The following foundation of correct reasoning simultaneously gets rid of
Gödel Incompleteness Tarski Undefinability the principle of explosion
and every other divergence from correct reasoning that is allowed by
logic systems since the syllogism.

Just like with syllogisms conclusions a semantically necessary
consequence of their premises

Semantic Necessity operator: ⊨□

(a) Some expressions of language L are stipulated to have the property
of Boolean true.
(b) Some expressions of language L are a semantically necessary
consequence of others.
P is a subset of expressions of language L
T is a subset of (a)

Provable(P,X) means P ⊨□ X
True(T,X) means X ∈ (a) or T ⊨□ X
False(T,X) means T ⊨□ ~X

The above system only applies to the analytic side of the analytic
synthetic distinction which includes all of math and logic yet excludes
expressions of language that can only be verified as true with input
from the sense organs.

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

On 4/1/23 5:14 PM, olcott wrote:
> The following foundation of correct reasoning simultaneously gets rid of
> Gödel Incompleteness Tarski Undefinability the principle of explosion
> and every other divergence from correct reasoning that is allowed by
> logic systems since the syllogism.
>
> Just like with syllogisms conclusions a semantically necessary
> consequence of their premises
>
> Semantic Necessity operator: ⊨□
>
> (a) Some expressions of language L are stipulated to have the property
> of Boolean true.
> (b) Some expressions of language L are a semantically necessary
> consequence of others.
> P is a subset of expressions of language L
> T is a subset of (a)
>
> Provable(P,X)   means P ⊨□ X

Which differs from classical logic, so you have lost all ability to
refer to ANYTHING from classical logic until you reestablih it, since
classical logic requries that Provable means a FINITE chain of logic
from P to X, not just "any" chain.

Also, Provable tends to be based not a arbitrary subset of expressions
of languge (which doesn't even require them to be known true) but is
provable in a "Theory" where we start from a subset of the truth-makers
(a). of the Theory.

> True(T,X)       means X ∈ (a) or T ⊨□ X
> False(T,X)      means T ⊨□ ~X
>
> The above system only applies to the analytic side of the analytic
> synthetic distinction which includes all of math and logic yet excludes
> expressions of language that can only be verified as true with input
> from the sense organs.
>

But since you disagree on key points to the existing system, you need to
start at the bottom of the logic tree, you don't even have 1+1 = 2
anymore until you actually prove it.

On 4/1/2023 4:14 PM, olcott wrote:
> The following foundation of correct reasoning simultaneously gets rid of
> Gödel Incompleteness Tarski Undefinability the principle of explosion
> and every other divergence from correct reasoning that is allowed by
> logic systems since the syllogism.
>
> Just like with syllogisms conclusions a semantically necessary
> consequence of their premises
>
> Semantic Necessity operator: ⊨□
>
> (a) Some expressions of language L are stipulated to have the property
> of Boolean true.
> (b) Some expressions of language L are a semantically necessary
> consequence of others.
> P is a subset of expressions of language L
> T is a subset of (a)
>
> Provable(P,X)   means P ⊨□ X
> True(T,X)       means X ∈ (a) or T ⊨□ X
> False(T,X)      means T ⊨□ ~X
>
> The above system only applies to the analytic side of the analytic
> synthetic distinction which includes all of math and logic yet excludes
> expressions of language that can only be verified as true with input
> from the sense organs.
>

When this is called the foundation of correct reasoning it is called
that because this is the actual way that analytic truth really works.

When any existing formal system violates the way that analytic truth
really works then it is incorrect in the absolute sense because all
formal systems and mathematics are instances of analytic truth.

When other formal systems are requited to inherit True(x), Provable(x)
and False(x) from this foundation then only their divergence is
abolished.

Semantic relations that are specified syntactically are still allowed
and long as they are semantically coherent.

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

On 4/1/23 5:58 PM, olcott wrote:
> On 4/1/2023 4:14 PM, olcott wrote:
>> The following foundation of correct reasoning simultaneously gets rid of
>> Gödel Incompleteness Tarski Undefinability the principle of explosion
>> and every other divergence from correct reasoning that is allowed by
>> logic systems since the syllogism.
>>
>> Just like with syllogisms conclusions a semantically necessary
>> consequence of their premises
>>
>> Semantic Necessity operator: ⊨□
>>
>> (a) Some expressions of language L are stipulated to have the property
>> of Boolean true.
>> (b) Some expressions of language L are a semantically necessary
>> consequence of others.
>> P is a subset of expressions of language L
>> T is a subset of (a)
>>
>> Provable(P,X)   means P ⊨□ X
>> True(T,X)       means X ∈ (a) or T ⊨□ X
>> False(T,X)      means T ⊨□ ~X
>>
>> The above system only applies to the analytic side of the analytic
>> synthetic distinction which includes all of math and logic yet excludes
>> expressions of language that can only be verified as true with input
>> from the sense organs.
>>
>
> When this is called the foundation of correct reasoning it is called
> that because this is the actual way that analytic truth really works.
>

And, since you are changing the foundations of the existing logic
system, you need to throw them ALL out and start fresh.

> When any existing formal system violates the way that analytic truth
> really works then it is incorrect in the absolute sense because all
> formal systems and mathematics are instances of analytic truth.

And since you have made a change at the fundamental level, you need to
throw out ALL previous work in logic and start over. PERIOD.

>
> When other formal systems are requited to inherit True(x), Provable(x)
> and False(x) from this foundation then only their divergence is
> abolished.

And since you are changing the base of ALL formal systems, you need to
verify EVERY proposition proven in them is still valid under your new
rules. Depending on your meaning of "Semantic" it may be easy to move
through many of them, or it may be very slow.

YOU need to do this before you can processed.

Show us that in your system 1 + 1 is still 2, remember, you need to go
back to the full set of first principles in each system it is based on,
not just assume you can use the existing logical results.

This means you are first going to need to start at basic logic and
deteremine what can actually be shown to still work.

>
> Semantic relations that are specified syntactically are still allowed
> and long as they are semantically coherent.
>

You like throwing out the words, what do you actually MEAN.

I think you don't understand the actual problem, because you don't
actually underestand what you are doing.

Is "Semantic", based on "The Meaning of the Word", (and how can a
syntactically defined relationship be coherent for all meaning of the
words?)

Or, is "Semantic" what is classically defined, which basically negates
all your meaning as it basically means that which can be shown as
necessity by the syntactic rules.

On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
> On 4/1/2023 4:14 PM, olcott wrote:
> > The following foundation of correct reasoning simultaneously gets rid of
> > Gödel Incompleteness Tarski Undefinability the principle of explosion
> > and every other divergence from correct reasoning that is allowed by
> > logic systems since the syllogism.
> >
> > Just like with syllogisms conclusions a semantically necessary
> > consequence of their premises
> >
> > Semantic Necessity operator: ⊨□
> >
> > (a) Some expressions of language L are stipulated to have the property
> > of Boolean true.
> > (b) Some expressions of language L are a semantically necessary
> > consequence of others.
> > P is a subset of expressions of language L
> > T is a subset of (a)
> >
> > Provable(P,X) means P ⊨□ X
> > True(T,X) means X ∈ (a) or T ⊨□ X
> > False(T,X) means T ⊨□ ~X
> >
> > The above system only applies to the analytic side of the analytic
> > synthetic distinction which includes all of math and logic yet excludes
> > expressions of language that can only be verified as true with input
> > from the sense organs.
> >
> When this is called the foundation of correct reasoning it is called
> that because this is the actual way that analytic truth really works.
>
> When any existing formal system violates the way that analytic truth
> really works then it is incorrect in the absolute sense because all
> formal systems and mathematics are instances of analytic truth.
>
> When other formal systems are requited to inherit True(x), Provable(x)
> and False(x) from this foundation then only their divergence is
> abolished.
>
> Semantic relations that are specified syntactically are still allowed
> and long as they are semantically coherent.
>
I am inclined to view your (PO's) concept of semantic necessity as dependent on the senses and therefore, by definition, synthetic. That is: That there is a semantic relationship between two ideas cannot be detected except through uses of the senses. Unless some relationships exist that are not sense-based
but are not analytic your theory is meaningless.

On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
>> On 4/1/2023 4:14 PM, olcott wrote:
>>> The following foundation of correct reasoning simultaneously gets rid of
>>> Gödel Incompleteness Tarski Undefinability the principle of explosion
>>> and every other divergence from correct reasoning that is allowed by
>>> logic systems since the syllogism.
>>>
>>> Just like with syllogisms conclusions a semantically necessary
>>> consequence of their premises
>>>
>>> Semantic Necessity operator: ⊨□
>>>
>>> (a) Some expressions of language L are stipulated to have the property
>>> of Boolean true.
>>> (b) Some expressions of language L are a semantically necessary
>>> consequence of others.
>>> P is a subset of expressions of language L
>>> T is a subset of (a)
>>>
>>> Provable(P,X) means P ⊨□ X
>>> True(T,X) means X ∈ (a) or T ⊨□ X
>>> False(T,X) means T ⊨□ ~X
>>>
>>> The above system only applies to the analytic side of the analytic
>>> synthetic distinction which includes all of math and logic yet excludes
>>> expressions of language that can only be verified as true with input
>>> from the sense organs.
>>>
>> When this is called the foundation of correct reasoning it is called
>> that because this is the actual way that analytic truth really works.
>>
>> When any existing formal system violates the way that analytic truth
>> really works then it is incorrect in the absolute sense because all
>> formal systems and mathematics are instances of analytic truth.
>>
>> When other formal systems are requited to inherit True(x), Provable(x)
>> and False(x) from this foundation then only their divergence is
>> abolished.
>>
>> Semantic relations that are specified syntactically are still allowed
>> and long as they are semantically coherent.
>>
> I am inclined to view your (PO's) concept of semantic necessity as dependent on the senses and therefore, by definition, synthetic.

I have said that is not what I mean 1000 times.

> That is: That there is a semantic relationship between two ideas cannot be detected except through uses of the senses.

That is ridiculous.

> Unless some relationships exist that are not sense-based
> but are not analytic your theory is meaningless.

I HAVE SAID IT THIS WAY FOR THREE YEARS
Pure analytic means that it can be verified as completely true entirely
on the basis of its meaning without any input from the sense organs.

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

On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
>> On 4/1/2023 4:14 PM, olcott wrote:
>>> The following foundation of correct reasoning simultaneously gets rid of
>>> Gödel Incompleteness Tarski Undefinability the principle of explosion
>>> and every other divergence from correct reasoning that is allowed by
>>> logic systems since the syllogism.
>>>
>>> Just like with syllogisms conclusions a semantically necessary
>>> consequence of their premises
>>>
>>> Semantic Necessity operator: ⊨□
>>>
>>> (a) Some expressions of language L are stipulated to have the property
>>> of Boolean true.
>>> (b) Some expressions of language L are a semantically necessary
>>> consequence of others.
>>> P is a subset of expressions of language L
>>> T is a subset of (a)
>>>
>>> Provable(P,X) means P ⊨□ X
>>> True(T,X) means X ∈ (a) or T ⊨□ X
>>> False(T,X) means T ⊨□ ~X
>>>
>>> The above system only applies to the analytic side of the analytic
>>> synthetic distinction which includes all of math and logic yet excludes
>>> expressions of language that can only be verified as true with input
>>> from the sense organs.
>>>
>> When this is called the foundation of correct reasoning it is called
>> that because this is the actual way that analytic truth really works.
>>
>> When any existing formal system violates the way that analytic truth
>> really works then it is incorrect in the absolute sense because all
>> formal systems and mathematics are instances of analytic truth.
>>
>> When other formal systems are requited to inherit True(x), Provable(x)
>> and False(x) from this foundation then only their divergence is
>> abolished.
>>
>> Semantic relations that are specified syntactically are still allowed
>> and long as they are semantically coherent.
>>
> I am inclined to view your (PO's) concept of semantic necessity as dependent on the senses and therefore, by definition, synthetic.

Pure analytic means that it can be verified as completely true entirely
on the basis of its meaning without any input from the sense organs.
"Dogs" <are> "Animals"

I have renamed synthetic to empirical, this requires sense data from the
sense organs. "There is a dog in my living room right now".

> That is: That there is a semantic relationship between two ideas cannot be detected except through uses of the senses. Unless some relationships exist that are not sense-based
> but are not analytic your theory is meaningless.

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

On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
>> On 4/1/2023 4:14 PM, olcott wrote:
>>> The following foundation of correct reasoning simultaneously gets rid of
>>> Gödel Incompleteness Tarski Undefinability the principle of explosion
>>> and every other divergence from correct reasoning that is allowed by
>>> logic systems since the syllogism.
>>>
>>> Just like with syllogisms conclusions a semantically necessary
>>> consequence of their premises
>>>
>>> Semantic Necessity operator: ⊨□
>>>
>>> (a) Some expressions of language L are stipulated to have the property
>>> of Boolean true.
>>> (b) Some expressions of language L are a semantically necessary
>>> consequence of others.
>>> P is a subset of expressions of language L
>>> T is a subset of (a)
>>>
>>> Provable(P,X) means P ⊨□ X
>>> True(T,X) means X ∈ (a) or T ⊨□ X
>>> False(T,X) means T ⊨□ ~X
>>>
>>> The above system only applies to the analytic side of the analytic
>>> synthetic distinction which includes all of math and logic yet excludes
>>> expressions of language that can only be verified as true with input
>>> from the sense organs.
>>>
>> When this is called the foundation of correct reasoning it is called
>> that because this is the actual way that analytic truth really works.
>>
>> When any existing formal system violates the way that analytic truth
>> really works then it is incorrect in the absolute sense because all
>> formal systems and mathematics are instances of analytic truth.
>>
>> When other formal systems are requited to inherit True(x), Provable(x)
>> and False(x) from this foundation then only their divergence is
>> abolished.
>>
>> Semantic relations that are specified syntactically are still allowed
>> and long as they are semantically coherent.
>>
> I am inclined to view your (PO's) concept of semantic necessity as dependent on the senses and therefore, by definition, synthetic. That is: That there is a semantic relationship between two ideas cannot be detected except through uses of the senses. Unless some relationships exist that are not sense-based
> but are not analytic your theory is meaningless.

Analytic is
Anything that can be fully expressed in this:
(as a recursive inheritance hierarchy)
https://en.wikipedia.org/wiki/Ontology_(computer_science)

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

On 4/1/23 11:01 PM, olcott wrote:
> On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
>> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
>>> On 4/1/2023 4:14 PM, olcott wrote:
>>>> The following foundation of correct reasoning simultaneously gets
>>>> rid of
>>>> Gödel Incompleteness Tarski Undefinability the principle of explosion
>>>> and every other divergence from correct reasoning that is allowed by
>>>> logic systems since the syllogism.
>>>>
>>>> Just like with syllogisms conclusions a semantically necessary
>>>> consequence of their premises
>>>>
>>>> Semantic Necessity operator: ⊨□
>>>>
>>>> (a) Some expressions of language L are stipulated to have the property
>>>> of Boolean true.
>>>> (b) Some expressions of language L are a semantically necessary
>>>> consequence of others.
>>>> P is a subset of expressions of language L
>>>> T is a subset of (a)
>>>>
>>>> Provable(P,X)   means P ⊨□ X
>>>> True(T,X)       means X ∈ (a) or T ⊨□ X
>>>> False(T,X)      means T ⊨□ ~X
>>>>
>>>> The above system only applies to the analytic side of the analytic
>>>> synthetic distinction which includes all of math and logic yet excludes
>>>> expressions of language that can only be verified as true with input
>>>> from the sense organs.
>>>>
>>> When this is called the foundation of correct reasoning it is called
>>> that because this is the actual way that analytic truth really works.
>>>
>>> When any existing formal system violates the way that analytic truth
>>> really works then it is incorrect in the absolute sense because all
>>> formal systems and mathematics are instances of analytic truth.
>>>
>>> When other formal systems are requited to inherit True(x), Provable(x)
>>> and False(x) from this foundation then only their divergence is
>>> abolished.
>>>
>>> Semantic relations that are specified syntactically are still allowed
>>> and long as they are semantically coherent.
>>>
>> I am inclined to view your (PO's) concept of semantic necessity as
>> dependent on the senses and therefore, by definition, synthetic.
>
> I have said that is not what I mean 1000 times.
>
>> That is: That there is a semantic relationship between two ideas
>> cannot be detected except through uses of the senses.
>
> That is ridiculous.
>
>> Unless some relationships exist that are not sense-based
>> but are not analytic your theory is meaningless.
>
> I HAVE SAID IT THIS WAY FOR THREE YEARS
> Pure analytic means that it can be verified as completely true entirely
> on the basis of its meaning without any input from the sense organs.
>
>

So, is the fact that no number satisfies a given mathematical
relationship an analytic fact, even if the only way to "verify" this is
to test every single number, which being an infinite set, might not be
able to be done?

Your use of the wrod "verified" seems to imply that analytic truths must
be "knowable", but that leads to issues like propositions like the
Collatz conjecture can't by treated as a logical truth value, because we
don't know how to verify that.

This is the fundamental issue with your system, you can't seem to
formally define exactly what your terms mean.

On Saturday, April 1, 2023 at 10:21:05 PM UTC-7, olcott wrote:
> On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
> > On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
> >> On 4/1/2023 4:14 PM, olcott wrote:
> >>> The following foundation of correct reasoning simultaneously gets rid of
> >>> Gödel Incompleteness Tarski Undefinability the principle of explosion
> >>> and every other divergence from correct reasoning that is allowed by
> >>> logic systems since the syllogism.
> >>>
> >>> Just like with syllogisms conclusions a semantically necessary
> >>> consequence of their premises
> >>>
> >>> Semantic Necessity operator: ⊨□
> >>>
> >>> (a) Some expressions of language L are stipulated to have the property
> >>> of Boolean true.
> >>> P is a subset of expressions of language L
> >>> T is a subset of (a)
> >>>
> >>> Provable(P,X) means P ⊨□ X
> >>> True(T,X) means X ∈ (a) or T ⊨□ X
> >>> False(T,X) means T ⊨□ ~X
> >>>
> >>> The above system only applies to the analytic side of the analytic
> >>> synthetic distinction which includes all of math and logic yet excludes
> >>> expressions of language that can only be verified as true with input
> >>> from the sense organs.
> >>>
> >> When this is called the foundation of correct reasoning it is called
> >> that because this is the actual way that analytic truth really works.
> >>
> >> When any existing formal system violates the way that analytic truth
> >> really works then it is incorrect in the absolute sense because all
> >> formal systems and mathematics are instances of analytic truth.
> >>
> >> When other formal systems are requited to inherit True(x), Provable(x)
> >> and False(x) from this foundation then only their divergence is
> >> abolished.
> >>
> >> Semantic relations that are specified syntactically are still allowed
> >> and long as they are semantically coherent.
> >>
> > I am inclined to view your (PO's) concept of semantic necessity as dependent on the senses and therefore, by definition, synthetic. That is: That there is a semantic relationship between two ideas cannot be detected except through uses of the senses. Unless some relationships exist that are not sense-based
> > but are not analytic your theory is meaningless.
> Analytic is
> Anything that can be fully expressed in this:
> (as a recursive inheritance hierarchy)
> https://en.wikipedia.org/wiki/Ontology_(computer_science)
>
I'm not arguing against your concept of analytic. I'm arguing against your idea of semantic necessity.

An example of your (b) above would help. "Some expressions of language L are a semantically necessary
consequence of others.". Examples are no help unless they are not examples of ordinary logic.

Your usage of "Ontology" Is peculiar. As I see it: Knowledge is a set of triples. A triple is <subject, verb, object>. A is an attribute of B if there is a triple <A attribute B>. An attribute T is transitive if
A T B and B T C implies A T C
An ontology is a set of triples with transitive attribute T

The ontology that is most common is one based of the "is a" attribute.

On 4/2/2023 4:23 PM, dklei...@gmail.com wrote:
> On Saturday, April 1, 2023 at 10:21:05 PM UTC-7, olcott wrote:
>> On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
>>> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
>>>> On 4/1/2023 4:14 PM, olcott wrote:
>>>>> The following foundation of correct reasoning simultaneously gets rid of
>>>>> Gödel Incompleteness Tarski Undefinability the principle of explosion
>>>>> and every other divergence from correct reasoning that is allowed by
>>>>> logic systems since the syllogism.
>>>>>
>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>> consequence of their premises
>>>>>
>>>>> Semantic Necessity operator: ⊨□
>>>>>
>>>>> (a) Some expressions of language L are stipulated to have the property
>>>>> of Boolean true.
>>>>> P is a subset of expressions of language L
>>>>> T is a subset of (a)
>>>>>
>>>>> Provable(P,X) means P ⊨□ X
>>>>> True(T,X) means X ∈ (a) or T ⊨□ X
>>>>> False(T,X) means T ⊨□ ~X
>>>>>
>>>>> The above system only applies to the analytic side of the analytic
>>>>> synthetic distinction which includes all of math and logic yet excludes
>>>>> expressions of language that can only be verified as true with input
>>>>> from the sense organs.
>>>>>
>>>> When this is called the foundation of correct reasoning it is called
>>>> that because this is the actual way that analytic truth really works.
>>>>
>>>> When any existing formal system violates the way that analytic truth
>>>> really works then it is incorrect in the absolute sense because all
>>>> formal systems and mathematics are instances of analytic truth.
>>>>
>>>> When other formal systems are requited to inherit True(x), Provable(x)
>>>> and False(x) from this foundation then only their divergence is
>>>> abolished.
>>>>
>>>> Semantic relations that are specified syntactically are still allowed
>>>> and long as they are semantically coherent.
>>>>
>>> I am inclined to view your (PO's) concept of semantic necessity as dependent on the senses and therefore, by definition, synthetic. That is: That there is a semantic relationship between two ideas cannot be detected except through uses of the senses. Unless some relationships exist that are not sense-based
>>> but are not analytic your theory is meaningless.
>> Analytic is
>> Anything that can be fully expressed in this:
>> (as a recursive inheritance hierarchy)
>> https://en.wikipedia.org/wiki/Ontology_(computer_science)
>>
> I'm not arguing against your concept of analytic. I'm arguing against your idea of semantic necessity.
>

It is the exactly same idea as a syllogism, ever here about them?

> An example of your (b) above would help. "Some expressions of language L are a semantically necessary
> consequence of others.". Examples are no help unless they are not examples of ordinary logic.
>

Billions of syllogisms provide these examples. It is the first thing
that people should learn about logic.

> Your usage of "Ontology" Is peculiar. As I see it: Knowledge is a set of triples.

In other words the infinite set of predicates in higher order logic is
ALWAYS tertiary ?

> A triple is <subject, verb, object>. A is an attribute of B if there is a triple <A attribute B>. An attribute T is transitive if
> A T B and B T C implies A T C
> An ontology is a set of triples with transitive attribute T
>
> The ontology that is most common is one based of the "is a" attribute.

OK that is very good. "has a" is also important.
{I just bought a farm house from Jane today for $100,000} is not tertiary.

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

On 4/2/23 6:22 PM, olcott wrote:
> On 4/2/2023 4:23 PM, dklei...@gmail.com wrote:
>> On Saturday, April 1, 2023 at 10:21:05 PM UTC-7, olcott wrote:
>>> On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
>>>> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
>>>>> On 4/1/2023 4:14 PM, olcott wrote:
>>>>>> The following foundation of correct reasoning simultaneously gets
>>>>>> rid of
>>>>>> Gödel Incompleteness Tarski Undefinability the principle of explosion
>>>>>> and every other divergence from correct reasoning that is allowed by
>>>>>> logic systems since the syllogism.
>>>>>>
>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>> consequence of their premises
>>>>>>
>>>>>> Semantic Necessity operator: ⊨□
>>>>>>
>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>> property
>>>>>> of Boolean true.
>>>>>> P is a subset of expressions of language L
>>>>>> T is a subset of (a)
>>>>>>
>>>>>> Provable(P,X) means P ⊨□ X
>>>>>> True(T,X) means X ∈ (a) or T ⊨□ X
>>>>>> False(T,X) means T ⊨□ ~X
>>>>>>
>>>>>> The above system only applies to the analytic side of the analytic
>>>>>> synthetic distinction which includes all of math and logic yet
>>>>>> excludes
>>>>>> expressions of language that can only be verified as true with input
>>>>>> from the sense organs.
>>>>>>
>>>>> When this is called the foundation of correct reasoning it is called
>>>>> that because this is the actual way that analytic truth really works.
>>>>>
>>>>> When any existing formal system violates the way that analytic truth
>>>>> really works then it is incorrect in the absolute sense because all
>>>>> formal systems and mathematics are instances of analytic truth.
>>>>>
>>>>> When other formal systems are requited to inherit True(x), Provable(x)
>>>>> and False(x) from this foundation then only their divergence is
>>>>> abolished.
>>>>>
>>>>> Semantic relations that are specified syntactically are still allowed
>>>>> and long as they are semantically coherent.
>>>>>
>>>> I am inclined to view your (PO's) concept of semantic necessity as
>>>> dependent on the senses and therefore, by definition, synthetic.
>>>> That is: That there is a semantic relationship between two ideas
>>>> cannot be detected except through uses of the senses. Unless some
>>>> relationships exist that are not sense-based
>>>> but are not analytic your theory is meaningless.
>>> Analytic is
>>> Anything that can be fully expressed in this:
>>> (as a recursive inheritance hierarchy)
>>> https://en.wikipedia.org/wiki/Ontology_(computer_science)
>>>
>> I'm not arguing against your concept of analytic. I'm arguing against
>> your idea of semantic necessity.
>>
>
> It is the exactly same idea as a syllogism, ever here about them?

Then way not use the classical word?

And, if you concept of semantic necessity is limited to just the power
of a syllogism, you logic will be very weak, as there ARE logical forms
beyond that, and they are needed to get to the power of Mathematics.

>
>> An example of your (b) above would help. "Some expressions of language
>> L are a semantically necessary
>> consequence of others.". Examples are no help unless they are not
>> examples of ordinary logic.
>>
>
> Billions of syllogisms provide these examples. It is the first thing
> that people should learn about logic.

And if you mean syllogism, why don't you use the term.

>
>> Your usage of "Ontology" Is peculiar. As I see it: Knowledge is a set
>> of triples.
>
> In other words the infinite set of predicates in higher order logic is
> ALWAYS tertiary ?

At least most "higher order" predicates can be decomposed into a set of
triples.

>
>
>> A triple is <subject, verb, object>. A is an attribute of B if there
>> is a triple <A attribute B>. An attribute T is transitive if
>>        A T B and B T C implies A T C
>> An ontology is a set of triples with transitive attribute T
>>
>> The ontology that is most common is one based of the "is a" attribute.
>
> OK that is very good. "has a" is also important.
> {I just bought a farm house from Jane today for $100,000} is not tertiary.
>
>

On Sunday, April 2, 2023 at 3:22:04 PM UTC-7, olcott wrote:
> On 4/2/2023 4:23 PM, dklei...@gmail.com wrote:
> > On Saturday, April 1, 2023 at 10:21:05 PM UTC-7, olcott wrote:
> >> On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
> >>> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
> >>>> On 4/1/2023 4:14 PM, olcott wrote:
> >>>>> The following foundation of correct reasoning simultaneously gets rid of
> >>>>> Gödel Incompleteness Tarski Undefinability the principle of explosion
> >>>>> and every other divergence from correct reasoning that is allowed by
> >>>>> logic systems since the syllogism.
> >>>>>
> >>>>> Just like with syllogisms conclusions a semantically necessary
> >>>>> consequence of their premises
> >>>>>
> >>>>> Semantic Necessity operator: ⊨□
> >>>>>
> >>>>> (a) Some expressions of language L are stipulated to have the property
> >>>>> of Boolean true.
> >>>>> P is a subset of expressions of language L
> >>>>> T is a subset of (a)
> >>>>>
> >>>>> Provable(P,X) means P ⊨□ X
> >>>>> True(T,X) means X ∈ (a) or T ⊨□ X
> >>>>> False(T,X) means T ⊨□ ~X
> >>>>>
> >>>>> The above system only applies to the analytic side of the analytic
> >>>>> synthetic distinction which includes all of math and logic yet excludes
> >>>>> expressions of language that can only be verified as true with input
> >>>>> from the sense organs.
> >>>>>
> >>>> When this is called the foundation of correct reasoning it is called
> >>>> that because this is the actual way that analytic truth really works..
> >>>>
> >>>> When any existing formal system violates the way that analytic truth
> >>>> really works then it is incorrect in the absolute sense because all
> >>>> formal systems and mathematics are instances of analytic truth.
> >>>>
> >>>> When other formal systems are requited to inherit True(x), Provable(x)
> >>>> and False(x) from this foundation then only their divergence is
> >>>> abolished.
> >>>>
> >>>> Semantic relations that are specified syntactically are still allowed
> >>>> and long as they are semantically coherent.
> >>>>
> >>> I am inclined to view your (PO's) concept of semantic necessity as dependent on the senses and therefore, by definition, synthetic. That is: That there is a semantic relationship between two ideas cannot be detected except through uses of the senses. Unless some relationships exist that are not sense-based
> >>> but are not analytic your theory is meaningless.
> >> Analytic is
> >> Anything that can be fully expressed in this:
> >> (as a recursive inheritance hierarchy)
> >> https://en.wikipedia.org/wiki/Ontology_(computer_science)
> >>
> > I'm not arguing against your concept of analytic. I'm arguing against your idea of semantic necessity.
> >
> It is the exactly same idea as a syllogism, ever here about them?
> > An example of your (b) above would help. "Some expressions of language L are a semantically necessary
> > consequence of others.". Examples are no help unless they are not examples of ordinary logic.
> >
> Billions of syllogisms provide these examples. It is the first thing
> that people should learn about logic.
> > Your usage of "Ontology" Is peculiar. As I see it: Knowledge is a set of triples.
> In other words the infinite set of predicates in higher order logic is
> ALWAYS tertiary ?
> > A triple is <subject, verb, object>. A is an attribute of B if there is a triple <A attribute B>. An attribute T is transitive if
> > A T B and B T C implies A T C
> > An ontology is a set of triples with transitive attribute T
> >
> > The ontology that is most common is one based of the "is a" attribute.
> OK that is very good. "has a" is also important.
> {I just bought a farm house from Jane today for $100,000} is not tertiary..
>
event action purchase
event buyer self
event object farmhouse
farmhouse is-a house
event seller Jane
event date today
event price $100,000

The "just" seems to be undesirable when there is already a date,

On 4/3/2023 4:20 AM, dklei...@gmail.com wrote:
> On Sunday, April 2, 2023 at 3:22:04 PM UTC-7, olcott wrote:
>> On 4/2/2023 4:23 PM, dklei...@gmail.com wrote:
>>> On Saturday, April 1, 2023 at 10:21:05 PM UTC-7, olcott wrote:
>>>> On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
>>>>> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
>>>>>> On 4/1/2023 4:14 PM, olcott wrote:
>>>>>>> The following foundation of correct reasoning simultaneously gets rid of
>>>>>>> Gödel Incompleteness Tarski Undefinability the principle of explosion
>>>>>>> and every other divergence from correct reasoning that is allowed by
>>>>>>> logic systems since the syllogism.
>>>>>>>
>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>> consequence of their premises
>>>>>>>
>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>
>>>>>>> (a) Some expressions of language L are stipulated to have the property
>>>>>>> of Boolean true.
>>>>>>> P is a subset of expressions of language L
>>>>>>> T is a subset of (a)
>>>>>>>
>>>>>>> Provable(P,X) means P ⊨□ X
>>>>>>> True(T,X) means X ∈ (a) or T ⊨□ X
>>>>>>> False(T,X) means T ⊨□ ~X
>>>>>>>
>>>>>>> The above system only applies to the analytic side of the analytic
>>>>>>> synthetic distinction which includes all of math and logic yet excludes
>>>>>>> expressions of language that can only be verified as true with input
>>>>>>> from the sense organs.
>>>>>>>
>>>>>> When this is called the foundation of correct reasoning it is called
>>>>>> that because this is the actual way that analytic truth really works.
>>>>>>
>>>>>> When any existing formal system violates the way that analytic truth
>>>>>> really works then it is incorrect in the absolute sense because all
>>>>>> formal systems and mathematics are instances of analytic truth.
>>>>>>
>>>>>> When other formal systems are requited to inherit True(x), Provable(x)
>>>>>> and False(x) from this foundation then only their divergence is
>>>>>> abolished.
>>>>>>
>>>>>> Semantic relations that are specified syntactically are still allowed
>>>>>> and long as they are semantically coherent.
>>>>>>
>>>>> I am inclined to view your (PO's) concept of semantic necessity as dependent on the senses and therefore, by definition, synthetic. That is: That there is a semantic relationship between two ideas cannot be detected except through uses of the senses. Unless some relationships exist that are not sense-based
>>>>> but are not analytic your theory is meaningless.
>>>> Analytic is
>>>> Anything that can be fully expressed in this:
>>>> (as a recursive inheritance hierarchy)
>>>> https://en.wikipedia.org/wiki/Ontology_(computer_science)
>>>>
>>> I'm not arguing against your concept of analytic. I'm arguing against your idea of semantic necessity.
>>>
>> It is the exactly same idea as a syllogism, ever here about them?
>>> An example of your (b) above would help. "Some expressions of language L are a semantically necessary
>>> consequence of others.". Examples are no help unless they are not examples of ordinary logic.
>>>
>> Billions of syllogisms provide these examples. It is the first thing
>> that people should learn about logic.
>>> Your usage of "Ontology" Is peculiar. As I see it: Knowledge is a set of triples.
>> In other words the infinite set of predicates in higher order logic is
>> ALWAYS tertiary ?
>>> A triple is <subject, verb, object>. A is an attribute of B if there is a triple <A attribute B>. An attribute T is transitive if
>>> A T B and B T C implies A T C
>>> An ontology is a set of triples with transitive attribute T
>>>
>>> The ontology that is most common is one based of the "is a" attribute.
>> OK that is very good. "has a" is also important.
>> {I just bought a farm house from Jane today for $100,000} is not tertiary.
>>
> event action purchase
> event buyer self
> event object farmhouse
> farmhouse is-a house
> event seller Jane
> event date today
> event price $100,000
>
> The "just" seems to be undesirable when there is already a date,

Yes something like that.
Events have a type and a variable number of parameters.

We don't need to say that a farmhouse is a house, farmhouse links
this discourse knowledge ontology to a general knowledge ontology.

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

On Monday, April 3, 2023 at 6:21:58 AM UTC-7, olcott wrote:
> On 4/3/2023 4:20 AM, dklei...@gmail.com wrote:
> > On Sunday, April 2, 2023 at 3:22:04 PM UTC-7, olcott wrote:
> >> On 4/2/2023 4:23 PM, dklei...@gmail.com wrote:
> >>> On Saturday, April 1, 2023 at 10:21:05 PM UTC-7, olcott wrote:
> >>>> On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
> >>>>> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
> >>>>>> On 4/1/2023 4:14 PM, olcott wrote:
> >>>>>>> The following foundation of correct reasoning simultaneously gets rid of
> >>>>>>> Gödel Incompleteness Tarski Undefinability the principle of explosion
> >>>>>>> and every other divergence from correct reasoning that is allowed by
> >>>>>>> logic systems since the syllogism.
> >>>>>>>
> >>>>>>> Just like with syllogisms conclusions a semantically necessary
> >>>>>>> consequence of their premises
> >>>>>>>
> >>>>>>> Semantic Necessity operator: ⊨□
> >>>>>>>
> >>>>>>> (a) Some expressions of language L are stipulated to have the property
> >>>>>>> of Boolean true.
> >>>>>>> P is a subset of expressions of language L
> >>>>>>> T is a subset of (a)
> >>>>>>>
> >>>>>>> Provable(P,X) means P ⊨□ X
> >>>>>>> True(T,X) means X ∈ (a) or T ⊨□ X
> >>>>>>> False(T,X) means T ⊨□ ~X
> >>>>>>>
> >>>>>>> The above system only applies to the analytic side of the analytic
> >>>>>>> synthetic distinction which includes all of math and logic yet excludes
> >>>>>>> expressions of language that can only be verified as true with input
> >>>>>>> from the sense organs.
> >>>>>>>
> >>>>>> When this is called the foundation of correct reasoning it is called
> >>>>>> that because this is the actual way that analytic truth really works.
> >>>>>>
> >>>>>> When any existing formal system violates the way that analytic truth
> >>>>>> really works then it is incorrect in the absolute sense because all
> >>>>>> formal systems and mathematics are instances of analytic truth.
> >>>>>>
> >>>>>> When other formal systems are requited to inherit True(x), Provable(x)
> >>>>>> and False(x) from this foundation then only their divergence is
> >>>>>> abolished.
> >>>>>>
> >>>>>> Semantic relations that are specified syntactically are still allowed
> >>>>>> and long as they are semantically coherent.
> >>>>>>
> >>>>> I am inclined to view your (PO's) concept of semantic necessity as dependent on the senses and therefore, by definition, synthetic. That is: That there is a semantic relationship between two ideas cannot be detected except through uses of the senses. Unless some relationships exist that are not sense-based
> >>>>> but are not analytic your theory is meaningless.
> >>>> Analytic is
> >>>> Anything that can be fully expressed in this:
> >>>> (as a recursive inheritance hierarchy)
> >>>> https://en.wikipedia.org/wiki/Ontology_(computer_science)
> >>>>
> >>> I'm not arguing against your concept of analytic. I'm arguing against your idea of semantic necessity.
> >>>
> >> It is the exactly same idea as a syllogism, ever here about them?
> >>> An example of your (b) above would help. "Some expressions of language L are a semantically necessary
> >>> consequence of others.". Examples are no help unless they are not examples of ordinary logic.
> >>>
> >> Billions of syllogisms provide these examples. It is the first thing
> >> that people should learn about logic.
> >>> Your usage of "Ontology" Is peculiar. As I see it: Knowledge is a set of triples.
> >> In other words the infinite set of predicates in higher order logic is
> >> ALWAYS tertiary ?
> >>> A triple is <subject, verb, object>. A is an attribute of B if there is a triple <A attribute B>. An attribute T is transitive if
> >>> A T B and B T C implies A T C
> >>> An ontology is a set of triples with transitive attribute T
> >>>
> >>> The ontology that is most common is one based of the "is a" attribute..
> >> OK that is very good. "has a" is also important.
> >> {I just bought a farm house from Jane today for $100,000} is not tertiary.
> >>
> > event action purchase
> > event buyer self
> > event object farmhouse
> > farmhouse is-a house
> > event seller Jane
> > event date today
> > event price $100,000
> >
> > The "just" seems to be undesirable when there is already a date,
> Yes something like that.
> Events have a type and a variable number of parameters.
>
> We don't need to say that a farmhouse is a house, farmhouse links
> this discourse knowledge ontology to a general knowledge ontology.
>
The specific farmhouse you bought has to be identified as a farm house to match your example. But here there is an ambiguity to resolve. Your question says "a farm house" which usually means, because of the "a", one random member of a pile of farm houses. But that is not what you did. You bought a specific house. In the real world you might have said "that farm house".

On 4/3/2023 8:57 PM, dklei...@gmail.com wrote:
> On Monday, April 3, 2023 at 6:21:58 AM UTC-7, olcott wrote:
>> On 4/3/2023 4:20 AM, dklei...@gmail.com wrote:
>>> On Sunday, April 2, 2023 at 3:22:04 PM UTC-7, olcott wrote:
>>>> On 4/2/2023 4:23 PM, dklei...@gmail.com wrote:
>>>>> On Saturday, April 1, 2023 at 10:21:05 PM UTC-7, olcott wrote:
>>>>>> On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
>>>>>>> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
>>>>>>>> On 4/1/2023 4:14 PM, olcott wrote:
>>>>>>>>> The following foundation of correct reasoning simultaneously gets rid of
>>>>>>>>> Gödel Incompleteness Tarski Undefinability the principle of explosion
>>>>>>>>> and every other divergence from correct reasoning that is allowed by
>>>>>>>>> logic systems since the syllogism.
>>>>>>>>>
>>>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>>>> consequence of their premises
>>>>>>>>>
>>>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>>>
>>>>>>>>> (a) Some expressions of language L are stipulated to have the property
>>>>>>>>> of Boolean true.
>>>>>>>>> P is a subset of expressions of language L
>>>>>>>>> T is a subset of (a)
>>>>>>>>>
>>>>>>>>> Provable(P,X) means P ⊨□ X
>>>>>>>>> True(T,X) means X ∈ (a) or T ⊨□ X
>>>>>>>>> False(T,X) means T ⊨□ ~X
>>>>>>>>>
>>>>>>>>> The above system only applies to the analytic side of the analytic
>>>>>>>>> synthetic distinction which includes all of math and logic yet excludes
>>>>>>>>> expressions of language that can only be verified as true with input
>>>>>>>>> from the sense organs.
>>>>>>>>>
>>>>>>>> When this is called the foundation of correct reasoning it is called
>>>>>>>> that because this is the actual way that analytic truth really works.
>>>>>>>>
>>>>>>>> When any existing formal system violates the way that analytic truth
>>>>>>>> really works then it is incorrect in the absolute sense because all
>>>>>>>> formal systems and mathematics are instances of analytic truth.
>>>>>>>>
>>>>>>>> When other formal systems are requited to inherit True(x), Provable(x)
>>>>>>>> and False(x) from this foundation then only their divergence is
>>>>>>>> abolished.
>>>>>>>>
>>>>>>>> Semantic relations that are specified syntactically are still allowed
>>>>>>>> and long as they are semantically coherent.
>>>>>>>>
>>>>>>> I am inclined to view your (PO's) concept of semantic necessity as dependent on the senses and therefore, by definition, synthetic. That is: That there is a semantic relationship between two ideas cannot be detected except through uses of the senses. Unless some relationships exist that are not sense-based
>>>>>>> but are not analytic your theory is meaningless.
>>>>>> Analytic is
>>>>>> Anything that can be fully expressed in this:
>>>>>> (as a recursive inheritance hierarchy)
>>>>>> https://en.wikipedia.org/wiki/Ontology_(computer_science)
>>>>>>
>>>>> I'm not arguing against your concept of analytic. I'm arguing against your idea of semantic necessity.
>>>>>
>>>> It is the exactly same idea as a syllogism, ever here about them?
>>>>> An example of your (b) above would help. "Some expressions of language L are a semantically necessary
>>>>> consequence of others.". Examples are no help unless they are not examples of ordinary logic.
>>>>>
>>>> Billions of syllogisms provide these examples. It is the first thing
>>>> that people should learn about logic.
>>>>> Your usage of "Ontology" Is peculiar. As I see it: Knowledge is a set of triples.
>>>> In other words the infinite set of predicates in higher order logic is
>>>> ALWAYS tertiary ?
>>>>> A triple is <subject, verb, object>. A is an attribute of B if there is a triple <A attribute B>. An attribute T is transitive if
>>>>> A T B and B T C implies A T C
>>>>> An ontology is a set of triples with transitive attribute T
>>>>>
>>>>> The ontology that is most common is one based of the "is a" attribute.
>>>> OK that is very good. "has a" is also important.
>>>> {I just bought a farm house from Jane today for $100,000} is not tertiary.
>>>>
>>> event action purchase
>>> event buyer self
>>> event object farmhouse
>>> farmhouse is-a house
>>> event seller Jane
>>> event date today
>>> event price $100,000
>>>
>>> The "just" seems to be undesirable when there is already a date,
>> Yes something like that.
>> Events have a type and a variable number of parameters.
>>
>> We don't need to say that a farmhouse is a house, farmhouse links
>> this discourse knowledge ontology to a general knowledge ontology.
>>
> The specific farmhouse you bought has to be identified as a farm house to match your example. But here there is an ambiguity to resolve. Your question says "a farm house" which usually means, because of the "a", one random member of a pile of farm houses. But that is not what you did. You bought a specific house. In the real world you might have said "that farm house".

The vagueness of natural language must also be modeled or too many
things would be inexpressible.

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

On 4/3/23 10:08 PM, olcott wrote:
> On 4/3/2023 8:57 PM, dklei...@gmail.com wrote:
>> On Monday, April 3, 2023 at 6:21:58 AM UTC-7, olcott wrote:
>>> On 4/3/2023 4:20 AM, dklei...@gmail.com wrote:
>>>> On Sunday, April 2, 2023 at 3:22:04 PM UTC-7, olcott wrote:
>>>>> On 4/2/2023 4:23 PM, dklei...@gmail.com wrote:
>>>>>> On Saturday, April 1, 2023 at 10:21:05 PM UTC-7, olcott wrote:
>>>>>>> On 4/1/2023 8:30 PM, dklei...@gmail.com wrote:
>>>>>>>> On Saturday, April 1, 2023 at 2:58:28 PM UTC-7, olcott wrote:
>>>>>>>>> On 4/1/2023 4:14 PM, olcott wrote:
>>>>>>>>>> The following foundation of correct reasoning simultaneously
>>>>>>>>>> gets rid of
>>>>>>>>>> Gödel Incompleteness Tarski Undefinability the principle of
>>>>>>>>>> explosion
>>>>>>>>>> and every other divergence from correct reasoning that is
>>>>>>>>>> allowed by
>>>>>>>>>> logic systems since the syllogism.
>>>>>>>>>>
>>>>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>>>>> consequence of their premises
>>>>>>>>>>
>>>>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>>>>
>>>>>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>>>>>> property
>>>>>>>>>> of Boolean true.
>>>>>>>>>> P is a subset of expressions of language L
>>>>>>>>>> T is a subset of (a)
>>>>>>>>>>
>>>>>>>>>> Provable(P,X) means P ⊨□ X
>>>>>>>>>> True(T,X) means X ∈ (a) or T ⊨□ X
>>>>>>>>>> False(T,X) means T ⊨□ ~X
>>>>>>>>>>
>>>>>>>>>> The above system only applies to the analytic side of the
>>>>>>>>>> analytic
>>>>>>>>>> synthetic distinction which includes all of math and logic yet
>>>>>>>>>> excludes
>>>>>>>>>> expressions of language that can only be verified as true with
>>>>>>>>>> input
>>>>>>>>>> from the sense organs.
>>>>>>>>>>
>>>>>>>>> When this is called the foundation of correct reasoning it is
>>>>>>>>> called
>>>>>>>>> that because this is the actual way that analytic truth really
>>>>>>>>> works.
>>>>>>>>>
>>>>>>>>> When any existing formal system violates the way that analytic
>>>>>>>>> truth
>>>>>>>>> really works then it is incorrect in the absolute sense because
>>>>>>>>> all
>>>>>>>>> formal systems and mathematics are instances of analytic truth.
>>>>>>>>>
>>>>>>>>> When other formal systems are requited to inherit True(x),
>>>>>>>>> Provable(x)
>>>>>>>>> and False(x) from this foundation then only their divergence is
>>>>>>>>> abolished.
>>>>>>>>>
>>>>>>>>> Semantic relations that are specified syntactically are still
>>>>>>>>> allowed
>>>>>>>>> and long as they are semantically coherent.
>>>>>>>>>
>>>>>>>> I am inclined to view your (PO's) concept of semantic necessity
>>>>>>>> as dependent on the senses and therefore, by definition,
>>>>>>>> synthetic. That is: That there is a semantic relationship
>>>>>>>> between two ideas cannot be detected except through uses of the
>>>>>>>> senses. Unless some relationships exist that are not sense-based
>>>>>>>> but are not analytic your theory is meaningless.
>>>>>>> Analytic is
>>>>>>> Anything that can be fully expressed in this:
>>>>>>> (as a recursive inheritance hierarchy)
>>>>>>> https://en.wikipedia.org/wiki/Ontology_(computer_science)
>>>>>>>
>>>>>> I'm not arguing against your concept of analytic. I'm arguing
>>>>>> against your idea of semantic necessity.
>>>>>>
>>>>> It is the exactly same idea as a syllogism, ever here about them?
>>>>>> An example of your (b) above would help. "Some expressions of
>>>>>> language L are a semantically necessary
>>>>>> consequence of others.". Examples are no help unless they are not
>>>>>> examples of ordinary logic.
>>>>>>
>>>>> Billions of syllogisms provide these examples. It is the first thing
>>>>> that people should learn about logic.
>>>>>> Your usage of "Ontology" Is peculiar. As I see it: Knowledge is a
>>>>>> set of triples.
>>>>> In other words the infinite set of predicates in higher order logic is
>>>>> ALWAYS tertiary ?
>>>>>> A triple is <subject, verb, object>. A is an attribute of B if
>>>>>> there is a triple <A attribute B>. An attribute T is transitive if
>>>>>> A T B and B T C implies A T C
>>>>>> An ontology is a set of triples with transitive attribute T
>>>>>>
>>>>>> The ontology that is most common is one based of the "is a"
>>>>>> attribute.
>>>>> OK that is very good. "has a" is also important.
>>>>> {I just bought a farm house from Jane today for $100,000} is not
>>>>> tertiary.
>>>>>
>>>> event action purchase
>>>> event buyer self
>>>> event object farmhouse
>>>> farmhouse is-a house
>>>> event seller Jane
>>>> event date today
>>>> event price $100,000
>>>>
>>>> The "just" seems to be undesirable when there is already a date,
>>> Yes something like that.
>>> Events have a type and a variable number of parameters.
>>>
>>> We don't need to say that a farmhouse is a house, farmhouse links
>>> this discourse knowledge ontology to a general knowledge ontology.
>>>
>> The specific farmhouse you bought has to be identified as a farm house
>> to match your example. But here there is an ambiguity to resolve. Your
>> question says "a farm house" which usually means, because of the "a",
>> one random member of a pile of farm houses. But that is not what you
>> did. You bought a specific house.  In the real world you might have
>> said "that farm house".
>
> The vagueness of natural language must also be modeled or too many
> things would be inexpressible.
>

NO!

Formal logic needs to be precisely defined so that it can give correct
answers.

IT should have a way to express uncertainty to allow it to express the
ambiquity of natural language expressions, but that should become explicit.

Maybe this statement becomes

my-farm-house is-a-member-of set-of-farm-houses

(and then use my-farm-house) in the event object tag, to indicate that
we haven't defined WHICH farm house we are talking about.