Deeper than primes - Continuation

[jsfisher]

Platonic existence, as I define it, is....

Yes. As you define it.... Others are interested in your definition, so I'll let them continue with this thought.

...
Traditional Mathematics does not deal with tautological existence, and as a result ∃x (where in the case of ZFC, x is the notion of set) is not a valid expression of its domain of discourse.

I'm almost speechless. I think we have a break-through here.

 

[realpaladin]

So by this finer resolution about existence, set x tautological existence (notated by the outer "{" and "}") is inaccessible to any form of existence that is not tautological existence (where this form of existence, that is also defined as no existence at all) is between the outer "{" and "}".

Ok. Cool. Groovy. Now what?

EDIT: Are we on track with the direct perception again? Because honestly, I could not give a hootenanny about what you call it, I am, after more than 7 years, still waiting for the inkling of the beginning of the start of a result.

 

[doronshadmi]

Yes. As you define it....

The basic notion about tautological existence is its independence of any domain of discourse (it is logically unconditional existence, whether it is discovered or not, or whether it is addressed according to the invented rules of a given domain of discourse, or not).

Yet this discovered tautological existence is the basis of the invented rules of any domain of discourse that are used to define identities, properties, relations etc., which can't deduced without the independent platonic existence (which is independent of the moment of discovery, unlike the existence of the invented rules of a given domain of discourse, which depends on the moment of invention).

Two examples of such domains of discourse, are the rules of ZFC or the rules of WFF, where in both cases the invention of these rules are deduced from the discovered tautological existence, but not vice versa.

In case of ZFC, the signature of the discovered tautological existence is called set.

In case of WFF, the signature of the discovered tautological existence is called term.

It has to be stressed that that if invented rules of any given domain of discourse are related to the discovered tautological existence, the result is always invented things that do not have tautological existence.

Some example:

The square root of 9 is an invented thing that does not have tautological existence, yet it is based on the discovered tautological existence called number.

Generally, by using an extended notion of Reflection principle ( http://en.wikipedia.org/wiki/Absolute_Infinite ), concepts like, set, term, number etc. are some signatures of the discovered tautological existence within given domains of discourse, which is not limited by any domain of discourse.

 

[doronshadmi]

So logically, Existence is total existence (tautological existence, which is not limited by any domain of discourse) total non-existence (contradictory existence, which is limited by any domain of discourse in order to save its consistency) and any existence that is not total existence AND not total non-existence.

Traditional Mathematics excludes total existence (tautological existence, which is not limited by any domain of discourse) and as a result we get context-dependent-only domains of discourse, where only invented existence or total non-existence are openly used, and total existence's signature (for example: set within ZFC domain of discourse, term within WFF domain of discourse, etc.) is used as hidden assumption within each domain of discourse, which is no more than context-dependent framework.

My suggested mathematical framework does not exclude total existence (tautological existence, which is not limited by any domain of discourse) and as a result we get cross-contexts framework, where context-dependent frameworks are its organs that are related to it by openly use total existence's signatures (like set, term, number etc.) within each domain of discourse.

 

[realpaladin]

So logically, Existence is total existence (tautological existence, which is not limited by any domain of discourse) total non-existence (contradictory existence, which is limited by any domain of discourse in order to save its consistency) and any existence that is not total existence AND not total non-existence.

Traditional Mathematics excludes total existence (tautological existence, which is not limited by any domain of discourse) and as a result we get context-dependent-only domains of discourse, where only invented existence or total non-existence are openly used, and total existence's signature (for example: set within ZFC domain of discourse, term within WFF domain of discourse, etc.) is used as hidden assumption within each domain of discourse, which is no more than context-dependent framework.

My suggested mathematical framework does not exclude total existence (tautological existence, which is not limited by any domain of discourse) and as a result we get cross-contexts framework, where context-dependent frameworks are its organs that are related to it by openly use total existence's signatures (like set, term, number etc.) within each domain of discourse.

Ok. Excellent. How to proceed?

 

[doronshadmi]

We simply have to ask what happens to Mathematics if total existence (tautological existence, which is not limited by any domain of discourse) is its essential foundation.

One of the given answers is that no collection is tautological existence.

 

[Innocuous]

Yes. As you define it.... Others are interested in your definition, so I'll let them continue with this thought.

I tried, but I can't make any sense of his definitions (perhaps there is a language barrier). Is "platonic existence" just something he made up, or does it really mean something in the field of logic or philosophy?

 

[realpaladin]

We simply have to ask what happens to Mathematics if total existence (tautological existence, which is not limited by any domain of discourse) is its essential foundation.

One of the given answers is that no collection is tautological existence.

So, I will ask.

- What happens to mathematics if total existence is it's essential foundation?

- What is the significance of 'no collection is tautological existence'?

 

[realpaladin]

I tried, but I can't make any sense of his definitions (perhaps there is a language barrier). Is "platonic existence" just something he made up, or does it really mean something in the field of logic or philosophy?

There is, it seems, a barrier of perception; either you get it, or you don't.

That is why I am asking questions that Doron, and apparently only Doron, using his invention, can solve.

If it is not possible for me to understand, then I want to see it at work.

He should tread carefully though, if he digresses again so as to halt progress to this thread (which he succesfully has done for over 7 years) I will move to ask this thread be moved into Abandon All Hope.

 

[jsfisher]

I tried, but I can't make any sense of his definitions (perhaps there is a language barrier). Is "platonic existence" just something he made up, or does it really mean something in the field of logic or philosophy?

A language barrier problem doesn't adequately explain things. There seems to be some problem with multi-step reasoning. As for "platonic existence", that is something he made up, probably by splicing two discordant concepts.

 

[doronshadmi]

Is "platonic existence" just something he made up, or does it really mean something in the field of logic or philosophy?

Philosophically one can't make up (where make up means invent) platonic existence, exactly because platonic existence is essentially independent of any inventor, the moment of invention or any particular domain of discourse.

Moreover, platonic existence is discovered, where discovery means that a given existence is logically a tautology (its existence is always true, independently of any discoverer, the moment of discovery or any particular domain of discourse).

So, also logically one can't make up (where make up means invent) platonic existence.

Any attempt to define properties, identities, relations etc. for platonic existence, are done by inventions (by making up things, which are philosophically and/or logically not platonic existence (not tautological existence)).

But given domains of discourse like ZFC or WFF, set is the signature of platonic existence within ZFC (set always exists within ZFC), exactly as term is the signature of platonic existence within WFF (term always exists within WFF).

I use ∃x ("There exists" x, where x is the platonic reality, and at this first stage (notated by ∃x) all is known is that it exists).

 

[realpaladin]

Philosophically one can't make up (where make up means invent) platonic existence, exactly because platonic existence is essentially independent of any inventor, the moment of invention or any particular domain of discourse.

Moreover, platonic existence is discovered, where discovery means that a given existence is logically a tautology (its existence is always true, independently of any discoverer, the moment of discovery or any particular domain of discourse).

So, also logically one can't make up (where make up means invent) platonic existence.

Any attempt to define properties, identities, relations etc. for platonic existence, are done by inventions (by making up things, which are philosophically and/or logically not platonic existence (not tautological existence)).

But given domains of discourse like ZFC or WFF, set is the signature of platonic existence within ZFC (set always exists within ZFC), exactly as term is the signature of platonic existence within WFF (term always exists within WFF).

I use ∃x ("There exists" x, where x is the platonic reality, and at this first stage (notated by ∃x) all is known is that it exists).

Don't dwell on this too long Doron, provide a link as you normally do.

You have now stated what you use. Now use it.

 

[doronshadmi]

By following the notion that no collection is tautological existence, one easily deduces that no relative measure within ZFC is accessible to set existence (which is the signature of tautological existence within ZFC) and as a result only set is actual infinity within ZFC.

This simple notion is notated by the outer "{" and "}", which is logically inaccessible to anything between them, simply because all of what is between "{" and "}" (which is always some form of collection (or its absence)) does not have tautological existence.

So, the notion is also intuitively well addressed by the used notation, which helps to understand the notion of tautological existence within ZFC.

 

[jsfisher]

By following the notion that no collection is tautological existence, one easily deduces that no relative measure within ZFC is accessible to set existence (which is the signature of tautological existence within ZFC) and as a result only set is actual infinity within ZFC.

"Accessible to set" is gibberish. And since you seem to have borrowed the word, signature, from first order logic, your usage of it is gibberish as well.

This simple notion is notated by the outer "{" and "}", which is logically inaccessible to anything between them, simply because all of what is between "{" and "}" (which is always some form of collection (or its absence)) does not have tautological existence.

There is no such notion within ZFC.

So, the notion is also intuitively well addressed by the used notion, which helps to understand the notion of tautological existence within ZFC.

I see you have abandoned all the progress you had made. No, this does not exist within ZFC.

 

[doronshadmi]

"Accessible to set" is gibberish.

Maybe, but not "accessible to set existence", where set is the signature of tautological existence within ZFC (set always exists within ZFC domain of discourse).

And since you seem to have borrowed the word, signature, from first order logic, your usage of it is gibberish as well.

And since you think I have borrowed the word, signature, from first order logic, you think that my usage of it is gibberish.

Signature, as I use it, is an extension of the Reflection principle which says that tautological existence is also held within given domains of discourse like ZFC (set always exists within ZFC domain of discourse).

There is no such notion within ZFC.

There is no such notion within ZFC according to the agreed reasoning.

Since this is philosophical forum, I do not have to follow after the agreed reasoning, which excludes platonic existence from ZFC domain of discourse.

Since I include the signature of platonic existence within ZFC domain of discourse, I use it as follows:

If the domain of discourse is ZFC, then set is the platonic existence of ZFC that does not need any identity or relation in order to exist.

By following the notion of set's tautological existence, ∃x is the expression of it, and it can be found, for example, within ZFC Axiom Of Infinity, as follows:

"There exists a set x (or ∃x)" (this is the platonic existence, that does not need any identity or relation in order to exist (it is a tautological existence)) "such that" (this is the non-platonic existence, that needs identity and/or relation in order to exist (it is not a tautological existence))"the empty set is a member of x and, whenever a set y is a member of x, then S is also a member of x."

So by this finer resolution about existence, set x tautological existence (notated by the outer "{" and "}") is inaccessible to any form of existence that is not tautological existence (where this form of existence, that is also defined as no existence at all) is between the outer "{" and "}".

Traditional Mathematics does not deal with tautological existence, and as a result ∃x (where in the case of ZFC, x is the notion of set) is not a valid expression of its domain of discourse.

I see you have abandoned all the progress you had made. No, this does not exist within ZFC.

I see that you are still stuck at the atomic formula stage.

 

[jsfisher]

There is no such notion within ZFC according to the agreed reasoning.

There is no such notion within ZFC according to its axiomatic foundation. Philosophic babble has nothing to do with it.

...
I see that you are still stuck at the atomic formula stage.

No, just the meaning of things. Something you so thoroughly ignore. Your arguments carry as much weight as this:

According to the traditional Websterization, 'chow' can be viewed as referring to food. This traditional view excludes the broader perspective and thereby fails to recognize the equally valid meaning of a breed of dog. Chow therefore means 'dog food'. This meaning is inaccessible under the agreed upon reasoning. Moreover, since 'ciao' in Italian is homophonic to 'chow', under the signature of platonic existence in Italy, chow is a key to our moral survival telling us, as humans, to say good-bye to dog food and eat more nutritious, healthy foods.

 

[doronshadmi]

There is no such notion within ZFC according to its axiomatic foundation.

There is no such notion within ZFC according to the agreed reasoning of its axiomatic foundation.

No, just the meaning of things. Something you so thoroughly ignore.

No, just the meaning of things according to the agreed reasoning. Something you so thoroughly ignore.


By the agreed reasoning tautological existence's signature is not included in any domain of discourse, and this simple fact can't be covered by any Sir Gibberish of Speech maneuvers (which is no more than some attempt to avoid the simple fact).

 

[realpaladin]

There is no such notion within ZFC according to the agreed reasoning of its axiomatic foundation.



No, just the meaning of things according to the agreed reasoning. Something you so thoroughly ignore.


By the agreed reasoning tautological existence's signature is not included in any domain of discourse, and this simple fact can't be covered by any Sir Gibberish of Speech maneuvers (which is no more than some attempt to avoid the simple fact).

It seems Doron graps every straw to kibitz so as to avoid making progress...

I can say this thread now officially has deteriorated to junk status.

 

[doronshadmi]

The progress into Unity awareness (which is beyond objective (platonic existence)\subjective (non-platonic existence) dichotomy) is addressed in https://drive.google.com/file/d/0B3hcPBRBCzClQ3ZFMjVrQzBkc0E/edit?usp=sharing.

 

[doronshadmi]

The right link in the previous post has to be https://drive.google.com/file/d/0B3hcPBRBCzClakdJZjNNOW5RSTQ/edit?usp=sharing