Deeper than primes

[doronshadmi]

http://www.internationalskeptics.com/forums/showpost.php?p=4655701&postcount=2531

The Axiom of the Empty Set does not create anything.

http://www.internationalskeptics.com/forums/showpost.php?p=4659490&postcount=2595

There is also a temporal component to his mis-comprehension, so things like the Empty Set in axiomatic set theory can exist before there's an axiom to establish their existence.

All of this is nonsense,

It is indeed nonsense since you claim X AND its negation about the dependency of existence of the empty set on the ZF axiom of the empty set.

Doron is spellbound by anthropomorphism.

Here is a part from http://www.geocities.com/complementarytheory/OMPT.pdf which clarify what I am:

The Ideal and the Real

OM's development is possible because we determine the limits of the researchable by using the weak limit (Emptiness) and the strong limit (Fullness). Cantor distinguished three levels of existences:

1) In the mind of God (the Intellectus Divinum)

2) In the mind of man (in abstracto)

3) In the physical universe (in concreto)

By using Fullness as "that has no successor" we show that Cantor's in abstracto Transfinite system is not an actual infinity. We also show how Distinction is a first-order property of any collection. These developments are based on a cognitive approach of the mathematical science. In "On the Reality of the Continuum" [10] (page 124) we find this sentence:

"From the realist standpoint, numbers and other real things do not need admitting or legitimating by humans to come into existence."

From the idealist standpoint, numbers and other real things do need admitting or legitimating by humans to come into existence. In both cases the term "real thing" has to be understood. According to the realist if "real things" are "real" iff they are totally independent of each other, then no collection is a "real thing" (total independency does not able things to be gathered).

According to the idealist if "real things" are "real" iff they are totally dependent of each other, then no collection is a "real thing" (total dependency does not able things to be identified). No collection exists in terms of total dependency (total connectivity) or total independency (total isolation). Since totalities are not researchable on their own, then any research cannot avoid the existence of collections, where collections are the only researchable "real things". Actually we find that a researchable realm is both ideal (has relations) and real (has elements).

We have to notice that there is no symmetry in using concepts like "Realist standpoint" in order to understand "real things" because if the requested result is "real things" then we actually give a privilege to the Realist standpoint over the Idealist standpoint about the requested "real thing". This asymmetry can be avoided by changing the requested results to "researchable things" instead of "real things". In that case the concept of Collection is researchable exactly because it is not totally real and not totally ideal.

Here is the last part of the quote from [10]:

"Furthermore, real objects are always legitimate objects of study in the sciences, even if they are not fully understood or known."

We agree with this quote because "real objects" are valuable for science iff they are researchable, or in other words, they are both real and ideal.

[10] Anne Newstead & James Franklin, On the Reality of the Continuum Philosophy 83
(2008), 117-27 http://web.maths.unsw.edu.au/~jim/newsteadcontinuum.pdf .

 

[The Man]

It is pre-axiomatic. Again we are talking about the philosophy of the foundations of the mathematical science.

To translate from Doron speak:

“Axioms? I ain't got no axioms. I don't need no axioms! I don't have to show you any stinkin' Axioms!”

 

[doronshadmi]

To translate from Doron speak:

“Axioms? I ain't got no axioms. I don't need no axioms! I don't have to show you any stinkin' Axioms!”

Before axioms you have to understand with what you deal with.

It is clearly shown that your ability to undertand abstarct things was not developed by the school of thouhgt that does not teach you how to think without axioms.

I do not agree with the "all you need is axiom" song.

First Notion, only then Axiom.

 

[The Man]

This relates to a point I was intending to (re-)make. Doron is spellbound by anthropomorphism. Sets can't simply have cardinality as a property; instead, it must be measured (by whom or what isn't yet clear) and for there to be a measurement, there must be a measurement tool. There is also a temporal component to his mis-comprehension, so things like the Empty Set in axiomatic set theory can exist before there's an axiom to establish their existence.

All of this is nonsense, and the only purpose it serves is to further muddle Doron's thinking.

Doron, sets are not measurement tools, cardinality does not require measurement, and despite all your hand-waving and word salad, your so-called magnitude of existence is nothing more than cardinality plus one. That means it is contrived and trivial, and no where near ontological.

You are lying to yourself if you think otherwise.

By the way, how's that explanation of what you mean by "distinction is a first-order property" coming along?

Well it is even more bizarre then that since he insists on measuring something that he and his given reference claims is impossible, his ‘empty fusion’. In order to do this the ‘cardinality’ of the empty set now becomes not a property of that set but of that impossible ‘empty fusion’ and by some even more bizarre reasoning (or lack there of) it becomes that his ‘empty fusion’ simply does not exist on its own. Yet his own ‘measure’ of existence with his own ‘measuring tool’ is 0 and by his own assertions indicates that his ‘empty fusion’ does in fact not exist. So he is measuring what he claims ‘does not exist on its own’ by using a property of a set that can not have it or any members (including impossible ones) to asset that it does not exist after all.

 

[The Man]

Before axioms you have to understand with what you deal with.

Are you planning to get to that understanding anytime soon? Just a hint, you seem to be running around in circles and not going anywhere.

It is clearly shown that your ability to undertand abstarct things was not developed by the school of thouhgt that does not teach you how to think without axioms.

Ain’t that like a triple negative?

I do not agree with the "all you need is axiom" song.

First Notion, only then Axiom.

Well I have always preferred the one that goes

“When words can explain, this notion in your brain

That’s axiomatic.”

 

[jsfisher]

The fact is this: we have an existing {} that its cardinal is 0.

(Highlighting added.)
You know, you'd be less damaging to your own credibility if you actually used the correct word.

Cardinal, the noun, is either a high-ranking official of the Roman Catholic Church or a particular red finch indigenous to North America. Neither usage fits in your sentence.

Note the sentence reworked to include the correct word:

The fact is, (in ZF and most other formulations of set theory) we have an empty set, established by axiom, that has a cardinality of 0.​

Note also the correct credit for the null set's existence.

You inability to communicate coherently is of your own making, Doron. You rightfully can blame no one except yourself. Take the time to learn even just what a few words mean. It would help tremendously.

 

[jsfisher]

Well it is even more bizarre then that since he insists on measuring something that he and his given reference claims is impossible, his ‘empty fusion’. In order to do this the ‘cardinality’ of the empty set now becomes not a property of that set but of that impossible ‘empty fusion’ and by some even more bizarre reasoning (or lack there of) it becomes that his ‘empty fusion’ simply does not exist on its own. Yet his own ‘measure’ of existence with his own ‘measuring tool’ is 0 and by his own assertions indicates that his ‘empty fusion’ does in fact not exist. So he is measuring what he claims ‘does not exist on its own’ by using a property of a set that can not have it or any members (including impossible ones) to asset that it does not exist after all.

This may well be just an extension of an earlier Doron contradiction, that for some A and some S, A can both be a member of S and not be a member of S.

Doron has also told us that if B is a member of T and B is a member of U, then the two B's involved are different from each other.

Doron has told us so very many stupid things.

 

[jsfisher]

http://www.internationalskeptics.com/forums/showpost.php?p=4655701&postcount=2531

The Axiom of the Empty Set does not create anything.

http://www.internationalskeptics.com/forums/showpost.php?p=4659490&postcount=2595

There is also a temporal component to his mis-comprehension, so things like the Empty Set in axiomatic set theory can exist before there's an axiom to establish their existence.

All of this is nonsense,

It is indeed nonsense since you claim X AND its negation about the dependency of existence of the empty set on the ZF axiom of the empty set.

More reading comprehension difficulties, there, Doron?

Axioms don't create things, and I said so in the first quotation you cite. The Axiom of the Empty Set makes a declaration, that the empty set is a set in ZF. Nothing more, nothing less. No act of creation took place. Also, axioms don't have a temporal perspective. That was the point of the second quotation you cited.

Perhaps you are confused by the phrase "establish there existence"? That doesn't mean "create". As already noted, axioms do not create. The Axiom of the Empty Set establishes that the empty set exists within ZF. Nothing more, nothing less. The axiom does this with a simple declaration.

Do you need to see the axiom again? Here it is:

[latex]$$$ \exists x \forall y \neg ( y \in x ) $$$[/latex]​

See? No creating at all. Just a simple declaration establishing that a particular set is included in ZF.

Doron is spellbound by anthropomorphism.

Here is a part from http://www.geocities.com/complementarytheory/OMPT.pdf which clarify what I am:

...<irrelevance snipped>...

Since your response is unrelated to the post of mine you quote, I must conclude you don't know what anthropomorphism means, do you.

 

[doronshadmi]

(Highlighting added.)
You know, you'd be less damaging to your own credibility if you actually used the correct word.

Cardinal, the noun, is either a high-ranking official of the Roman Catholic Church or a particular red finch indigenous to North America. Neither usage fits in your sentence.

Note the sentence reworked to include the correct word:

The fact is, (in ZF and most other formulations of set theory) we have an empty set, established by axiom, that has a cardinality of 0.​

Note also the correct credit for the null set's existence.

You inability to communicate coherently is of your own making, Doron. You rightfully can blame no one except yourself. Take the time to learn even just what a few words mean. It would help tremendously.

ok, let us correct it.

we have an existing {} that its cardinality (that is determined by the magnitude of existence of its members) is 0.

 

[doronshadmi]

This may well be just an extension of an earlier Doron contradiction, that for some A and some S, A can both be a member of S and not be a member of S.

Doron has also told us that if B is a member of T and B is a member of U, then the two B's involved are different from each other.

Doron has told us so very many stupid things.

Possible = exists.

Impossible = does not exist.

{} cardinality is determined by the magnitude of existence of the impossible.

It is impossible to do it without the existing {}.

 

[doronshadmi]

More reading comprehension difficulties, there, Doron?

Axioms don't create things, and I said so in the first quotation you cite. The Axiom of the Empty Set makes a declaration, that the empty set is a set in ZF. Nothing more, nothing less. No act of creation took place. Also, axioms don't have a temporal perspective. That was the point of the second quotation you cited.

Perhaps you are confused by the phrase "establish there existence"? That doesn't mean "create". As already noted, axioms do not create. The Axiom of the Empty Set establishes that the empty set exists within ZF. Nothing more, nothing less. The axiom does this with a simple declaration.

Do you need to see the axiom again? Here it is:

[latex]$$$ \exists x \forall y \neg ( y \in x ) $$$[/latex]​

See? No creating at all. Just a simple declaration establishing that a particular set is included in ZF.



Since your response is unrelated to the post of mine you quote, I must conclude you don't know what anthropomorphism means, do you.

This is a good example of how the "no more, no less" approach misses the ontological notion of what's going on.

What's going on form the ontological point of view is that the cardinality of an existing thing is determined by the non-exists, called empty fusion=no members=emptiness=nothing.

As a result one misses the understanding of the full set (the opposite of the empty set) and does not understand the actual non-finite.

From an ontological view point "nothing more" then the existence of a collection is called emptiness.

From an ontological view point "nothing less" then the existence of a collection is called fullness.

Now we can understand how the "nothing more, no less" ontological view point gets things only in terms of collection.

Furthermore, jsfisher did the "impossible", he used the concept "nothing" in order to explain something.

Thank you jsfisher , "nothing more, nothing less".

 

[doronshadmi]

This may well be just an extension of an earlier Doron contradiction, that for some A and some S, A can both be a member of S and not be a member of S.

Doron has also told us that if B is a member of T and B is a member of U, then the two B's involved are different from each other.

Doron has told us so very many stupid things.

jsfisher does not understand the full set.

As a result he continue to get things only in terms of level 2 of existence (the level of collections) ( see why at http://www.internationalskeptics.com/forums/showpost.php?p=4660997&postcount=2611 ) .

He indeed staying stupid.

 

[doronshadmi]

This is just a lame excuse. Deep in your heart you know that when it comes to formulae, the vacuousness of all your words will be exposed as clear as can be.

Deep in my heart know that "There exists X such that ..." mechanical style of axioms says nothing about the terms that enable X to exist, in the first place.

In other words, the axiomatic approach is not a good ontological tool.

In my papers I am focused on ontological notions, which are pre-axiomatic by nature.

Only by this way something like the full-set can be discovered\invented.

We do not have to go far in order to show the inability of the ZF axiom of the empty set to provide the ontological basis for the existence of the empty set.

The ZF axiom of the empty set only establishes the properties of it but say nothing about its ontological basis.

In order to do that a pre-axiomatic research has to be done, and this is exactly the nature of my work.

Take for example the "nothing more, nothing less" approach of jsfisher.

He simply accepts the axioms declaration "There exists X such that ..." as it is without using any ontological research.

In other words, jsfisher is a user of axiomatic systems.

On the contrary I am a researcher of the ontological basis of the axiomatic system.

We are not working on the same level.

 

[jsfisher]

ok, let us correct it.

we have an existing {} that its cardinality (that is determined by the magnitude of existence of its members) is 0.

Poor job of correction. Not even worth half credit.

 

[zooterkin]

In other words, jsfisher is a user of axiomatic systems.

On the contrary I am a researcher of the ontological basis of the axiomatic system.

We are not working on the same level.

You do realise that in this context, "axiomatic" means pretty much the same as "ontological", don't you?

Axiom: Logic, maths, a self-consistent, self-evident statement that is a universally accepted truth.

Ontology: Logic, the set of entities presupposed by a theory

 

[jsfisher]

Possible = exists.

No.

Impossible = does not exist.

Yes.

{} cardinality is determined by the magnitude of existence of the impossible.

No.

It is impossible to do it without the existing {}.

You have indefinite antecedent and an ambiguous but likely redundant gerund. You have also "verbified" yet another noun. There's more wrong than right, here, so no.

Hmmm, one out of four. Poorly done. Luckily we aren't using organic fours - there are more of them it has been said. Your score would have been even worse.

 

[doronshadmi]

Since your response is unrelated to the post of mine you quote, I must conclude you don't know what anthropomorphism means, do you.

Wrong conclusion.

You claim that I am X.

In http://www.internationalskeptics.com/forums/showpost.php?p=4659662&postcount=2601 I show that I show what I am.

 

[jsfisher]

jsfisher does not understand the full set.

Not true. I understand what you mean by it just fine. It is another of your fantastical inventions, founded in contradiction and nonsense.

 

[jsfisher]

Wrong conclusion.

You claim that I am X.

I suppose if I state, "Two is a prime number", you'll counter with, "No, you are wrong because two is an even number".

I claimed you have a certain property, a property you continue to demonstrate you have. That, however, in no way excludes you from having other properties.

In http://www.internationalskeptics.com/forums/showpost.php?p=4659662&postcount=2601 I show that I show what I am.

You show nothing. You merely assert. And your assertions are not founded in very much evidence.

 

[doronshadmi]

No.



Yes.



No.



You have indefinite antecedent and an ambiguous but likely redundant gerund. You have also "verbified" yet another noun. There's more wrong than right, here, so no.

Hmmm, one out of four. Poorly done. Luckily we aren't using organic fours - there are more of them it has been said. Your score would have been even worse.

You did not get it.

Possible = exists as a possibility ( for example possibility X, or {X} )

Impossible = does not exist ( for example, the member of {} )