulating that this includes meanings specified in the formal
>>>> languages of formal systems.
>>>
>>> And again your stipulation has no bearing on how the terms are
>>> actually used. If you want to be understood you need to use terms as
>>> they are conventionally used.
>>>
>>> You seem to think that 'stipulating' is some sort of magical
>>> incantation.
>>>
>>> André
>>>
>>
>> *I must use a stipulative definitions because there are no*
>> *conventional terms for the meanings that I must refer to*
>>
>>
>> A stipulative definition is a type of definition in which a new or
>> currently existing term is given a new specific meaning for the purposes
>> of argument or discussion in a given context...
>>
>> a stipulative definition cannot be "correct" or "incorrect"; it can only
>> differ from other definitions, but it can be useful for its intended
>> purpose.  https://en.wikipedia.org/wiki/Stipulative_definition
>>
>>
>> Analytic propositions(olcott)
>> "Analytic propositions are true or not true solely by virtue of
>> their meaning..."
>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>
>> I am stipulating that this includes meanings specified in the formal
>> languages of formal systems.
>>
>> semantic tautology(olcott)
>> I am stipulating that a {semantic tautology} includes every expression
>> of formal or natural language that can be verified as completely true
>> entirely on the basis of its semantic meaning.
>>
>>
>> *PURE REASONING WILL CONFIRM*
>> When the body of analytic truth is construed as being entirely
>> comprised of elements of semantic_tautology(olcott) then True(L,x)
>> is (always and only) established on the basis of semantic connections
>> between elements.
>>
>> True(L,x) always requires this semantic connection thus there cannot
>> be a case of True(L,x) that does not include establishing this semantic
>> connection through Provable(L,x).
>>
>> *As Richard pointed out*
>> In cases where the elements of the set of analytic truth are outside
>> of the set of analytic knowledge (such as the Goldbach conjecture)
>> the semantic connection may require an infinite number of steps.
>>
>> Within the semantic meanings that I stipulated a notion of formal
>> system can be defined such that incompleteness is impossible and a
>> consistent and correct True(L,x) can always be defined.
>>
>> It this system that I defined unprovable simply mean untrue, yet
>> not necessarily false.
>>
>>
>>
>
> Which means you are just admitting to being a Pathological Liar by
> changing the meaning of the key words,

On 7/7/23 10:44 PM, olcott wrote:
> On 7/7/2023 9:37 PM, Richard Damon wrote:
>> On 7/7/23 10:15 PM, olcott wrote:
>>> On 7/7/2023 8:53 PM, Richard Damon wrote:
>>>> On 7/7/23 8:33 PM, olcott wrote:
>>>>
>>>>> PURE REASONING WILL CONFIRM:
>>>>> Within the semantic meanings that I stipulated a notion of formal
>>>>> system can be defined such that incompleteness is impossible and a
>>>>> consistent and correct True(L,x) can always be defined.
>>>>>
>>>>> It this system that I defined unprovable simply mean untrue, yet
>>>>> not necessarily false.
>>>>>
>>>>> In cases where the elements of the set of analytic truth are outside
>>>>> of the set of analytic knowledge (such as the Goldbach conjecture)
>>>>> the semantic connection may require an infinite number of steps.
>>>>>
>>>>>
>>>>
>>>>
>>>>
>>>> In other words, you are ignoring the definition of standard logic
>>>> and making up your own.
>>>>
>>>
>>> *I must use a stipulative definitions because there are no*
>>> *conventional terms for the meanings that I must refer to*
>>
>> And since your stipulation don't match the actual definitions, it
>> means all your work is WORTHLESS when you try to relate it to the
>> classical works.
> Not at all. When you apply my new ideas specified by these stipulative
> definitions you derive a notion of a formal system with the same
> capabilities as the conventional notions, yet incompleteness and
> undefinability are eliminated.
>
>

Nope, you have equivocacted and assumed two different things are the
same. "Standard Logic" and "Olcottian Logic" are NOT the same, so
anything you say about Olcottian logic is inapplicable to Standard Logic.

You have done NOTHING to show that Olcottian Logic has any use, because
you haven't actually shown that it can do anything, because you don't
even require that you follow it, since you acccpt everything you want
that wasn't based on it.

You are just proving that you are a pathological liar that doesn't
understand the basic meaning of Truth.

You CLAIM a lot, but have proven NOTHING except that you are incompetent
at logic.

You system has gone BOOM but you refuse to see it, so your mind went
BOOM too.

On 7/7/23 10:47 PM, olcott wrote:
> On 7/7/2023 9:39 PM, Richard Damon wrote:
>> On 7/7/23 10:14 PM, olcott wrote:
>>> On 7/7/2023 8:33 PM, André G. Isaak wrote:
>>>> On 2023-07-07 15:14, olcott wrote:
>>>>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>>>>> On 2023-07-07 12:00, olcott wrote:
>>>>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>>>>
>>>>>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't a
>>>>>>>>>>>>>> Tautology (unless you have restricted your univerese of
>>>>>>>>>>>>>> systems to make the DEFINITION of "Human" include that is
>>>>>>>>>>>>>> is a "Mammal"
>>>>>>>>>>>>>
>>>>>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>>>>
>>>>>>>>>>>> Right, and I gave an example of a set of properties that can
>>>>>>>>>>>> define "Human" that means that not all "Humans" might be
>>>>>>>>>>>> Mammals.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> The way that tautologies work is that humans <are> mammals is
>>>>>>>>>>> stipulated
>>>>>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>>>>>> rejected as
>>>>>>>>>>> counter-factual.
>>>>>>>>>>
>>>>>>>>>> No. That's not the way tautologies work.
>>>>>>>>>>
>>>>>>>>>> A tautology is a statement which is true in every model. Put
>>>>>>>>>> slightly differently, a tautology is a statement whose truth
>>>>>>>>>> stems entirely from the meaning *of the logical connectives*.
>>>>>>>>>>
>>>>>>>>>> André
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Welcome back, you are one of very few reviewers that I consider
>>>>>>>>> very competent.
>>>>>>>>>
>>>>>>>>> tautology, in logic, a statement so framed that it cannot be
>>>>>>>>> denied
>>>>>>>>> without inconsistency. Thus, “All humans are mammals” is held
>>>>>>>>> to assert
>>>>>>>>> with regard to anything whatsoever that either it is not a
>>>>>>>>> human or it
>>>>>>>>> is a mammal. But that universal “truth” follows not from any
>>>>>>>>> facts noted
>>>>>>>>> about real humans but only from the actual use of human and
>>>>>>>>> mammal and
>>>>>>>>> is thus purely a matter of definition.
>>>>>>>>> https://www.britannica.com/topic/tautology
>>>>>>>>>
>>>>>>>>> I used to refer to the above as a {semantic tautology} until I
>>>>>>>>> found
>>>>>>>>> this reference that already incorporates that meaning.
>>>>>>>>
>>>>>>>> That example is terrible. If you want to learn about logic (or
>>>>>>>> any other technical subject), Encyclopaedia Britannica is *not*
>>>>>>>> a reliable source of information.
>>>>>>>>
>>>>>>>>> You understand that expressions of natural language that can be
>>>>>>>>> verified
>>>>>>>>> as completely true entirely on the basis of their semantic
>>>>>>>>> meaning are
>>>>>>>>> also: statements "that it cannot be denied without inconsistency",
>>>>>>>>> don't you?
>>>>>>>>>
>>>>>>>>> "Baby kittens are not any type of ten story office building."
>>>>>>>>> is an
>>>>>>>>> example of this broader scoped tautology.
>>>>>>
>>>>>> 'baby kittens' as opposed to 'adult kittens'.
>>>>>>
>>>>>>>> That's not a tautology either.
>>>>>>>>
>>>>>>>
>>>>>>> Can you deny it without inconsistency ?
>>>>>>
>>>>>> Of course I can. Do you understand what 'inconsistency' means?
>>>>>> hint: it doesn't mean something which fails to match the real
>>>>>> world; it means something in which a given proposition X is both
>>>>>> true and false.
>>>>>>
>>>>>> Consider a model in which there are exactly two entities, fluffy
>>>>>> and mittens, and exactly two predicates: Kitten() and
>>>>>> OfficeBuilding().
>>>>>>
>>>>>> What is inconsistent about the following assignment?
>>>>>>
>>>>>> Kitten = {fluffy, mittens}
>>>>>> OfficeBuilding = {fluffy}
>>>>>>
>>>>>>> That it does not match the definition of tautology that you are
>>>>>>> accustomed to does not mean that it does not match the more broadly
>>>>>>> defined term of {semantic tautology} that I and Britannica refer to.
>>>>>>
>>>>>> Britannica's definition is fine. It is their example which is
>>>>>> terrible.
>>>>>>
>>>>>>> Any expression of natural or formal language cannot be denied
>>>>>>> without
>>>>>>> inconsistency is a semantic tautology.
>>>>>>>
>>>>>>>>> My use of the term {tautology} is simply broader than the
>>>>>>>>> typical use of
>>>>>>>>> the term within formal logic. That does not mean that I am
>>>>>>>>> incorrect. My
>>>>>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>>>>>
>>>>>>>> If you use it in a way that doesn't conform to standard usage
>>>>>>>> then yes,
>>>>>>>
>>>>>>> In the field of the philosophy of logic we must deal with things
>>>>>>> such as
>>>>>>> the analytic/synthetic distinction. Formal logic doesn't care
>>>>>>> about such
>>>>>>> things and is limited to only going by the book.
>>>>>>
>>>>>> The analytic/synthetic distinction is part of the philosophy of
>>>>>> *language*, not the philosophy of logic. And it is unrelated to
>>>>>> the notion of a tautology.
>>>>>>
>>>>>
>>>>> I am stipulating that anything that pertains to the nature of truth
>>>>> pertains to the philosophy of logic.
>>>>
>>>> And I am stipulating that anything pertaining to elephants pertains
>>>> to the philosophy of logic. Of course, this stipulation has
>>>> absolutely no effect on how the term is actually used.
>>>>
>>>>>> An analytic sentence is a sentence which is true based on the
>>>>>> meanings of the words involved. This is not a particularly useful
>>>>>> concept and always applied to a very small, uninteresting subset
>>>>>> of sentences.
>>>>>>
>>>>>
>>>>>     "Analytic propositions are true or not true solely by virtue of
>>>>>     their meaning..."
>>>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>>>
>>>>> I am stipulating that this includes meanings specified in the formal
>>>>> languages of formal systems.
>>>>
>>>> And again your stipulation has no bearing on how the terms are
>>>> actually used. If you want to be understood you need to use terms as
>>>> they are conventionally used.
>>>>
>>>> You seem to think that 'stipulating' is some sort of magical
>>>> incantation.
>>>>
>>>> André
>>>>
>>>
>>> *I must use a stipulative definitions because there are no*
>>> *conventional terms for the meanings that I must refer to*
>>>
>>>
>>> A stipulative definition is a type of definition in which a new or
>>> currently existing term is given a new specific meaning for the purposes
>>> of argument or discussion in a given context...
>>>
>>> a stipulative definition cannot be "correct" or "incorrect"; it can only
>>> differ from other definitions, but it can be useful for its intended
>>> purpose.  https://en.wikipedia.org/wiki/Stipulative_definition
>>>
>>>
>>> Analytic propositions(olcott)
>>> "Analytic propositions are true or not true solely by virtue of
>>> their meaning..."
>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>
>>> I am stipulating that this includes meanings specified in the formal
>>> languages of formal systems.
>>>
>>> semantic tautology(olcott)
>>> I am stipulating that a {semantic tautology} includes every expression
>>> of formal or natural language that can be verified as completely true
>>> entirely on the basis of its semantic meaning.
>>>
>>>
>>> *PURE REASONING WILL CONFIRM*
>>> When the body of analytic truth is construed as being entirely
>>> comprised of elements of semantic_tautology(olcott) then True(L,x)
>>> is (always and only) established on the basis of semantic connections
>>> between elements.
>>>
>>> True(L,x) always requires this semantic connection thus there cannot
>>> be a case of True(L,x) that does not include establishing this semantic
>>> connection through Provable(L,x).
>>>
>>> *As Richard pointed out*
>>> In cases where the elements of the set of analytic truth are outside
>>> of the set of analytic knowledge (such as the Goldbach conjecture)
>>> the semantic connection may require an infinite number of steps.
>>>
>>> Within the semantic meanings that I stipulated a notion of formal
>>> system can be defined such that incompleteness is impossible and a
>>> consistent and correct True(L,x) can always be defined.
>>>
>>> It this system that I defined unprovable simply mean untrue, yet
>>> not necessarily false.
>>>
>>>
>>>
>>
>> Which means you are just admitting to being a Pathological Liar by
>> changing the meaning of the key words,
>
> I have proven that stipulative definitions are a perfectly legitimate
> notion. If you just don't like this then construe my new meanings to be
> assigned to these GUIDs:
>
> ADF816E1-74B1-4379-AC38-17A48033696B
> EF518F6E-D7B6-442B-89C4-3BFE71EC5B59
>

On 7/7/2023 8:33 PM, André G. Isaak wrote:
> On 2023-07-07 15:14, olcott wrote:
>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>> On 2023-07-07 12:00, olcott wrote:
>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>
>>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't a
>>>>>>>>>>> Tautology (unless you have restricted your univerese of
>>>>>>>>>>> systems to make the DEFINITION of "Human" include that is is
>>>>>>>>>>> a "Mammal"
>>>>>>>>>>
>>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>
>>>>>>>>> Right, and I gave an example of a set of properties that can
>>>>>>>>> define "Human" that means that not all "Humans" might be Mammals.
>>>>>>>>>
>>>>>>>>
>>>>>>>> The way that tautologies work is that humans <are> mammals is
>>>>>>>> stipulated
>>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>>> rejected as
>>>>>>>> counter-factual.
>>>>>>>
>>>>>>> No. That's not the way tautologies work.
>>>>>>>
>>>>>>> A tautology is a statement which is true in every model. Put
>>>>>>> slightly differently, a tautology is a statement whose truth
>>>>>>> stems entirely from the meaning *of the logical connectives*.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> Welcome back, you are one of very few reviewers that I consider
>>>>>> very competent.
>>>>>>
>>>>>> tautology, in logic, a statement so framed that it cannot be denied
>>>>>> without inconsistency. Thus, “All humans are mammals” is held to
>>>>>> assert
>>>>>> with regard to anything whatsoever that either it is not a human
>>>>>> or it
>>>>>> is a mammal. But that universal “truth” follows not from any facts
>>>>>> noted
>>>>>> about real humans but only from the actual use of human and mammal
>>>>>> and
>>>>>> is thus purely a matter of definition.
>>>>>> https://www.britannica.com/topic/tautology
>>>>>>
>>>>>> I used to refer to the above as a {semantic tautology} until I found
>>>>>> this reference that already incorporates that meaning.
>>>>>
>>>>> That example is terrible. If you want to learn about logic (or any
>>>>> other technical subject), Encyclopaedia Britannica is *not* a
>>>>> reliable source of information.
>>>>>
>>>>>> You understand that expressions of natural language that can be
>>>>>> verified
>>>>>> as completely true entirely on the basis of their semantic meaning
>>>>>> are
>>>>>> also: statements "that it cannot be denied without inconsistency",
>>>>>> don't you?
>>>>>>
>>>>>> "Baby kittens are not any type of ten story office building." is an
>>>>>> example of this broader scoped tautology.
>>>
>>> 'baby kittens' as opposed to 'adult kittens'.
>>>
>>>>> That's not a tautology either.
>>>>>
>>>>
>>>> Can you deny it without inconsistency ?
>>>
>>> Of course I can. Do you understand what 'inconsistency' means? hint:
>>> it doesn't mean something which fails to match the real world; it
>>> means something in which a given proposition X is both true and false.
>>>
>>> Consider a model in which there are exactly two entities, fluffy and
>>> mittens, and exactly two predicates: Kitten() and OfficeBuilding().
>>>
>>> What is inconsistent about the following assignment?
>>>
>>> Kitten = {fluffy, mittens}
>>> OfficeBuilding = {fluffy}
>>>
>>>> That it does not match the definition of tautology that you are
>>>> accustomed to does not mean that it does not match the more broadly
>>>> defined term of {semantic tautology} that I and Britannica refer to.
>>>
>>> Britannica's definition is fine. It is their example which is terrible.
>>>
>>>> Any expression of natural or formal language cannot be denied without
>>>> inconsistency is a semantic tautology.
>>>>
>>>>>> My use of the term {tautology} is simply broader than the typical
>>>>>> use of
>>>>>> the term within formal logic. That does not mean that I am
>>>>>> incorrect. My
>>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>>
>>>>> If you use it in a way that doesn't conform to standard usage then
>>>>> yes,
>>>>
>>>> In the field of the philosophy of logic we must deal with things
>>>> such as
>>>> the analytic/synthetic distinction. Formal logic doesn't care about
>>>> such
>>>> things and is limited to only going by the book.
>>>
>>> The analytic/synthetic distinction is part of the philosophy of
>>> *language*, not the philosophy of logic. And it is unrelated to the
>>> notion of a tautology.
>>>
>>
>> I am stipulating that anything that pertains to the nature of truth
>> pertains to the philosophy of logic.
>
> And I am stipulating that anything pertaining to elephants pertains to
> the philosophy of logic. Of course, this stipulation has absolutely no
> effect on how the term is actually used.
>
>>> An analytic sentence is a sentence which is true based on the
>>> meanings of the words involved. This is not a particularly useful
>>> concept and always applied to a very small, uninteresting subset of
>>> sentences.
>>>
>>
>>     "Analytic propositions are true or not true solely by virtue of
>>     their meaning..."
>>     https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>
>> I am stipulating that this includes meanings specified in the formal
>> languages of formal systems.
>
> And again your stipulation has no bearing on how the terms are actually
> used. If you want to be understood you need to use terms as they are
> conventionally used.
>
> You seem to think that 'stipulating' is some sort of magical incantation.
>
> André
>

Stipulative definition is the only way that brand new concepts that have
no corresponding existing term can be referenced. To forbid Stipulative
definitions prevents many new ideas from being expressed.

The simple essence of what I am saying is already modeled in the Prolog
language. If a formal system only has Prolog:Facts (similar to axioms)
and Prolog:Rules rules of inference, then unprovable simply mean untrue
and thus the mathematical notion of incompleteness cannot exist.

It is also the case that when a system such as Prolog is extended to
handle type theory / HOL then (to the best of my knowledge) all
mathematical concepts can be fully represented.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 7/7/23 11:39 PM, olcott wrote:
> On 7/7/2023 8:33 PM, André G. Isaak wrote:
>> On 2023-07-07 15:14, olcott wrote:
>>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>>> On 2023-07-07 12:00, olcott wrote:
>>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>>
>>>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't a
>>>>>>>>>>>> Tautology (unless you have restricted your univerese of
>>>>>>>>>>>> systems to make the DEFINITION of "Human" include that is is
>>>>>>>>>>>> a "Mammal"
>>>>>>>>>>>
>>>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>>
>>>>>>>>>> Right, and I gave an example of a set of properties that can
>>>>>>>>>> define "Human" that means that not all "Humans" might be Mammals.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The way that tautologies work is that humans <are> mammals is
>>>>>>>>> stipulated
>>>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>>>> rejected as
>>>>>>>>> counter-factual.
>>>>>>>>
>>>>>>>> No. That's not the way tautologies work.
>>>>>>>>
>>>>>>>> A tautology is a statement which is true in every model. Put
>>>>>>>> slightly differently, a tautology is a statement whose truth
>>>>>>>> stems entirely from the meaning *of the logical connectives*.
>>>>>>>>
>>>>>>>> André
>>>>>>>>
>>>>>>>
>>>>>>> Welcome back, you are one of very few reviewers that I consider
>>>>>>> very competent.
>>>>>>>
>>>>>>> tautology, in logic, a statement so framed that it cannot be denied
>>>>>>> without inconsistency. Thus, “All humans are mammals” is held to
>>>>>>> assert
>>>>>>> with regard to anything whatsoever that either it is not a human
>>>>>>> or it
>>>>>>> is a mammal. But that universal “truth” follows not from any
>>>>>>> facts noted
>>>>>>> about real humans but only from the actual use of human and
>>>>>>> mammal and
>>>>>>> is thus purely a matter of definition.
>>>>>>> https://www.britannica.com/topic/tautology
>>>>>>>
>>>>>>> I used to refer to the above as a {semantic tautology} until I found
>>>>>>> this reference that already incorporates that meaning.
>>>>>>
>>>>>> That example is terrible. If you want to learn about logic (or any
>>>>>> other technical subject), Encyclopaedia Britannica is *not* a
>>>>>> reliable source of information.
>>>>>>
>>>>>>> You understand that expressions of natural language that can be
>>>>>>> verified
>>>>>>> as completely true entirely on the basis of their semantic
>>>>>>> meaning are
>>>>>>> also: statements "that it cannot be denied without inconsistency",
>>>>>>> don't you?
>>>>>>>
>>>>>>> "Baby kittens are not any type of ten story office building." is an
>>>>>>> example of this broader scoped tautology.
>>>>
>>>> 'baby kittens' as opposed to 'adult kittens'.
>>>>
>>>>>> That's not a tautology either.
>>>>>>
>>>>>
>>>>> Can you deny it without inconsistency ?
>>>>
>>>> Of course I can. Do you understand what 'inconsistency' means? hint:
>>>> it doesn't mean something which fails to match the real world; it
>>>> means something in which a given proposition X is both true and false.
>>>>
>>>> Consider a model in which there are exactly two entities, fluffy and
>>>> mittens, and exactly two predicates: Kitten() and OfficeBuilding().
>>>>
>>>> What is inconsistent about the following assignment?
>>>>
>>>> Kitten = {fluffy, mittens}
>>>> OfficeBuilding = {fluffy}
>>>>
>>>>> That it does not match the definition of tautology that you are
>>>>> accustomed to does not mean that it does not match the more broadly
>>>>> defined term of {semantic tautology} that I and Britannica refer to.
>>>>
>>>> Britannica's definition is fine. It is their example which is terrible.
>>>>
>>>>> Any expression of natural or formal language cannot be denied without
>>>>> inconsistency is a semantic tautology.
>>>>>
>>>>>>> My use of the term {tautology} is simply broader than the typical
>>>>>>> use of
>>>>>>> the term within formal logic. That does not mean that I am
>>>>>>> incorrect. My
>>>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>>>
>>>>>> If you use it in a way that doesn't conform to standard usage then
>>>>>> yes,
>>>>>
>>>>> In the field of the philosophy of logic we must deal with things
>>>>> such as
>>>>> the analytic/synthetic distinction. Formal logic doesn't care about
>>>>> such
>>>>> things and is limited to only going by the book.
>>>>
>>>> The analytic/synthetic distinction is part of the philosophy of
>>>> *language*, not the philosophy of logic. And it is unrelated to the
>>>> notion of a tautology.
>>>>
>>>
>>> I am stipulating that anything that pertains to the nature of truth
>>> pertains to the philosophy of logic.
>>
>> And I am stipulating that anything pertaining to elephants pertains to
>> the philosophy of logic. Of course, this stipulation has absolutely no
>> effect on how the term is actually used.
>>
>>>> An analytic sentence is a sentence which is true based on the
>>>> meanings of the words involved. This is not a particularly useful
>>>> concept and always applied to a very small, uninteresting subset of
>>>> sentences.
>>>>
>>>
>>>     "Analytic propositions are true or not true solely by virtue of
>>>     their meaning..."
>>>     https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>
>>> I am stipulating that this includes meanings specified in the formal
>>> languages of formal systems.
>>
>> And again your stipulation has no bearing on how the terms are
>> actually used. If you want to be understood you need to use terms as
>> they are conventionally used.
>>
>> You seem to think that 'stipulating' is some sort of magical incantation.
>>
>> André
>>
>
> Stipulative definition is the only way that brand new concepts that have
> no corresponding existing term can be referenced. To forbid Stipulative
> definitions prevents many new ideas from being expressed.
>
> The simple essence of what I am saying is already modeled in the Prolog
> language. If a formal system only has Prolog:Facts (similar to axioms)
> and Prolog:Rules rules of inference, then unprovable simply mean untrue
> and thus the mathematical notion of incompleteness cannot exist.
>
> It is also the case that when a system such as Prolog is extended to
> handle type theory / HOL then (to the best of my knowledge) all
> mathematical concepts can be fully represented.
>

On 7/7/23 11:39 PM, olcott wrote:
>
> It is also the case that when a system such as Prolog is extended to
> handle type theory / HOL then (to the best of my knowledge) all
> mathematical concepts can be fully represented.

Since Prolog can't even handle a full First Order Logic, that is a big
claim. As I remember, Prolog can't handle infinte sets (like the Natural
Numbers) so you are strictly limited.

In fact, the key point is that since logic has been shown to be
non-computable, (there can't be a compuation that computes the
evaluation of any logical property) extending Prolog to do that has been
shown to be impossible.

At best, you can cripple you logic to limit what it can express, to keep
it computable, but that limit is much smaller than you want to do most
times.

On 7/8/2023 8:40 AM, Richard Damon wrote:
> On 7/7/23 11:39 PM, olcott wrote:
>> On 7/7/2023 8:33 PM, André G. Isaak wrote:
>>> On 2023-07-07 15:14, olcott wrote:
>>>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>>>> On 2023-07-07 12:00, olcott wrote:
>>>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>>>
>>>>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't a
>>>>>>>>>>>>> Tautology (unless you have restricted your univerese of
>>>>>>>>>>>>> systems to make the DEFINITION of "Human" include that is
>>>>>>>>>>>>> is a "Mammal"
>>>>>>>>>>>>
>>>>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>>>
>>>>>>>>>>> Right, and I gave an example of a set of properties that can
>>>>>>>>>>> define "Human" that means that not all "Humans" might be
>>>>>>>>>>> Mammals.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> The way that tautologies work is that humans <are> mammals is
>>>>>>>>>> stipulated
>>>>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>>>>> rejected as
>>>>>>>>>> counter-factual.
>>>>>>>>>
>>>>>>>>> No. That's not the way tautologies work.
>>>>>>>>>
>>>>>>>>> A tautology is a statement which is true in every model. Put
>>>>>>>>> slightly differently, a tautology is a statement whose truth
>>>>>>>>> stems entirely from the meaning *of the logical connectives*.
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>>
>>>>>>>>
>>>>>>>> Welcome back, you are one of very few reviewers that I consider
>>>>>>>> very competent.
>>>>>>>>
>>>>>>>> tautology, in logic, a statement so framed that it cannot be denied
>>>>>>>> without inconsistency. Thus, “All humans are mammals” is held to
>>>>>>>> assert
>>>>>>>> with regard to anything whatsoever that either it is not a human
>>>>>>>> or it
>>>>>>>> is a mammal. But that universal “truth” follows not from any
>>>>>>>> facts noted
>>>>>>>> about real humans but only from the actual use of human and
>>>>>>>> mammal and
>>>>>>>> is thus purely a matter of definition.
>>>>>>>> https://www.britannica.com/topic/tautology
>>>>>>>>
>>>>>>>> I used to refer to the above as a {semantic tautology} until I
>>>>>>>> found
>>>>>>>> this reference that already incorporates that meaning.
>>>>>>>
>>>>>>> That example is terrible. If you want to learn about logic (or
>>>>>>> any other technical subject), Encyclopaedia Britannica is *not* a
>>>>>>> reliable source of information.
>>>>>>>
>>>>>>>> You understand that expressions of natural language that can be
>>>>>>>> verified
>>>>>>>> as completely true entirely on the basis of their semantic
>>>>>>>> meaning are
>>>>>>>> also: statements "that it cannot be denied without inconsistency",
>>>>>>>> don't you?
>>>>>>>>
>>>>>>>> "Baby kittens are not any type of ten story office building." is an
>>>>>>>> example of this broader scoped tautology.
>>>>>
>>>>> 'baby kittens' as opposed to 'adult kittens'.
>>>>>
>>>>>>> That's not a tautology either.
>>>>>>>
>>>>>>
>>>>>> Can you deny it without inconsistency ?
>>>>>
>>>>> Of course I can. Do you understand what 'inconsistency' means?
>>>>> hint: it doesn't mean something which fails to match the real
>>>>> world; it means something in which a given proposition X is both
>>>>> true and false.
>>>>>
>>>>> Consider a model in which there are exactly two entities, fluffy
>>>>> and mittens, and exactly two predicates: Kitten() and
>>>>> OfficeBuilding().
>>>>>
>>>>> What is inconsistent about the following assignment?
>>>>>
>>>>> Kitten = {fluffy, mittens}
>>>>> OfficeBuilding = {fluffy}
>>>>>
>>>>>> That it does not match the definition of tautology that you are
>>>>>> accustomed to does not mean that it does not match the more broadly
>>>>>> defined term of {semantic tautology} that I and Britannica refer to.
>>>>>
>>>>> Britannica's definition is fine. It is their example which is
>>>>> terrible.
>>>>>
>>>>>> Any expression of natural or formal language cannot be denied without
>>>>>> inconsistency is a semantic tautology.
>>>>>>
>>>>>>>> My use of the term {tautology} is simply broader than the
>>>>>>>> typical use of
>>>>>>>> the term within formal logic. That does not mean that I am
>>>>>>>> incorrect. My
>>>>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>>>>
>>>>>>> If you use it in a way that doesn't conform to standard usage
>>>>>>> then yes,
>>>>>>
>>>>>> In the field of the philosophy of logic we must deal with things
>>>>>> such as
>>>>>> the analytic/synthetic distinction. Formal logic doesn't care
>>>>>> about such
>>>>>> things and is limited to only going by the book.
>>>>>
>>>>> The analytic/synthetic distinction is part of the philosophy of
>>>>> *language*, not the philosophy of logic. And it is unrelated to the
>>>>> notion of a tautology.
>>>>>
>>>>
>>>> I am stipulating that anything that pertains to the nature of truth
>>>> pertains to the philosophy of logic.
>>>
>>> And I am stipulating that anything pertaining to elephants pertains
>>> to the philosophy of logic. Of course, this stipulation has
>>> absolutely no effect on how the term is actually used.
>>>
>>>>> An analytic sentence is a sentence which is true based on the
>>>>> meanings of the words involved. This is not a particularly useful
>>>>> concept and always applied to a very small, uninteresting subset of
>>>>> sentences.
>>>>>
>>>>
>>>>     "Analytic propositions are true or not true solely by virtue of
>>>>     their meaning..."
>>>>
>>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>>
>>>> I am stipulating that this includes meanings specified in the formal
>>>> languages of formal systems.
>>>
>>> And again your stipulation has no bearing on how the terms are
>>> actually used. If you want to be understood you need to use terms as
>>> they are conventionally used.
>>>
>>> You seem to think that 'stipulating' is some sort of magical
>>> incantation.
>>>
>>> André
>>>
>>
>> Stipulative definition is the only way that brand new concepts that have
>> no corresponding existing term can be referenced. To forbid Stipulative
>> definitions prevents many new ideas from being expressed.
>>
>> The simple essence of what I am saying is already modeled in the Prolog
>> language. If a formal system only has Prolog:Facts (similar to axioms)
>> and Prolog:Rules rules of inference, then unprovable simply mean untrue
>> and thus the mathematical notion of incompleteness cannot exist.
>>
>> It is also the case that when a system such as Prolog is extended to
>> handle type theory / HOL then (to the best of my knowledge) all
>> mathematical concepts can be fully represented.
>>
>
> But, what you don't seem to understand is that tryng to CHANGE the
> definition of a fundamental term means that nothing you do has any
> application to the original system.
>
> Yes, you can create your new system of logic with your new alternate
> definitons, but what can that logic system do? You can't just assume
> work done with the original definitions is applicable! In fact, since
> your goal is to try to "plug a hole" in the standard logic system, you
> should know that much will NOT be applicable.
>

On 7/8/2023 9:32 AM, Richard Damon wrote:
> On 7/7/23 11:39 PM, olcott wrote:
>>
>> It is also the case that when a system such as Prolog is extended to
>> handle type theory / HOL then (to the best of my knowledge) all
>> mathematical concepts can be fully represented.
>
> Since Prolog can't even handle a full First Order Logic, that is a big
> claim. As I remember, Prolog can't handle infinte sets (like the Natural
> Numbers) so you are strictly limited.
>
> In fact, the key point is that since logic has been shown to be
> non-computable, (there can't be a compuation that computes the
> evaluation of any logical property) extending Prolog to do that has been
> shown to be impossible.
>
> At best, you can cripple you logic to limit what it can express, to keep
> it computable, but that limit is much smaller than you want to do most
> times.

The essential notion of Prolog based entirely on Fact and Rules can be
extended extended to cover the much broader scope that you refer to.

The key aspect of Prolog that I refer to causes all pathological
instances of decision problems to simply be rejected as semantically
unsound rather than this being incorrectly attributed to incompleteness
of the formal system.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Le 08/07/2023 à 18:50, olcott a écrit :
> On 7/8/2023 9:32 AM, Richard Damon wrote:
>> On 7/7/23 11:39 PM, olcott wrote:
>>>
>>> It is also the case that when a system such as Prolog is extended to
>>> handle type theory / HOL then (to the best of my knowledge) all
>>> mathematical concepts can be fully represented.
>>
>> Since Prolog can't even handle a full First Order Logic, that is a big
>> claim. As I remember, Prolog can't handle infinte sets (like the
>> Natural Numbers) so you are strictly limited.
>>
>> In fact, the key point is that since logic has been shown to be
>> non-computable, (there can't be a compuation that computes the
>> evaluation of any logical property) extending Prolog to do that has
>> been shown to be impossible.
>>
>> At best, you can cripple you logic to limit what it can express, to
>> keep it computable, but that limit is much smaller than you want to do
>> most times.
>
> The essential notion of Prolog based entirely on Fact and Rules can be
> extended extended to cover the much broader scope that you refer to.

That's not true. Even the creators of Prolog know that.

On 7/8/23 12:44 PM, olcott wrote:
> On 7/8/2023 8:40 AM, Richard Damon wrote:
>> On 7/7/23 11:39 PM, olcott wrote:
>>> On 7/7/2023 8:33 PM, André G. Isaak wrote:
>>>> On 2023-07-07 15:14, olcott wrote:
>>>>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>>>>> On 2023-07-07 12:00, olcott wrote:
>>>>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>>>>
>>>>>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't a
>>>>>>>>>>>>>> Tautology (unless you have restricted your univerese of
>>>>>>>>>>>>>> systems to make the DEFINITION of "Human" include that is
>>>>>>>>>>>>>> is a "Mammal"
>>>>>>>>>>>>>
>>>>>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>>>>
>>>>>>>>>>>> Right, and I gave an example of a set of properties that can
>>>>>>>>>>>> define "Human" that means that not all "Humans" might be
>>>>>>>>>>>> Mammals.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> The way that tautologies work is that humans <are> mammals is
>>>>>>>>>>> stipulated
>>>>>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>>>>>> rejected as
>>>>>>>>>>> counter-factual.
>>>>>>>>>>
>>>>>>>>>> No. That's not the way tautologies work.
>>>>>>>>>>
>>>>>>>>>> A tautology is a statement which is true in every model. Put
>>>>>>>>>> slightly differently, a tautology is a statement whose truth
>>>>>>>>>> stems entirely from the meaning *of the logical connectives*.
>>>>>>>>>>
>>>>>>>>>> André
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Welcome back, you are one of very few reviewers that I consider
>>>>>>>>> very competent.
>>>>>>>>>
>>>>>>>>> tautology, in logic, a statement so framed that it cannot be
>>>>>>>>> denied
>>>>>>>>> without inconsistency. Thus, “All humans are mammals” is held
>>>>>>>>> to assert
>>>>>>>>> with regard to anything whatsoever that either it is not a
>>>>>>>>> human or it
>>>>>>>>> is a mammal. But that universal “truth” follows not from any
>>>>>>>>> facts noted
>>>>>>>>> about real humans but only from the actual use of human and
>>>>>>>>> mammal and
>>>>>>>>> is thus purely a matter of definition.
>>>>>>>>> https://www.britannica.com/topic/tautology
>>>>>>>>>
>>>>>>>>> I used to refer to the above as a {semantic tautology} until I
>>>>>>>>> found
>>>>>>>>> this reference that already incorporates that meaning.
>>>>>>>>
>>>>>>>> That example is terrible. If you want to learn about logic (or
>>>>>>>> any other technical subject), Encyclopaedia Britannica is *not*
>>>>>>>> a reliable source of information.
>>>>>>>>
>>>>>>>>> You understand that expressions of natural language that can be
>>>>>>>>> verified
>>>>>>>>> as completely true entirely on the basis of their semantic
>>>>>>>>> meaning are
>>>>>>>>> also: statements "that it cannot be denied without inconsistency",
>>>>>>>>> don't you?
>>>>>>>>>
>>>>>>>>> "Baby kittens are not any type of ten story office building."
>>>>>>>>> is an
>>>>>>>>> example of this broader scoped tautology.
>>>>>>
>>>>>> 'baby kittens' as opposed to 'adult kittens'.
>>>>>>
>>>>>>>> That's not a tautology either.
>>>>>>>>
>>>>>>>
>>>>>>> Can you deny it without inconsistency ?
>>>>>>
>>>>>> Of course I can. Do you understand what 'inconsistency' means?
>>>>>> hint: it doesn't mean something which fails to match the real
>>>>>> world; it means something in which a given proposition X is both
>>>>>> true and false.
>>>>>>
>>>>>> Consider a model in which there are exactly two entities, fluffy
>>>>>> and mittens, and exactly two predicates: Kitten() and
>>>>>> OfficeBuilding().
>>>>>>
>>>>>> What is inconsistent about the following assignment?
>>>>>>
>>>>>> Kitten = {fluffy, mittens}
>>>>>> OfficeBuilding = {fluffy}
>>>>>>
>>>>>>> That it does not match the definition of tautology that you are
>>>>>>> accustomed to does not mean that it does not match the more broadly
>>>>>>> defined term of {semantic tautology} that I and Britannica refer to.
>>>>>>
>>>>>> Britannica's definition is fine. It is their example which is
>>>>>> terrible.
>>>>>>
>>>>>>> Any expression of natural or formal language cannot be denied
>>>>>>> without
>>>>>>> inconsistency is a semantic tautology.
>>>>>>>
>>>>>>>>> My use of the term {tautology} is simply broader than the
>>>>>>>>> typical use of
>>>>>>>>> the term within formal logic. That does not mean that I am
>>>>>>>>> incorrect. My
>>>>>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>>>>>
>>>>>>>> If you use it in a way that doesn't conform to standard usage
>>>>>>>> then yes,
>>>>>>>
>>>>>>> In the field of the philosophy of logic we must deal with things
>>>>>>> such as
>>>>>>> the analytic/synthetic distinction. Formal logic doesn't care
>>>>>>> about such
>>>>>>> things and is limited to only going by the book.
>>>>>>
>>>>>> The analytic/synthetic distinction is part of the philosophy of
>>>>>> *language*, not the philosophy of logic. And it is unrelated to
>>>>>> the notion of a tautology.
>>>>>>
>>>>>
>>>>> I am stipulating that anything that pertains to the nature of truth
>>>>> pertains to the philosophy of logic.
>>>>
>>>> And I am stipulating that anything pertaining to elephants pertains
>>>> to the philosophy of logic. Of course, this stipulation has
>>>> absolutely no effect on how the term is actually used.
>>>>
>>>>>> An analytic sentence is a sentence which is true based on the
>>>>>> meanings of the words involved. This is not a particularly useful
>>>>>> concept and always applied to a very small, uninteresting subset
>>>>>> of sentences.
>>>>>>
>>>>>
>>>>>     "Analytic propositions are true or not true solely by virtue of
>>>>>     their meaning..."
>>>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>>>
>>>>> I am stipulating that this includes meanings specified in the formal
>>>>> languages of formal systems.
>>>>
>>>> And again your stipulation has no bearing on how the terms are
>>>> actually used. If you want to be understood you need to use terms as
>>>> they are conventionally used.
>>>>
>>>> You seem to think that 'stipulating' is some sort of magical
>>>> incantation.
>>>>
>>>> André
>>>>
>>>
>>> Stipulative definition is the only way that brand new concepts that have
>>> no corresponding existing term can be referenced. To forbid Stipulative
>>> definitions prevents many new ideas from being expressed.
>>>
>>> The simple essence of what I am saying is already modeled in the Prolog
>>> language. If a formal system only has Prolog:Facts (similar to axioms)
>>> and Prolog:Rules rules of inference, then unprovable simply mean untrue
>>> and thus the mathematical notion of incompleteness cannot exist.
>>>
>>> It is also the case that when a system such as Prolog is extended to
>>> handle type theory / HOL then (to the best of my knowledge) all
>>> mathematical concepts can be fully represented.
>>>
>>
>> But, what you don't seem to understand is that tryng to CHANGE the
>> definition of a fundamental term means that nothing you do has any
>> application to the original system.
>>
>> Yes, you can create your new system of logic with your new alternate
>> definitons, but what can that logic system do? You can't just assume
>> work done with the original definitions is applicable! In fact, since
>> your goal is to try to "plug a hole" in the standard logic system, you
>> should know that much will NOT be applicable.
>>
>
> By comparing the two systems it becomes obvious that the conventional
> notion of mathematical incompleteness and undefinability is merely an
> artifact of the incoherent analytical framework of the conventional
> systems and thus no actual absolute limit to mathematical systems in
> general.
>

On 7/8/23 12:50 PM, olcott wrote:
> On 7/8/2023 9:32 AM, Richard Damon wrote:
>> On 7/7/23 11:39 PM, olcott wrote:
>>>
>>> It is also the case that when a system such as Prolog is extended to
>>> handle type theory / HOL then (to the best of my knowledge) all
>>> mathematical concepts can be fully represented.
>>
>> Since Prolog can't even handle a full First Order Logic, that is a big
>> claim. As I remember, Prolog can't handle infinte sets (like the
>> Natural Numbers) so you are strictly limited.
>>
>> In fact, the key point is that since logic has been shown to be
>> non-computable, (there can't be a compuation that computes the
>> evaluation of any logical property) extending Prolog to do that has
>> been shown to be impossible.
>>
>> At best, you can cripple you logic to limit what it can express, to
>> keep it computable, but that limit is much smaller than you want to do
>> most times.
>
> The essential notion of Prolog based entirely on Fact and Rules can be
> extended extended to cover the much broader scope that you refer to.
>
> The key aspect of Prolog that I refer to causes all pathological
> instances of decision problems to simply be rejected as semantically
> unsound rather than this being incorrectly attributed to incompleteness
> of the formal system.
>
>
>

So, you don't understand the proven limits of compuation, and are just
making baseless claims of what you think you can do.

I believe that Prolog is rejecting your "pathological" statements just
because in can't handle self-reference at all.

You are just proving your foolishness.

On 7/8/2023 12:43 PM, Richard Damon wrote:
> On 7/8/23 12:44 PM, olcott wrote:
>> On 7/8/2023 8:40 AM, Richard Damon wrote:
>>> On 7/7/23 11:39 PM, olcott wrote:
>>>> On 7/7/2023 8:33 PM, André G. Isaak wrote:
>>>>> On 2023-07-07 15:14, olcott wrote:
>>>>>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>>>>>> On 2023-07-07 12:00, olcott wrote:
>>>>>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>>>>>
>>>>>>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't
>>>>>>>>>>>>>>> a Tautology (unless you have restricted your univerese of
>>>>>>>>>>>>>>> systems to make the DEFINITION of "Human" include that is
>>>>>>>>>>>>>>> is a "Mammal"
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Right, and I gave an example of a set of properties that
>>>>>>>>>>>>> can define "Human" that means that not all "Humans" might
>>>>>>>>>>>>> be Mammals.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> The way that tautologies work is that humans <are> mammals
>>>>>>>>>>>> is stipulated
>>>>>>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>>>>>>> rejected as
>>>>>>>>>>>> counter-factual.
>>>>>>>>>>>
>>>>>>>>>>> No. That's not the way tautologies work.
>>>>>>>>>>>
>>>>>>>>>>> A tautology is a statement which is true in every model. Put
>>>>>>>>>>> slightly differently, a tautology is a statement whose truth
>>>>>>>>>>> stems entirely from the meaning *of the logical connectives*.
>>>>>>>>>>>
>>>>>>>>>>> André
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Welcome back, you are one of very few reviewers that I
>>>>>>>>>> consider very competent.
>>>>>>>>>>
>>>>>>>>>> tautology, in logic, a statement so framed that it cannot be
>>>>>>>>>> denied
>>>>>>>>>> without inconsistency. Thus, “All humans are mammals” is held
>>>>>>>>>> to assert
>>>>>>>>>> with regard to anything whatsoever that either it is not a
>>>>>>>>>> human or it
>>>>>>>>>> is a mammal. But that universal “truth” follows not from any
>>>>>>>>>> facts noted
>>>>>>>>>> about real humans but only from the actual use of human and
>>>>>>>>>> mammal and
>>>>>>>>>> is thus purely a matter of definition.
>>>>>>>>>> https://www.britannica.com/topic/tautology
>>>>>>>>>>
>>>>>>>>>> I used to refer to the above as a {semantic tautology} until I
>>>>>>>>>> found
>>>>>>>>>> this reference that already incorporates that meaning.
>>>>>>>>>
>>>>>>>>> That example is terrible. If you want to learn about logic (or
>>>>>>>>> any other technical subject), Encyclopaedia Britannica is *not*
>>>>>>>>> a reliable source of information.
>>>>>>>>>
>>>>>>>>>> You understand that expressions of natural language that can
>>>>>>>>>> be verified
>>>>>>>>>> as completely true entirely on the basis of their semantic
>>>>>>>>>> meaning are
>>>>>>>>>> also: statements "that it cannot be denied without
>>>>>>>>>> inconsistency",
>>>>>>>>>> don't you?
>>>>>>>>>>
>>>>>>>>>> "Baby kittens are not any type of ten story office building."
>>>>>>>>>> is an
>>>>>>>>>> example of this broader scoped tautology.
>>>>>>>
>>>>>>> 'baby kittens' as opposed to 'adult kittens'.
>>>>>>>
>>>>>>>>> That's not a tautology either.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Can you deny it without inconsistency ?
>>>>>>>
>>>>>>> Of course I can. Do you understand what 'inconsistency' means?
>>>>>>> hint: it doesn't mean something which fails to match the real
>>>>>>> world; it means something in which a given proposition X is both
>>>>>>> true and false.
>>>>>>>
>>>>>>> Consider a model in which there are exactly two entities, fluffy
>>>>>>> and mittens, and exactly two predicates: Kitten() and
>>>>>>> OfficeBuilding().
>>>>>>>
>>>>>>> What is inconsistent about the following assignment?
>>>>>>>
>>>>>>> Kitten = {fluffy, mittens}
>>>>>>> OfficeBuilding = {fluffy}
>>>>>>>
>>>>>>>> That it does not match the definition of tautology that you are
>>>>>>>> accustomed to does not mean that it does not match the more broadly
>>>>>>>> defined term of {semantic tautology} that I and Britannica refer
>>>>>>>> to.
>>>>>>>
>>>>>>> Britannica's definition is fine. It is their example which is
>>>>>>> terrible.
>>>>>>>
>>>>>>>> Any expression of natural or formal language cannot be denied
>>>>>>>> without
>>>>>>>> inconsistency is a semantic tautology.
>>>>>>>>
>>>>>>>>>> My use of the term {tautology} is simply broader than the
>>>>>>>>>> typical use of
>>>>>>>>>> the term within formal logic. That does not mean that I am
>>>>>>>>>> incorrect. My
>>>>>>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>>>>>>
>>>>>>>>> If you use it in a way that doesn't conform to standard usage
>>>>>>>>> then yes,
>>>>>>>>
>>>>>>>> In the field of the philosophy of logic we must deal with things
>>>>>>>> such as
>>>>>>>> the analytic/synthetic distinction. Formal logic doesn't care
>>>>>>>> about such
>>>>>>>> things and is limited to only going by the book.
>>>>>>>
>>>>>>> The analytic/synthetic distinction is part of the philosophy of
>>>>>>> *language*, not the philosophy of logic. And it is unrelated to
>>>>>>> the notion of a tautology.
>>>>>>>
>>>>>>
>>>>>> I am stipulating that anything that pertains to the nature of truth
>>>>>> pertains to the philosophy of logic.
>>>>>
>>>>> And I am stipulating that anything pertaining to elephants pertains
>>>>> to the philosophy of logic. Of course, this stipulation has
>>>>> absolutely no effect on how the term is actually used.
>>>>>
>>>>>>> An analytic sentence is a sentence which is true based on the
>>>>>>> meanings of the words involved. This is not a particularly useful
>>>>>>> concept and always applied to a very small, uninteresting subset
>>>>>>> of sentences.
>>>>>>>
>>>>>>
>>>>>>     "Analytic propositions are true or not true solely by virtue of
>>>>>>     their meaning..."
>>>>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>>>>
>>>>>> I am stipulating that this includes meanings specified in the formal
>>>>>> languages of formal systems.
>>>>>
>>>>> And again your stipulation has no bearing on how the terms are
>>>>> actually used. If you want to be understood you need to use terms
>>>>> as they are conventionally used.
>>>>>
>>>>> You seem to think that 'stipulating' is some sort of magical
>>>>> incantation.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> Stipulative definition is the only way that brand new concepts that
>>>> have
>>>> no corresponding existing term can be referenced. To forbid Stipulative
>>>> definitions prevents many new ideas from being expressed.
>>>>
>>>> The simple essence of what I am saying is already modeled in the Prolog
>>>> language. If a formal system only has Prolog:Facts (similar to axioms)
>>>> and Prolog:Rules rules of inference, then unprovable simply mean untrue
>>>> and thus the mathematical notion of incompleteness cannot exist.
>>>>
>>>> It is also the case that when a system such as Prolog is extended to
>>>> handle type theory / HOL then (to the best of my knowledge) all
>>>> mathematical concepts can be fully represented.
>>>>
>>>
>>> But, what you don't seem to understand is that tryng to CHANGE the
>>> definition of a fundamental term means that nothing you do has any
>>> application to the original system.
>>>
>>> Yes, you can create your new system of logic with your new alternate
>>> definitons, but what can that logic system do? You can't just assume
>>> work done with the original definitions is applicable! In fact, since
>>> your goal is to try to "plug a hole" in the standard logic system,
>>> you should know that much will NOT be applicable.
>>>
>>
>> By comparing the two systems it becomes obvious that the conventional
>> notion of mathematical incompleteness and undefinability is merely an
>> artifact of the incoherent analytical framework of the conventional
>> systems and thus no actual absolute limit to mathematical systems in
>> general.
>>
>
> So, you are admitting to the error of equivocation.
>

On 7/8/23 5:57 PM, olcott wrote:
> On 7/8/2023 12:43 PM, Richard Damon wrote:
>> On 7/8/23 12:44 PM, olcott wrote:
>>> On 7/8/2023 8:40 AM, Richard Damon wrote:
>>>> On 7/7/23 11:39 PM, olcott wrote:
>>>>> On 7/7/2023 8:33 PM, André G. Isaak wrote:
>>>>>> On 2023-07-07 15:14, olcott wrote:
>>>>>>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>>>>>>> On 2023-07-07 12:00, olcott wrote:
>>>>>>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>>>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>>>>> But Humans are Mammals is not. It may be True, but isn't
>>>>>>>>>>>>>>>> a Tautology (unless you have restricted your univerese
>>>>>>>>>>>>>>>> of systems to make the DEFINITION of "Human" include
>>>>>>>>>>>>>>>> that is is a "Mammal"
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> So maybe humans are really boxcars? {Human} is a placeholder
>>>>>>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Right, and I gave an example of a set of properties that
>>>>>>>>>>>>>> can define "Human" that means that not all "Humans" might
>>>>>>>>>>>>>> be Mammals.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> The way that tautologies work is that humans <are> mammals
>>>>>>>>>>>>> is stipulated
>>>>>>>>>>>>> to be an axiom, thus changing this from <are> to {might} is
>>>>>>>>>>>>> rejected as
>>>>>>>>>>>>> counter-factual.
>>>>>>>>>>>>
>>>>>>>>>>>> No. That's not the way tautologies work.
>>>>>>>>>>>>
>>>>>>>>>>>> A tautology is a statement which is true in every model. Put
>>>>>>>>>>>> slightly differently, a tautology is a statement whose truth
>>>>>>>>>>>> stems entirely from the meaning *of the logical connectives*.
>>>>>>>>>>>>
>>>>>>>>>>>> André
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Welcome back, you are one of very few reviewers that I
>>>>>>>>>>> consider very competent.
>>>>>>>>>>>
>>>>>>>>>>> tautology, in logic, a statement so framed that it cannot be
>>>>>>>>>>> denied
>>>>>>>>>>> without inconsistency. Thus, “All humans are mammals” is held
>>>>>>>>>>> to assert
>>>>>>>>>>> with regard to anything whatsoever that either it is not a
>>>>>>>>>>> human or it
>>>>>>>>>>> is a mammal. But that universal “truth” follows not from any
>>>>>>>>>>> facts noted
>>>>>>>>>>> about real humans but only from the actual use of human and
>>>>>>>>>>> mammal and
>>>>>>>>>>> is thus purely a matter of definition.
>>>>>>>>>>> https://www.britannica.com/topic/tautology
>>>>>>>>>>>
>>>>>>>>>>> I used to refer to the above as a {semantic tautology} until
>>>>>>>>>>> I found
>>>>>>>>>>> this reference that already incorporates that meaning.
>>>>>>>>>>
>>>>>>>>>> That example is terrible. If you want to learn about logic (or
>>>>>>>>>> any other technical subject), Encyclopaedia Britannica is
>>>>>>>>>> *not* a reliable source of information.
>>>>>>>>>>
>>>>>>>>>>> You understand that expressions of natural language that can
>>>>>>>>>>> be verified
>>>>>>>>>>> as completely true entirely on the basis of their semantic
>>>>>>>>>>> meaning are
>>>>>>>>>>> also: statements "that it cannot be denied without
>>>>>>>>>>> inconsistency",
>>>>>>>>>>> don't you?
>>>>>>>>>>>
>>>>>>>>>>> "Baby kittens are not any type of ten story office building."
>>>>>>>>>>> is an
>>>>>>>>>>> example of this broader scoped tautology.
>>>>>>>>
>>>>>>>> 'baby kittens' as opposed to 'adult kittens'.
>>>>>>>>
>>>>>>>>>> That's not a tautology either.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Can you deny it without inconsistency ?
>>>>>>>>
>>>>>>>> Of course I can. Do you understand what 'inconsistency' means?
>>>>>>>> hint: it doesn't mean something which fails to match the real
>>>>>>>> world; it means something in which a given proposition X is both
>>>>>>>> true and false.
>>>>>>>>
>>>>>>>> Consider a model in which there are exactly two entities, fluffy
>>>>>>>> and mittens, and exactly two predicates: Kitten() and
>>>>>>>> OfficeBuilding().
>>>>>>>>
>>>>>>>> What is inconsistent about the following assignment?
>>>>>>>>
>>>>>>>> Kitten = {fluffy, mittens}
>>>>>>>> OfficeBuilding = {fluffy}
>>>>>>>>
>>>>>>>>> That it does not match the definition of tautology that you are
>>>>>>>>> accustomed to does not mean that it does not match the more
>>>>>>>>> broadly
>>>>>>>>> defined term of {semantic tautology} that I and Britannica
>>>>>>>>> refer to.
>>>>>>>>
>>>>>>>> Britannica's definition is fine. It is their example which is
>>>>>>>> terrible.
>>>>>>>>
>>>>>>>>> Any expression of natural or formal language cannot be denied
>>>>>>>>> without
>>>>>>>>> inconsistency is a semantic tautology.
>>>>>>>>>
>>>>>>>>>>> My use of the term {tautology} is simply broader than the
>>>>>>>>>>> typical use of
>>>>>>>>>>> the term within formal logic. That does not mean that I am
>>>>>>>>>>> incorrect. My
>>>>>>>>>>> use of the term is perfectly apt within the philosophy of logic.
>>>>>>>>>>
>>>>>>>>>> If you use it in a way that doesn't conform to standard usage
>>>>>>>>>> then yes,
>>>>>>>>>
>>>>>>>>> In the field of the philosophy of logic we must deal with
>>>>>>>>> things such as
>>>>>>>>> the analytic/synthetic distinction. Formal logic doesn't care
>>>>>>>>> about such
>>>>>>>>> things and is limited to only going by the book.
>>>>>>>>
>>>>>>>> The analytic/synthetic distinction is part of the philosophy of
>>>>>>>> *language*, not the philosophy of logic. And it is unrelated to
>>>>>>>> the notion of a tautology.
>>>>>>>>
>>>>>>>
>>>>>>> I am stipulating that anything that pertains to the nature of truth
>>>>>>> pertains to the philosophy of logic.
>>>>>>
>>>>>> And I am stipulating that anything pertaining to elephants
>>>>>> pertains to the philosophy of logic. Of course, this stipulation
>>>>>> has absolutely no effect on how the term is actually used.
>>>>>>
>>>>>>>> An analytic sentence is a sentence which is true based on the
>>>>>>>> meanings of the words involved. This is not a particularly
>>>>>>>> useful concept and always applied to a very small, uninteresting
>>>>>>>> subset of sentences.
>>>>>>>>
>>>>>>>
>>>>>>>     "Analytic propositions are true or not true solely by virtue of
>>>>>>>     their meaning..."
>>>>>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>>>>>
>>>>>>> I am stipulating that this includes meanings specified in the formal
>>>>>>> languages of formal systems.
>>>>>>
>>>>>> And again your stipulation has no bearing on how the terms are
>>>>>> actually used. If you want to be understood you need to use terms
>>>>>> as they are conventionally used.
>>>>>>
>>>>>> You seem to think that 'stipulating' is some sort of magical
>>>>>> incantation.
>>>>>>
>>>>>> André
>>>>>>
>>>>>
>>>>> Stipulative definition is the only way that brand new concepts that
>>>>> have
>>>>> no corresponding existing term can be referenced. To forbid
>>>>> Stipulative
>>>>> definitions prevents many new ideas from being expressed.
>>>>>
>>>>> The simple essence of what I am saying is already modeled in the
>>>>> Prolog
>>>>> language. If a formal system only has Prolog:Facts (similar to axioms)
>>>>> and Prolog:Rules rules of inference, then unprovable simply mean
>>>>> untrue
>>>>> and thus the mathematical notion of incompleteness cannot exist.
>>>>>
>>>>> It is also the case that when a system such as Prolog is extended to
>>>>> handle type theory / HOL then (to the best of my knowledge) all
>>>>> mathematical concepts can be fully represented.
>>>>>
>>>>
>>>> But, what you don't seem to understand is that tryng to CHANGE the
>>>> definition of a fundamental term means that nothing you do has any
>>>> application to the original system.
>>>>
>>>> Yes, you can create your new system of logic with your new alternate
>>>> definitons, but what can that logic system do? You can't just assume
>>>> work done with the original definitions is applicable! In fact,
>>>> since your goal is to try to "plug a hole" in the standard logic
>>>> system, you should know that much will NOT be applicable.
>>>>
>>>
>>> By comparing the two systems it becomes obvious that the conventional
>>> notion of mathematical incompleteness and undefinability is merely an
>>> artifact of the incoherent analytical framework of the conventional
>>> systems and thus no actual absolute limit to mathematical systems in
>>> general.
>>>
>>
>> So, you are admitting to the error of equivocation.
>>
>
> Not at all. I am saying the the notion of a formal system can be
> redefined to have everything that conventional formal systems have
> except that mathematical incompleteness and Tarski undefinability
> are both made impossible.

On 7/8/2023 5:19 PM, Richard Damon wrote:
> On 7/8/23 5:57 PM, olcott wrote:
>> On 7/8/2023 12:43 PM, Richard Damon wrote:
>>> On 7/8/23 12:44 PM, olcott wrote:
>>>> On 7/8/2023 8:40 AM, Richard Damon wrote:
>>>>> On 7/7/23 11:39 PM, olcott wrote:
>>>>>> On 7/7/2023 8:33 PM, André G. Isaak wrote:
>>>>>>> On 2023-07-07 15:14, olcott wrote:
>>>>>>>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>>>>>>>> On 2023-07-07 12:00, olcott wrote:
>>>>>>>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>>>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> But Humans are Mammals is not. It may be True, but
>>>>>>>>>>>>>>>>> isn't a Tautology (unless you have restricted your
>>>>>>>>>>>>>>>>> univerese of systems to make the DEFINITION of "Human"
>>>>>>>>>>>>>>>>> include that is is a "Mammal"
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> So maybe humans are really boxcars? {Human} is a
>>>>>>>>>>>>>>>> placeholder
>>>>>>>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Right, and I gave an example of a set of properties that
>>>>>>>>>>>>>>> can define "Human" that means that not all "Humans" might
>>>>>>>>>>>>>>> be Mammals.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The way that tautologies work is that humans <are> mammals
>>>>>>>>>>>>>> is stipulated
>>>>>>>>>>>>>> to be an axiom, thus changing this from <are> to {might}
>>>>>>>>>>>>>> is rejected as
>>>>>>>>>>>>>> counter-factual.
>>>>>>>>>>>>>
>>>>>>>>>>>>> No. That's not the way tautologies work.
>>>>>>>>>>>>>
>>>>>>>>>>>>> A tautology is a statement which is true in every model.
>>>>>>>>>>>>> Put slightly differently, a tautology is a statement whose
>>>>>>>>>>>>> truth stems entirely from the meaning *of the logical
>>>>>>>>>>>>> connectives*.
>>>>>>>>>>>>>
>>>>>>>>>>>>> André
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Welcome back, you are one of very few reviewers that I
>>>>>>>>>>>> consider very competent.
>>>>>>>>>>>>
>>>>>>>>>>>> tautology, in logic, a statement so framed that it cannot be
>>>>>>>>>>>> denied
>>>>>>>>>>>> without inconsistency. Thus, “All humans are mammals” is
>>>>>>>>>>>> held to assert
>>>>>>>>>>>> with regard to anything whatsoever that either it is not a
>>>>>>>>>>>> human or it
>>>>>>>>>>>> is a mammal. But that universal “truth” follows not from any
>>>>>>>>>>>> facts noted
>>>>>>>>>>>> about real humans but only from the actual use of human and
>>>>>>>>>>>> mammal and
>>>>>>>>>>>> is thus purely a matter of definition.
>>>>>>>>>>>> https://www.britannica.com/topic/tautology
>>>>>>>>>>>>
>>>>>>>>>>>> I used to refer to the above as a {semantic tautology} until
>>>>>>>>>>>> I found
>>>>>>>>>>>> this reference that already incorporates that meaning.
>>>>>>>>>>>
>>>>>>>>>>> That example is terrible. If you want to learn about logic
>>>>>>>>>>> (or any other technical subject), Encyclopaedia Britannica is
>>>>>>>>>>> *not* a reliable source of information.
>>>>>>>>>>>
>>>>>>>>>>>> You understand that expressions of natural language that can
>>>>>>>>>>>> be verified
>>>>>>>>>>>> as completely true entirely on the basis of their semantic
>>>>>>>>>>>> meaning are
>>>>>>>>>>>> also: statements "that it cannot be denied without
>>>>>>>>>>>> inconsistency",
>>>>>>>>>>>> don't you?
>>>>>>>>>>>>
>>>>>>>>>>>> "Baby kittens are not any type of ten story office
>>>>>>>>>>>> building." is an
>>>>>>>>>>>> example of this broader scoped tautology.
>>>>>>>>>
>>>>>>>>> 'baby kittens' as opposed to 'adult kittens'.
>>>>>>>>>
>>>>>>>>>>> That's not a tautology either.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Can you deny it without inconsistency ?
>>>>>>>>>
>>>>>>>>> Of course I can. Do you understand what 'inconsistency' means?
>>>>>>>>> hint: it doesn't mean something which fails to match the real
>>>>>>>>> world; it means something in which a given proposition X is
>>>>>>>>> both true and false.
>>>>>>>>>
>>>>>>>>> Consider a model in which there are exactly two entities,
>>>>>>>>> fluffy and mittens, and exactly two predicates: Kitten() and
>>>>>>>>> OfficeBuilding().
>>>>>>>>>
>>>>>>>>> What is inconsistent about the following assignment?
>>>>>>>>>
>>>>>>>>> Kitten = {fluffy, mittens}
>>>>>>>>> OfficeBuilding = {fluffy}
>>>>>>>>>
>>>>>>>>>> That it does not match the definition of tautology that you are
>>>>>>>>>> accustomed to does not mean that it does not match the more
>>>>>>>>>> broadly
>>>>>>>>>> defined term of {semantic tautology} that I and Britannica
>>>>>>>>>> refer to.
>>>>>>>>>
>>>>>>>>> Britannica's definition is fine. It is their example which is
>>>>>>>>> terrible.
>>>>>>>>>
>>>>>>>>>> Any expression of natural or formal language cannot be denied
>>>>>>>>>> without
>>>>>>>>>> inconsistency is a semantic tautology.
>>>>>>>>>>
>>>>>>>>>>>> My use of the term {tautology} is simply broader than the
>>>>>>>>>>>> typical use of
>>>>>>>>>>>> the term within formal logic. That does not mean that I am
>>>>>>>>>>>> incorrect. My
>>>>>>>>>>>> use of the term is perfectly apt within the philosophy of
>>>>>>>>>>>> logic.
>>>>>>>>>>>
>>>>>>>>>>> If you use it in a way that doesn't conform to standard usage
>>>>>>>>>>> then yes,
>>>>>>>>>>
>>>>>>>>>> In the field of the philosophy of logic we must deal with
>>>>>>>>>> things such as
>>>>>>>>>> the analytic/synthetic distinction. Formal logic doesn't care
>>>>>>>>>> about such
>>>>>>>>>> things and is limited to only going by the book.
>>>>>>>>>
>>>>>>>>> The analytic/synthetic distinction is part of the philosophy of
>>>>>>>>> *language*, not the philosophy of logic. And it is unrelated to
>>>>>>>>> the notion of a tautology.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I am stipulating that anything that pertains to the nature of truth
>>>>>>>> pertains to the philosophy of logic.
>>>>>>>
>>>>>>> And I am stipulating that anything pertaining to elephants
>>>>>>> pertains to the philosophy of logic. Of course, this stipulation
>>>>>>> has absolutely no effect on how the term is actually used.
>>>>>>>
>>>>>>>>> An analytic sentence is a sentence which is true based on the
>>>>>>>>> meanings of the words involved. This is not a particularly
>>>>>>>>> useful concept and always applied to a very small,
>>>>>>>>> uninteresting subset of sentences.
>>>>>>>>>
>>>>>>>>
>>>>>>>>     "Analytic propositions are true or not true solely by virtue of
>>>>>>>>     their meaning..."
>>>>>>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>>>>>>
>>>>>>>> I am stipulating that this includes meanings specified in the
>>>>>>>> formal
>>>>>>>> languages of formal systems.
>>>>>>>
>>>>>>> And again your stipulation has no bearing on how the terms are
>>>>>>> actually used. If you want to be understood you need to use terms
>>>>>>> as they are conventionally used.
>>>>>>>
>>>>>>> You seem to think that 'stipulating' is some sort of magical
>>>>>>> incantation.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> Stipulative definition is the only way that brand new concepts
>>>>>> that have
>>>>>> no corresponding existing term can be referenced. To forbid
>>>>>> Stipulative
>>>>>> definitions prevents many new ideas from being expressed.
>>>>>>
>>>>>> The simple essence of what I am saying is already modeled in the
>>>>>> Prolog
>>>>>> language. If a formal system only has Prolog:Facts (similar to
>>>>>> axioms)
>>>>>> and Prolog:Rules rules of inference, then unprovable simply mean
>>>>>> untrue
>>>>>> and thus the mathematical notion of incompleteness cannot exist.
>>>>>>
>>>>>> It is also the case that when a system such as Prolog is extended to
>>>>>> handle type theory / HOL then (to the best of my knowledge) all
>>>>>> mathematical concepts can be fully represented.
>>>>>>
>>>>>
>>>>> But, what you don't seem to understand is that tryng to CHANGE the
>>>>> definition of a fundamental term means that nothing you do has any
>>>>> application to the original system.
>>>>>
>>>>> Yes, you can create your new system of logic with your new
>>>>> alternate definitons, but what can that logic system do? You can't
>>>>> just assume work done with the original definitions is applicable!
>>>>> In fact, since your goal is to try to "plug a hole" in the standard
>>>>> logic system, you should know that much will NOT be applicable.
>>>>>
>>>>
>>>> By comparing the two systems it becomes obvious that the conventional
>>>> notion of mathematical incompleteness and undefinability is merely an
>>>> artifact of the incoherent analytical framework of the conventional
>>>> systems and thus no actual absolute limit to mathematical systems in
>>>> general.
>>>>
>>>
>>> So, you are admitting to the error of equivocation.
>>>
>>
>> Not at all. I am saying the the notion of a formal system can be
>> redefined to have everything that conventional formal systems have
>> except that mathematical incompleteness and Tarski undefinability
>> are both made impossible.
>
> Nope, that is just your error of Equivocation.

On 7/8/23 7:01 PM, olcott wrote:
> On 7/8/2023 5:19 PM, Richard Damon wrote:
>> On 7/8/23 5:57 PM, olcott wrote:
>>> On 7/8/2023 12:43 PM, Richard Damon wrote:
>>>> On 7/8/23 12:44 PM, olcott wrote:
>>>>> On 7/8/2023 8:40 AM, Richard Damon wrote:
>>>>>> On 7/7/23 11:39 PM, olcott wrote:
>>>>>>> On 7/7/2023 8:33 PM, André G. Isaak wrote:
>>>>>>>> On 2023-07-07 15:14, olcott wrote:
>>>>>>>>> On 7/7/2023 1:57 PM, André G. Isaak wrote:
>>>>>>>>>> On 2023-07-07 12:00, olcott wrote:
>>>>>>>>>>> On 7/7/2023 12:18 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2023-07-07 10:40, olcott wrote:
>>>>>>>>>>>>> On 7/7/2023 9:56 AM, André G. Isaak wrote:
>>>>>>>>>>>>>> On 2023-07-07 08:50, olcott wrote:
>>>>>>>>>>>>>>> On 7/6/2023 11:18 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 7/7/23 12:02 AM, olcott wrote:
>>>>>>>>>>>>>>>>> On 7/6/2023 10:48 PM, Richard Damon wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> But Humans are Mammals is not. It may be True, but
>>>>>>>>>>>>>>>>>> isn't a Tautology (unless you have restricted your
>>>>>>>>>>>>>>>>>> univerese of systems to make the DEFINITION of "Human"
>>>>>>>>>>>>>>>>>> include that is is a "Mammal"
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> So maybe humans are really boxcars? {Human} is a
>>>>>>>>>>>>>>>>> placeholder
>>>>>>>>>>>>>>>>> for a set of properties that are assigned to it.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Right, and I gave an example of a set of properties that
>>>>>>>>>>>>>>>> can define "Human" that means that not all "Humans"
>>>>>>>>>>>>>>>> might be Mammals.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The way that tautologies work is that humans <are>
>>>>>>>>>>>>>>> mammals is stipulated
>>>>>>>>>>>>>>> to be an axiom, thus changing this from <are> to {might}
>>>>>>>>>>>>>>> is rejected as
>>>>>>>>>>>>>>> counter-factual.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> No. That's not the way tautologies work.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A tautology is a statement which is true in every model.
>>>>>>>>>>>>>> Put slightly differently, a tautology is a statement whose
>>>>>>>>>>>>>> truth stems entirely from the meaning *of the logical
>>>>>>>>>>>>>> connectives*.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> André
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Welcome back, you are one of very few reviewers that I
>>>>>>>>>>>>> consider very competent.
>>>>>>>>>>>>>
>>>>>>>>>>>>> tautology, in logic, a statement so framed that it cannot
>>>>>>>>>>>>> be denied
>>>>>>>>>>>>> without inconsistency. Thus, “All humans are mammals” is
>>>>>>>>>>>>> held to assert
>>>>>>>>>>>>> with regard to anything whatsoever that either it is not a
>>>>>>>>>>>>> human or it
>>>>>>>>>>>>> is a mammal. But that universal “truth” follows not from
>>>>>>>>>>>>> any facts noted
>>>>>>>>>>>>> about real humans but only from the actual use of human and
>>>>>>>>>>>>> mammal and
>>>>>>>>>>>>> is thus purely a matter of definition.
>>>>>>>>>>>>> https://www.britannica.com/topic/tautology
>>>>>>>>>>>>>
>>>>>>>>>>>>> I used to refer to the above as a {semantic tautology}
>>>>>>>>>>>>> until I found
>>>>>>>>>>>>> this reference that already incorporates that meaning.
>>>>>>>>>>>>
>>>>>>>>>>>> That example is terrible. If you want to learn about logic
>>>>>>>>>>>> (or any other technical subject), Encyclopaedia Britannica
>>>>>>>>>>>> is *not* a reliable source of information.
>>>>>>>>>>>>
>>>>>>>>>>>>> You understand that expressions of natural language that
>>>>>>>>>>>>> can be verified
>>>>>>>>>>>>> as completely true entirely on the basis of their semantic
>>>>>>>>>>>>> meaning are
>>>>>>>>>>>>> also: statements "that it cannot be denied without
>>>>>>>>>>>>> inconsistency",
>>>>>>>>>>>>> don't you?
>>>>>>>>>>>>>
>>>>>>>>>>>>> "Baby kittens are not any type of ten story office
>>>>>>>>>>>>> building." is an
>>>>>>>>>>>>> example of this broader scoped tautology.
>>>>>>>>>>
>>>>>>>>>> 'baby kittens' as opposed to 'adult kittens'.
>>>>>>>>>>
>>>>>>>>>>>> That's not a tautology either.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Can you deny it without inconsistency ?
>>>>>>>>>>
>>>>>>>>>> Of course I can. Do you understand what 'inconsistency' means?
>>>>>>>>>> hint: it doesn't mean something which fails to match the real
>>>>>>>>>> world; it means something in which a given proposition X is
>>>>>>>>>> both true and false.
>>>>>>>>>>
>>>>>>>>>> Consider a model in which there are exactly two entities,
>>>>>>>>>> fluffy and mittens, and exactly two predicates: Kitten() and
>>>>>>>>>> OfficeBuilding().
>>>>>>>>>>
>>>>>>>>>> What is inconsistent about the following assignment?
>>>>>>>>>>
>>>>>>>>>> Kitten = {fluffy, mittens}
>>>>>>>>>> OfficeBuilding = {fluffy}
>>>>>>>>>>
>>>>>>>>>>> That it does not match the definition of tautology that you are
>>>>>>>>>>> accustomed to does not mean that it does not match the more
>>>>>>>>>>> broadly
>>>>>>>>>>> defined term of {semantic tautology} that I and Britannica
>>>>>>>>>>> refer to.
>>>>>>>>>>
>>>>>>>>>> Britannica's definition is fine. It is their example which is
>>>>>>>>>> terrible.
>>>>>>>>>>
>>>>>>>>>>> Any expression of natural or formal language cannot be denied
>>>>>>>>>>> without
>>>>>>>>>>> inconsistency is a semantic tautology.
>>>>>>>>>>>
>>>>>>>>>>>>> My use of the term {tautology} is simply broader than the
>>>>>>>>>>>>> typical use of
>>>>>>>>>>>>> the term within formal logic. That does not mean that I am
>>>>>>>>>>>>> incorrect. My
>>>>>>>>>>>>> use of the term is perfectly apt within the philosophy of
>>>>>>>>>>>>> logic.
>>>>>>>>>>>>
>>>>>>>>>>>> If you use it in a way that doesn't conform to standard
>>>>>>>>>>>> usage then yes,
>>>>>>>>>>>
>>>>>>>>>>> In the field of the philosophy of logic we must deal with
>>>>>>>>>>> things such as
>>>>>>>>>>> the analytic/synthetic distinction. Formal logic doesn't care
>>>>>>>>>>> about such
>>>>>>>>>>> things and is limited to only going by the book.
>>>>>>>>>>
>>>>>>>>>> The analytic/synthetic distinction is part of the philosophy
>>>>>>>>>> of *language*, not the philosophy of logic. And it is
>>>>>>>>>> unrelated to the notion of a tautology.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I am stipulating that anything that pertains to the nature of
>>>>>>>>> truth
>>>>>>>>> pertains to the philosophy of logic.
>>>>>>>>
>>>>>>>> And I am stipulating that anything pertaining to elephants
>>>>>>>> pertains to the philosophy of logic. Of course, this stipulation
>>>>>>>> has absolutely no effect on how the term is actually used.
>>>>>>>>
>>>>>>>>>> An analytic sentence is a sentence which is true based on the
>>>>>>>>>> meanings of the words involved. This is not a particularly
>>>>>>>>>> useful concept and always applied to a very small,
>>>>>>>>>> uninteresting subset of sentences.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>     "Analytic propositions are true or not true solely by
>>>>>>>>> virtue of
>>>>>>>>>     their meaning..."
>>>>>>>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>>>>>>>
>>>>>>>>> I am stipulating that this includes meanings specified in the
>>>>>>>>> formal
>>>>>>>>> languages of formal systems.
>>>>>>>>
>>>>>>>> And again your stipulation has no bearing on how the terms are
>>>>>>>> actually used. If you want to be understood you need to use
>>>>>>>> terms as they are conventionally used.
>>>>>>>>
>>>>>>>> You seem to think that 'stipulating' is some sort of magical
>>>>>>>> incantation.
>>>>>>>>
>>>>>>>> André
>>>>>>>>
>>>>>>>
>>>>>>> Stipulative definition is the only way that brand new concepts
>>>>>>> that have
>>>>>>> no corresponding existing term can be referenced. To forbid
>>>>>>> Stipulative
>>>>>>> definitions prevents many new ideas from being expressed.
>>>>>>>
>>>>>>> The simple essence of what I am saying is already modeled in the
>>>>>>> Prolog
>>>>>>> language. If a formal system only has Prolog:Facts (similar to
>>>>>>> axioms)
>>>>>>> and Prolog:Rules rules of inference, then unprovable simply mean
>>>>>>> untrue
>>>>>>> and thus the mathematical notion of incompleteness cannot exist.
>>>>>>>
>>>>>>> It is also the case that when a system such as Prolog is extended to
>>>>>>> handle type theory / HOL then (to the best of my knowledge) all
>>>>>>> mathematical concepts can be fully represented.
>>>>>>>
>>>>>>
>>>>>> But, what you don't seem to understand is that tryng to CHANGE the
>>>>>> definition of a fundamental term means that nothing you do has any
>>>>>> application to the original system.
>>>>>>
>>>>>> Yes, you can create your new system of logic with your new
>>>>>> alternate definitons, but what can that logic system do? You can't
>>>>>> just assume work done with the original definitions is applicable!
>>>>>> In fact, since your goal is to try to "plug a hole" in the
>>>>>> standard logic system, you should know that much will NOT be
>>>>>> applicable.
>>>>>>
>>>>>
>>>>> By comparing the two systems it becomes obvious that the conventional
>>>>> notion of mathematical incompleteness and undefinability is merely an
>>>>> artifact of the incoherent analytical framework of the conventional
>>>>> systems and thus no actual absolute limit to mathematical systems in
>>>>> general.
>>>>>
>>>>
>>>> So, you are admitting to the error of equivocation.
>>>>
>>>
>>> Not at all. I am saying the the notion of a formal system can be
>>> redefined to have everything that conventional formal systems have
>>> except that mathematical incompleteness and Tarski undefinability
>>> are both made impossible.
>>
>> Nope, that is just your error of Equivocation.
>
> No equivocation what-so-ever. I am converting X into Y.

On 2023-07-07 20:14, olcott wrote:

> *I must use a stipulative definitions because there are no*
> *conventional terms for the meanings that I must refer to*

The problem is that you haven't offered any definitions at all,
stipulative or otherwise. You have simply 'stipulated' "facts" that are
contrary to reality.

Here is a contrafactual stipulation of "fact":

"I stipulate that the sky is green"

That statement is either false or indicates that I am using some
nonstandard definition of 'sky', 'green', or 'is', but gives absolutely
no indication of which term I am intending to redefine or how I intend
to redefine it.

Here is a stipulative definition:

"I stipulate that 'green' means, for purposes of this discussion, any
gas which contains at least 15% oxygen".

Do you see the difference?

All of your "stipulations" fall into the former class rather than the
latter. In fact, I don't think I have ever seen you offer a *definition*
of anything despite the fact that such have often been requested of you.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

On 7/8/2023 8:29 PM, André G. Isaak wrote:
> On 2023-07-07 20:14, olcott wrote:
>
>> *I must use a stipulative definitions because there are no*
>> *conventional terms for the meanings that I must refer to*
>
> The problem is that you haven't offered any definitions at all,
> stipulative or otherwise. You have simply 'stipulated' "facts" that are
> contrary to reality.
>

I am happy that you haven't given up on me, you have always been one of
my top reviewers.

*These are a very rough sketch starting point*

Analytic propositions(olcott)
"Analytic propositions are true or not true solely by virtue of
their meaning..."
https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction

I am stipulating that this includes meanings specified in the formal
languages of formal systems and the meanings from formalized natural
language.

In other words I am specifying the infinite set of propositions that
have the semantic property of Boolean true. Most of these propositions
refer to natural language meanings.

semantic tautology(olcott)
I am stipulating that a {semantic tautology} includes every expression
of formal or natural language that can be verified as completely true
entirely on the basis of its semantic meaning.

> Here is a contrafactual stipulation of "fact":
>
> "I stipulate that the sky is green"
>
> That statement is either false or indicates that I am using some
> nonstandard definition of 'sky', 'green', or 'is', but gives absolutely
> no indication of which term I am intending to redefine or how I intend
> to redefine it.
>

We reference these semantic meanings by their unique GUID in an acyclic
digraph general knowledge ontology.

> Here is a stipulative definition:
>
> "I stipulate that 'green' means, for purposes of this discussion, any
> gas which contains at least 15% oxygen".
>
> Do you see the difference?
>

I am defining brand new ideas that don't have existing terms so I am
assigning a term-of-the-art meaning to the closest existing term.

> All of your "stipulations" fall into the former class rather than the
> latter. In fact, I don't think I have ever seen you offer a *definition*
> of anything despite the fact that such have often been requested of you.
>
> André
>

My definitions need very much progressive refinement and are a very
rough sketch at maybe the high school level of quality. Even at this
very rough sketch level is is possible (although probably too difficult)
to see that incompleteness and undefinability are abolished.

What we cannot see at the very rough sketch level is whether or not
such a system can be actually implemented.

λProlog: Logic programming in higher-order logic
https://www.lix.polytechnique.fr/~dale/lProlog/

If the above system has the same Facts and Rules architecture of Prolog
such the unprovable simply means untrue then what I am proposing might
be able to be implemented in the above system. We have to skip the
natural language aspects until their encoding can be full automated.

Ordinary Prolog already rejects an enormously simplified version of the
Gödel sentence:

?- G = not(provable(F, G)).
G = not(provable(F, G)).

?- unify_with_occurs_check(G, not(provable(F, G))).
false.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 7/8/23 11:45 PM, olcott wrote:
> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>> On 2023-07-07 20:14, olcott wrote:
>>
>>> *I must use a stipulative definitions because there are no*
>>> *conventional terms for the meanings that I must refer to*
>>
>> The problem is that you haven't offered any definitions at all,
>> stipulative or otherwise. You have simply 'stipulated' "facts" that
>> are contrary to reality.
>>
>
> I am happy that you haven't given up on me, you have always been one of
> my top reviewers.
>
> *These are a very rough sketch starting point*
>
> Analytic propositions(olcott)
> "Analytic propositions are true or not true solely by virtue of
> their meaning..."
> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction

But what do you mean by "Meaning". Do you understand that this
definition means more than just the meaning of the words themselves, as
the proposition that the sum of the squares of the Hypotenuse of a
planar right triangle is equal to the sum of the squares of the other
two sides is a "True" statement, basd on the meaning, and the logical
operations

By exactly that same meaning, the statement that "the machine described
by the input to your Halt Decider H, when given H(D,D) is a Halting
Machine", is true since D(D) will halt since H(D,D) returns 0, and thus
the statement that Your program H is a correct Halt Decider is proven to
be WRONG.

>
> I am stipulating that this includes meanings specified in the formal
> languages of formal systems and the meanings from formalized natural
> language.
>
> In other words I am specifying the infinite set of propositions that
> have the semantic property of Boolean true. Most of these propositions
> refer to natural language meanings.
>
> semantic tautology(olcott)
> I am stipulating that a {semantic tautology} includes every expression
> of formal or natural language that can be verified as completely true
> entirely on the basis of its semantic meaning.
>
>
>> Here is a contrafactual stipulation of "fact":
>>
>> "I stipulate that the sky is green"
>>
>> That statement is either false or indicates that I am using some
>> nonstandard definition of 'sky', 'green', or 'is', but gives
>> absolutely no indication of which term I am intending to redefine or
>> how I intend to redefine it.
>>
>
> We reference these semantic meanings by their unique GUID in an acyclic
> digraph general knowledge ontology.

So DO So (and reference your source).

>
>> Here is a stipulative definition:
>>
>> "I stipulate that 'green' means, for purposes of this discussion, any
>> gas which contains at least 15% oxygen".
>>
>> Do you see the difference?
>>
>
> I am defining brand new ideas that don't have existing terms so I am
> assigning a term-of-the-art meaning to the closest existing term.

Which is WRONG. New ideas should be given new names, perhaps based on
the old term with a modifier.

The only time you can overload a new meaning to a term is if you don't
need to ever refer to the old meaning.

Note, by replacing a term with a new meaning, anything done based on the
old meaning can't be used in your new system, and since you are trying
to redefine fundamental terms in logic,

>
>> All of your "stipulations" fall into the former class rather than the
>> latter. In fact, I don't think I have ever seen you offer a
>> *definition* of anything despite the fact that such have often been
>> requested of you.
>>
>> André
>>
>
> My definitions need very much progressive refinement and are a very
> rough sketch at maybe the high school level of quality. Even at this
> very rough sketch level is is possible (although probably too difficult)
> to see that incompleteness and undefinability are abolished.
>
> What we cannot see at the very rough sketch level is whether or not
> such a system can be actually implemented.
>
> λProlog: Logic programming in higher-order logic
> https://www.lix.polytechnique.fr/~dale/lProlog/
>
> If the above system has the same Facts and Rules architecture of Prolog
> such the unprovable simply means untrue then what I am proposing might
> be able to be implemented in the above system. We have to skip the
> natural language aspects until their encoding can be full automated.

So, you are BY DEFINITION limiting your system to the level of logic
handled by Prolog?

That means you can't even handle full First Order Logic.

>
> Ordinary Prolog already rejects an enormously simplified version of the
> Gödel sentence:
>
> ?- G = not(provable(F, G)).
> G = not(provable(F, G)).
>
> ?- unify_with_occurs_check(G, not(provable(F, G))).
> false.
>
>

But since that ISN'T G, it doesn't say anything about the ACTUAL G.

You are just showing that you believe in that Strawman are good
replacements for the actual thing.

Also, since Godel uses HOL in his proof, Prolog rejecting it is
understandable, as it just can't handle that level of logic.

You are just proving your whole idea is a house of cards and doesn't do
what you claim it to do.