On 2/23/2022 6:52 PM, André G. Isaak wrote:
> On 2022-02-23 13:57, olcott wrote:
>> On 2/23/2022 1:08 PM, André G. Isaak wrote:
>>> On 2022-02-23 08:13, olcott wrote:
>>>> On 2/22/2022 11:45 PM, André G. Isaak wrote:
>>>>> On 2022-02-22 22:17, olcott wrote:
>>>>>> On 2/22/2022 11:04 PM, André G. Isaak wrote:
>>>>>>> On 2022-02-22 20:32, olcott wrote:
>
> <snippage
>
>>>> Because I formed this same view myself independently of Wittgenstein
>>>> I can say that his quoted words in my paper form a 100% complete
>>>> rebuttal that Gödel found a sentence that is both true and
>>>> unprovable. It is simply unprovable because it is untrue.
>>>
>>> It is quite possible for two people to independently reach the same
>>> wrong conclusion. So the above hardly constitutes an argument.
>>>
>>
>> It is very easy to see that true and unprovable is impossible once one
>> comprehends the self evident truth regrading how analytic truth itself
>> actually works.
>
> Which 'self-evident truth' is that?

The actual knowledge ontology structure of the body of analytic knowledge.

> Note that you have a bad track
> record of assuming that things which are demonstrably false are
> 'self-evidently true'.
>

I do use some terminology somewhat inconsistently with its conventional
meaning to overcome [strong linguistic determinism] that makes the ideas
that I need to express otherwise inexpressible.

strong version, or linguistic determinism, says that language determines
thought and that linguistic categories limit and determine cognitive
categories. https://en.wikipedia.org/wiki/Linguistic_relativity

> Note also that Gödel was not talking about analytic truth. He was
> talking about theories of arithmetic.

The body of analytic truth encompasses all of mathematics and logic and
only excludes knowledge that can only be validated by input from the
sense organs.

> The analytic/synthetic distinction
> is one made when discussing philosophy of language which deals with
> entirely different questions than arithmetic does.
>

The notion of analytic truth is the foundation of all mathematics and
logic.

> Different fields often use similar terms with subtly different meanings.
> You can't just assume that it is possible to import concepts from one
> field to another.
>

If one field overloads the term "true" to include expressions of
language that are not true, then it errs.

>
>> Most people "know" that a statement is true on the basis that someone
>> that they trust told them this statement is true. Most people here
>> "know" that I must be wrong simply because they trust that Gödel is
>> correct.
>
> Or, more likely, because they actually read the proof (which you have
> admitted to not having done) and found it compelling.
>

If its conclusion is incorrect then all of the steps can be ignored.

>>>>> What you are really saying is that you formed some view and then
>>>>> interpreted one of Wittgenstein's remarks in terms of that view.
>>>>>
>>>>>> Note that Haskell Curry is quoted before Wittgenstein has a
>>>>>> comparable notion of what "true in a formal system" means.
>>>>>>
>>>>>> Let 𝓣 be such a theory. Then the elementary statements which
>>>>>> belong to 𝓣 we shall call the elementary theorems of 𝓣; we also
>>>>>> say that these elementary statements are true for 𝓣. Thus, given
>>>>>> 𝓣, an elementary theorem is an elementary statement which is true...
>>>>>>
>>>>>> Olcott's true in a formal system 𝓣 is exactly Curry's elementary
>>>>>> theorems of 𝓣 and statements of 𝓣 derived by applying truth
>>>>>> preserving operations beginning with Curry's elementary theorems
>>>>>> of 𝓣 as premises.
>>>>>>
>>>>>> When you start with truth and only apply truth preserving
>>>>>> operations you always necessarily end up with truth.
>>>>>
>>>>>
>>>>> Which has nothing whatsoever to do with Gödel, since his theorem
>>>>> was not concerned with truth and made no mention of truth at all.
>>>>>
>>>>> André
>>>>
>>>> It has everything to do with all undecidable propositions.
>>>>
>>>> Undecidable propositions are simply not truth bearers
>>>
>>> The above claim is simply false. It is not consistent with the
>>> standard definitions of 'undecidable' and 'truth bearer'.
>>
>> It is consistent with the way that <truth> really works, thus
>> superseding and overriding all of the misconceptions that seem to
>> contradict it.
>
> I have no reason to believe that you have any understanding of how truth
> 'really works'.
>

Analytic truth is nothing more that a semantically connected set of
expressions of language each one known to be true.

>>>
>>> Moreover, it also doesn't follow from your above claim that "When you
>>> start with truth and only apply truth preserving operations you
>>> always necessarily end up with truth." So you're basically presenting
>>> a non-sequitur.
>>>
>>
>> Something that 100% perfectly logically follows is utterly
>> ridiculously characterized as non-sequitur.
>
> If you think the latter follows from the former you then you need a
> course in remedial logic.

If you start with expressions of language that are known to be true
(such as Haskell Curry's elementary theorems) and only apply truth
preserving operations you don't end up with peanut butter.

>>
>>>  > in the same way that the following sentence is neither true nor
>>> false:
>>>  > "What time is it?"
>>>
>>> That sentence is not a proposition. Gödels paper is concerned with
>>> undecidable *propositions*. And it isn't concerned with natural
>>> language at all.
>>>
>>
>> I wanted to make a very clear example of an expression of language
>> that very obviously cannot be resolved to true or false. Example form
>> formal language that are not truth bearers are placed in the incorrect
>> category of undecidable.
>
> There is no category in formal systems analogous to interrogatives.

There is one yet not one that you are aware of.

This is not my idea:
Questions are merely propositions with a missing piece.

> You seem to not grasp the distinction between ontology and epistemology.
> Whether we can *determine* whether a statement is true or false is an
> epistemological issue which has no bearing at all on whether the
> statement actually *is* true or false.
>

In computer science and information science, an ontology encompasses a
representation, formal naming, and definition of the categories,
properties, and relations between the concepts, data, and entities that
substantiate one, many, or all domains of discourse.
https://en.wikipedia.org/wiki/Ontology_(information_science)

>> Flibble is correct in that the reason these things are not properly
>> resolved is category error. When one assumes a term-of-the-art
>> definition that has hidden incoherence then these terms-of-the-art
>> make their own error inexpressible.
>>
>> The strong version, or linguistic determinism, says that language
>> determines thought and that linguistic categories limit and determine
>> cognitive categories. https://en.wikipedia.org/wiki/Linguistic_relativity
>
> Both a mischaracterization and utterly irrelevant.
>

A theory T is incomplete if and only if there is some sentence φ such
that (T ⊬ φ) and (T ⊬ ¬φ).

The above simply ignores the case where a syntactically correct
expression of a formal language is unprovable simply because at the
semantic level it is self-contradictory.

>>>> All expressions of formal or natural language that apply only truth
>>>> preserving operations beginning with a set of premises known to be
>>>> true (such as Haskell Curry's elementary theorems) are sound, else
>>>> unsound.
>>>
>>> Oh dear. You really are confused. You're making numerous category
>>> errors above. Soundness is not a property of arguments, not
>>> propositions (which is what Gödel is concerned with).
>>
>> I will use more generic language that has not been overridden
>> idiomatic terms-of-the-art meanings.
>>
>> expressions of language that were derived by applying truth preserving
>> operations to expressions of language known to be true necessarily
>> derive true expressions of language.
>>
>>> And 'expressions of formal or natural language' don't 'apply truth
>>> preserving operations'.
>>>
>>
>> If I have a cat then I have an animal applies the truth preserving
>> operation Is-A-Type_Of(cat, animal) on the basis of a knowledge
>> ontology that specifies all of the general knowledge.
>>
>>>> All expressions of formal or natural language that apply only truth
>>>> preserving operations beginning with a set of premises are valid,
>>>> else invalid.
>>>
>>> That sentence is incoherent.
>>>
>>
>> If one applies only truth preserving operations to a set of true
>> expressions of language then true expressions of language are derived.
>
> If one starts with true premises and uses valid deductive rules one is
> guaranteed to arrive at true conclusions.
> That does *NOT* entail that
> every true statement can be derived from some set of axioms using valid
> deductive rules.
>

For the body of analytic knowledge that includes all of mathematics and
logic an expression of language is true if:
(1) It is stipulated to be true like Curry's elementary theorems
(2) It is derived from applying truth preserving operations to (1) or (2).

>> If one applies only truth preserving operations to a set of
>> expressions of language then logically entailed expressions of
>> language are derived.
>>
>>>> valid reasoning requires conclusions to be a necessary consequence
>>>> of the premises.
>>>
>>> Which is not contradicted by Gödel. He would agree with this.
>>>
>>> André
>>
>> The key mistake is that he believes that his sentence is true and
>> unprovable which is analogous to a purebred cat that is a kind of dog.
>
> Gödel makes no claims at all about the truth or falsehood of Gödel
> sentences.
>
> André
>

He says that it is true that G is unprovable. The only way that we can
know that G is unprovable is by a proof that G is unprovable, hence
proving that G is provable.

--
Copyright 2021 Pete Olcott

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