Simplest possible notion of a formal system

What is the basis for reason? And mathematics?

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Eodnhoj7
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Re: Simplest possible notion of a formal system

Post by Eodnhoj7 » Sat Aug 10, 2019 2:30 am

RCSaunders wrote:
Sat Aug 10, 2019 2:27 am
PeteOlcott wrote:
Sat Aug 10, 2019 12:50 am
Do you know what a concept is? Is it analytic or synthetic?
A concept is neither. Even if the so-called analytic/synthetic dichotomy were true (it isn't), it would have nothing to do with concepts. I do not think you know what a concept is.

So, from, "Epistemology, Concepts:"

The Purpose Of Concepts

Words, in any language, represent concepts. Concepts have a single function which is to identify existents. Existents are anything that exists, ontologically (materially), or epistemologically. Material existents (entities) and epistemological existents are all that exists.

The Structure Of Concepts

"A concept consists of two components a "perceivable existent," and a "specification." The, "perceivable existent," is a symbol, usually a spoken or written word. The "specification" is a definition which specifies or indicates the existent or existents the concept identifies.

"The word (or other perceivable symbol) for a concept is not the concept. The word is our means of being conscious of the concept. The concept is the identification of an existent. The definition of a concept indicates what existent a concept identifies."

You'll have to read the rest of the article to truly understand concepts.
Actually language is a concept, cookie cutting defintions is conceptual as well. What primarily separates a concept from other phenomenon is the degree to which it manifests itself in empirical reality.

wtf
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Re: Simplest possible notion of a formal system

Post by wtf » Sat Aug 10, 2019 5:26 am

PeteOlcott wrote:
Fri Aug 09, 2019 9:13 pm
It seems that you are intentionally playing head games and are not interested in any honest dialogue.

That's entirely up to you. I prefer a lighthearted and give-and-take kind of interaction, and a degree of self-awareness on each person's part.

You initially wrote that your system was all about mathematics or was a superset of mathematics, but you definitely called out the name of mathematics. You did NOT bother to say, for example, that your system also encompasses the field of zoology. Of course it does, since your theory incorporates everything that's true. But you EXPLICITLY CALLED OUT mathematics.

Therefore I was ENTIRELY JUSTIFIED in assuming that you DID want readers to make mathematical references as they try to understand your system.

So it is PERFECTLY SENSIBLE to ask if your system, restricted to the arithmetic of the natural numbers, is related to the well-studied True Arithmetic, which is one of the favorite toys of mathematical logicians.

You then responded by asking why the HELL, and that was your word, I would talk about mathematics!! So of course I did the POLITE thing and instead of saying, DUH YOU JUST SAID MATHEMATICS DUMMY; I instead made a JOKE and asked if it was your cat who typed your reference to mathematics, since two minutes later you denied you had made such a reference and did so vehemently. And it's kind of a universally understood joke that cats write a lot of Internet content when their humans aren't looking. Maybe you have to be a cat person. So if you're not a cat person, maybe you didn't get the joke. Ok.

So if at this point you can't say, "Haha you're right I did mention mathematics first. Let's move on," then well we're done.

I did ask you a very sensible question. It's not even original with me. It was perfectly natural to someone else on Reddit to ask the same question. If you answered I don't recall it.

If you don't get that someone is making a serious attempt to understand you; by relating things that you know, to things I know; and if furthermore you would rather walk off in a snit than have a laugh when the jokes on you, then that's how you feel.

I'm good either way. I'd like to know about the connection, if any, to True Arithmetic.

Age
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Re: Simplest possible notion of a formal system

Post by Age » Sat Aug 10, 2019 6:01 am

https://plato.stanford.edu/entries/analytic-synthetic/

When one properly makes the analytic versus synthetic distinction one realizes that
the entire body of conceptual knowledge
is entirely comprised of stipulated relations between expressions of language.

This explicitly includes but is not limited to every single detail about every aspect of every mathematical system along with the semantics of every mathematical expression of any of these systems.

The only possible rebuttal to the above claim is to find a valid counter-example of a pure concept that is not entirely defined using language. As long as we stay on the analytic side of the analytic/synthetic distinction this is impossible.

To formalize the body of conceptual knowledge merely requires expressing the stipulated relations between expressions of language as relations between finite strings.

So we end up with the simplest possible notion of a formal system that can express every element of the entire body of conceptual knowledge as simply a set of stipulated relations between finite strings.

The notion of True(x) is simply the satisfaction of the stipulated relations in the body of conceptual knowledge and the notion of False(x) is the satisfaction of the negation of x in this same body of knowledge.

Why is the above copyrighted?

Skepdick
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Re: Simplest possible notion of a formal system

Post by Skepdick » Sat Aug 10, 2019 10:08 am

Eodnhoj7 wrote:
Sat Aug 10, 2019 2:23 am
Yes, here is my rebutal:



I am assuming I will have to explain it further.

But besides that I agree with everything else you said.
That's Mathematical knowledge.

https://en.wikipedia.org/wiki/Monad_(category_theory)
https://en.wikipedia.org/wiki/Monad_(fu ... ogramming)

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RCSaunders
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Re: Simplest possible notion of a formal system

Post by RCSaunders » Sat Aug 10, 2019 3:17 pm

Eodnhoj7 wrote:
Sat Aug 10, 2019 2:30 am
Actually language is a concept, cookie cutting defintions is conceptual as well. What primarily separates a concept from other phenomenon is the degree to which it manifests itself in empirical reality.
I believe you are using the word, "concept," with its common definition, such as:

1. A general idea or understanding of something: the concept of inertia; the concept of free will.
2. A plan or original idea: The original concept was for a building with 12 floors.
3. A unifying idea or theme, especially for a product or service: a new restaurant concept.

Or you may be referring to an, "idea," as a concept, which in epistemology is broader than the term concept and includes propositions and complex descriptions as well as concepts.

The meaning of the word, "concept," in epistemology is very much narrower and refers to the simplest elements of cogency out of which all knowledge is constructed. While I do not agree with the conclusions of either of the following sources (which is the reason for my article) it is only, "concepts," as discussed in IEP or the Stanford Encyclopedia of Philosophy, or any other text on epistemology, that my article refers to.

In epistemology, the word, "language," is a symbol for a concept only if refers to the identification of any of the human developed methods of verbally storing knowledge and communication. A language, itself, is not a concept, it is an epistemological existent, like mathematics, science, and history.

Does that seem reasonable to you?

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Eodnhoj7
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Re: Simplest possible notion of a formal system

Post by Eodnhoj7 » Sat Aug 10, 2019 4:35 pm

Skepdick wrote:
Sat Aug 10, 2019 10:08 am
Eodnhoj7 wrote:
Sat Aug 10, 2019 2:23 am
Yes, here is my rebutal:



I am assuming I will have to explain it further.

But besides that I agree with everything else you said.
That's Mathematical knowledge.

https://en.wikipedia.org/wiki/Monad_(category_theory)
https://en.wikipedia.org/wiki/Monad_(fu ... ogramming)
Yes, it is...but is it limited to mathematics alone?

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Eodnhoj7
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Re: Simplest possible notion of a formal system

Post by Eodnhoj7 » Sat Aug 10, 2019 4:53 pm

RCSaunders wrote:
Sat Aug 10, 2019 3:17 pm
Eodnhoj7 wrote:
Sat Aug 10, 2019 2:30 am
Actually language is a concept, cookie cutting defintions is conceptual as well. What primarily separates a concept from other phenomenon is the degree to which it manifests itself in empirical reality.
I believe you are using the word, "concept," with its common definition, such as:

1. A general idea or understanding of something: the concept of inertia; the concept of free will.
2. A plan or original idea: The original concept was for a building with 12 floors.
3. A unifying idea or theme, especially for a product or service: a new restaurant concept.

Or you may be referring to an, "idea," as a concept, which in epistemology is broader than the term concept and includes propositions and complex descriptions as well as concepts.

The meaning of the word, "concept," in epistemology is very much narrower and refers to the simplest elements of cogency out of which all knowledge is constructed. While I do not agree with the conclusions of either of the following sources (which is the reason for my article) it is only, "concepts," as discussed in IEP or the Stanford Encyclopedia of Philosophy, or any other text on epistemology, that my article refers to.

In epistemology, the word, "language," is a symbol for a concept only if refers to the identification of any of the human developed methods of verbally storing knowledge and communication. A language, itself, is not a concept, it is an epistemological existent, like mathematics, science, and history.

Does that seem reasonable to you?
If by reasonable you mean as well defined, then yes I would agree it is very well defined. But we are both left with assuming points of view as premises.

My point of view is assumed from (a) specific starting point(s).

Your point of view is assumed from (a) specific starting point(s).

What is constant is the repetition of assumed points of origin. You start with certain premises, connect them to other premises (to define concept), to form a new premise (relative to "concept" acting as a premise for a new argument...so on and so forth).

Even "point of view" is an assumption, thus when we are dealing with the nature of defintion we are left with the connection and separation of various points.

The point acts both an abstraction and empirical phenomenon in these respects (considering staring at a point empirically results in the same point if one stairs at it in the mind). Comceptualization becomes blurred in definition when offering a new variable.

Conceptualization thus is true within your context, and false in another....and vice versa.

However this leaves us with a hyper relativity then. All assumed premises are simultaneously right and wrong given a specific context. This paradoxically is a constant, as "context" becomes a repeated variable. The term "recursion" can be used.

Thus we are left with defining "concept" as a variation of "context" with there being variations of one context through many contexts. This necessitates a form of circularity, or self-referentiality, as a proof system in and of itself.

That which is able to maintain itself, self-reference, in spite of a perceived absence of order or exists as "proof" or "truth"...strictly because it is able to continually exist. However this is assumed much like its foundational form, "the circle" is assumed.

Assumption takes on an inherent form then, and is inseperable from truth.

PeteOlcott
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Re: Simplest possible notion of a formal system

Post by PeteOlcott » Sat Aug 10, 2019 5:53 pm

RCSaunders wrote:
Sat Aug 10, 2019 2:18 am
PeteOlcott wrote:
Fri Aug 09, 2019 8:46 pm
First of all the body of conceptual knowledge contains everything that anyone could ever say about anything in any language what-so-ever.
"Everything that anyone could ever say about anything in any language what-so-ever," is not knowledge. Some of it might be knowledge, but most of it would be just wrong or nonsense.

This sounds like a very basic epistemological mistake about the nature of knowledge.
I was dealing with an apparently woefully dishonest person (maybe he was just confused?) that was acting as if the entire body of all conceptual knowledge was limited to a certain kind of arithmetic so I had to use exaggeration to make my point.

If we make the analytic versus synthetic distinction this way:
Every expression of language that can be verified as completely
true entirely on the basis of the meaning of its words

Then we can understand that the definitions of these meanings simultaneously specify true and provable concurrently.

When we understand things this way we can see that true and provability cannot possibly
diverge and True(x) is always definable as the assigned meanings of words.

To generalize this so that it incorporates formal languages we calls words "finite strings"
and the meaning of words are stipulated relations between finite strings. Now we have a
notion of formal system such that True(x) is always provable and always definable.

PeteOlcott
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Re: Simplest possible notion of a formal system

Post by PeteOlcott » Sat Aug 10, 2019 7:13 pm

wtf wrote:
Sat Aug 10, 2019 5:26 am
PeteOlcott wrote:
Fri Aug 09, 2019 9:13 pm
It seems that you are intentionally playing head games and are not interested in any honest dialogue.
That's entirely up to you. I prefer a lighthearted and give-and-take kind of interaction, and a degree of self-awareness on each person's part.
My mother is suffering a grave injustice that can only be corrected if we get to the point of my refutation of Gödel and Tarski as quickly as possible without taking any unnecessary side tracks what-so-ever. I have no time for head games this causes real world suffering of my mother.

When my refutation of Tarski and Gödel is understood to be correct the bright spotlight of the media will shine on the perjurers and their perjury will no longer stand.

I redefine the entire notion of mathematics from first principles in terms of the much broader concept of conceptual truth.

When we compress all of the extraneous complexity of the notion of formal system into the much broader notion of conceptual truth we see that all conceptual truth about anything is formalized as stipulated relations between finite strings thus defining true and provable concurrently.

This proves that True(x) is always definable and True(x) cannot possibly ever diverge from Provable(x).

PeteOlcott
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Re: Simplest possible notion of a formal system

Post by PeteOlcott » Sat Aug 10, 2019 7:21 pm

Age wrote:
Sat Aug 10, 2019 6:01 am

Why is the above copyrighted?
The original post is my unique work and I use
the copyright notice to make everyone aware of this.

PeteOlcott
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Re: Simplest possible notion of a formal system

Post by PeteOlcott » Sat Aug 10, 2019 7:24 pm

Skepdick wrote:
Sat Aug 10, 2019 10:08 am
Eodnhoj7 wrote:
Sat Aug 10, 2019 2:23 am
Yes, here is my rebutal:



I am assuming I will have to explain it further.

But besides that I agree with everything else you said.
That's Mathematical knowledge.

https://en.wikipedia.org/wiki/Monad_(category_theory)
https://en.wikipedia.org/wiki/Monad_(fu ... ogramming)
If we make the analytic versus synthetic distinction this way:
Every expression of language that can be verified as completely
true entirely on the basis of the meaning of its words
Then we can understand that the definitions of these meanings
simultaneously specify true and provable concurrently.

When we understand things this way we can see that true and provability cannot possibly
diverge and True(x) is always definable as the assigned meanings of words.

To generalize this so that it incorporates formal languages we calls words "finite strings"
and the meaning of words are stipulated relations between finite strings. Now we have a
notion of formal system such that True(x) is always provable and always definable.

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

Re: Simplest possible notion of a formal system

Post by PeteOlcott » Sat Aug 10, 2019 7:27 pm

RCSaunders wrote:
Sat Aug 10, 2019 3:17 pm
Eodnhoj7 wrote:
Sat Aug 10, 2019 2:30 am
Actually language is a concept, cookie cutting defintions is conceptual as well. What primarily separates a concept from other phenomenon is the degree to which it manifests itself in empirical reality.
I believe you are using the word, "concept," with its common definition, such as:

1. A general idea or understanding of something: the concept of inertia; the concept of free will.
2. A plan or original idea: The original concept was for a building with 12 floors.
3. A unifying idea or theme, especially for a product or service: a new restaurant concept.

Or you may be referring to an, "idea," as a concept, which in epistemology is broader than the term concept and includes propositions and complex descriptions as well as concepts.

The meaning of the word, "concept," in epistemology is very much narrower and refers to the simplest elements of cogency out of which all knowledge is constructed. While I do not agree with the conclusions of either of the following sources (which is the reason for my article) it is only, "concepts," as discussed in IEP or the Stanford Encyclopedia of Philosophy, or any other text on epistemology, that my article refers to.

In epistemology, the word, "language," is a symbol for a concept only if refers to the identification of any of the human developed methods of verbally storing knowledge and communication. A language, itself, is not a concept, it is an epistemological existent, like mathematics, science, and history.

Does that seem reasonable to you?
I redefine all this stuff from first principles.
Formal and natural languages are simply stipulated relations between finite strings.
Concepts are the relations of these stipulated relations.

Skepdick
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Re: Simplest possible notion of a formal system

Post by Skepdick » Sat Aug 10, 2019 7:53 pm

Eodnhoj7 wrote:
Sat Aug 10, 2019 4:35 pm
Yes, it is...but is it limited to mathematics alone?
Mathematics is never limited to mathematics when it's applied to real-world problems.

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RCSaunders
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Re: Simplest possible notion of a formal system

Post by RCSaunders » Sat Aug 10, 2019 7:57 pm

PeteOlcott wrote:
Sat Aug 10, 2019 5:53 pm
I was dealing with an apparently woefully dishonest person (maybe he was just confused?) that was acting as if the entire body of all conceptual knowledge was limited to a certain kind of arithmetic so I had to use exaggeration to make my point.
I understand. I didn't really think you could have meant how that turned out.
PeteOlcott wrote:
Sat Aug 10, 2019 5:53 pm
If we make the analytic versus synthetic distinction this way:
Every expression of language that can be verified as completely
true entirely on the basis of the meaning of its words

Then we can understand that the definitions of these meanings simultaneously specify true and provable concurrently.
But I do not believe it is possible to verify anything is true solely on the basis of the definition of words. It is possible to form propositions with no wrongly defined words and no contradictions that are neither true or false (all future, hypothetical, and contingent propositions, "it will rain tomorrow") and statements of opinion, "SanMiguel is better than Budweiser," for example. The only real way of determining if any proposition is true is to determine if whatever it asserts is actually the case. "There are four pairs of shoes in the closet," may or may not be true, but no examination of the words can determine if it is true or not. Only looking in the closet will determine it.
PeteOlcott wrote:
Sat Aug 10, 2019 5:53 pm
When we understand things this way we can see that true and provability cannot possibly
diverge and True(x) is always definable as the assigned meanings of words.

To generalize this so that it incorporates formal languages we calls words "finite strings"
and the meaning of words are stipulated relations between finite strings. Now we have a
notion of formal system such that True(x) is always provable and always definable.
Well, I don't think so, as I already explained, but I'm not trying to convince you. I think any statement that is not about an actual existent or existents, material or epistemological, is actually about nothing, or simply fiction, in which case there is no question of, "truth." In all other cases, the truth of any statement can only be established by examining the actual existent or existents to determine if what is said about them is actually the case.

PeteOlcott
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Re: Simplest possible notion of a formal system

Post by PeteOlcott » Sat Aug 10, 2019 8:04 pm

RCSaunders wrote:
Sat Aug 10, 2019 7:57 pm
But I do not believe it is possible to verify anything is true solely on the basis of the definition of words.
Then your understanding of the analytic versus synthetic distinction is necessarily insufficient.
"cats are animals" is an instance of a the proof of a finite string being verified entirely on the basis of the meaning of its words.

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