The Man
Unbanned zombie poster
Indeed I was actively perusing research some years ago along those lines, but I kept running out of quarters.
Last edited:
Deeper than primes
- Thread starter doronshadmi
- Start date
-
- Tags
- deeper than primes
- Status
Indeed I was actively perusing research some years ago along those lines, but I kept running out of quarters.
The Man
Unbanned zombie poster
So your OM is simply based on a complete misunderstanding and misrepresentation of the axiom of the empty set by requiring a set to be, well, not empty.
doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
By OM, Cardinal is a measurment unit of the exictence of a thing where Set is an existing measurment tool that its magnitude of existence is > 0 and < ∞.
Michael Potter in his excellent book Set Theory and its Philosophy ( http://books.google.com/books?id=Fx...er&source=gbs_similarbooks_r&cad=4_2#PPA21,M1 )clearly explains in chapter 2 the difference between collection and fusion.
If Cardinality is used to measure the existence of what he calls aggregation, then:
1) If aggregation means fusion and the cardinal of an aggregation = 0, then no aggregation exists.
2) If aggregation means collection and the cardinal of an aggregation = 0, then there exists an aggregation with no members.
Let us think about the opposite cardinal 0, called cardinal ∞ .
Again, if Cardinality is used to measure the existence of what he calls aggregation, then:
3) If aggregation means fusion and the cardinal of an aggregation = ∞, then no aggregation exists because the existence of a fusion that has cardinal ∞ is stronger than the existence of aggregation, exactly as the existence of a fusion that has cardinal 0 is weaker than the existence of aggregation.
4) If aggregation means collection and the cardinal of an aggregation = ∞, then no members belong to the collection that has cardinal ∞ . Fullness is stronger than the existence of members, exactly as Emptiness is weaker than the existence of members.
Fusion is not researchable in the case of cardinal 0 or cardinal ∞, because Emptiness' existence is too weak and Fullness' existence is too strong.
On the contrary collection is researchable in the case of cardinal 0 or cardinal ∞, because the collection's existence has a cardinal
that is > 0 and < ∞.
In that case no collection of non-finite members is complete (its cardinal < ∞), and as a result its exact cardinality is non well-founded. In that case the universal quantifier "for all" does not hold in the case of non-finite collections.
A finite collection has an accurate cardinal because its magnitude of existence is well-founded. In order to understand it we have to use Distinction as a first-order property.
This is exactly what I did in "Organic Mathematics (A Non-Formal Introduction)" http://www.geocities.com/complementarytheory/OMPT.pdf .
Last edited:
doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
Set B is not the empty set A. You have missed it as usual.
In the quote that you used in http://www.internationalskeptics.com/forums/showpost.php?p=4651442&postcount=2482 I show that set A is an existing thing.
Last edited:
jsfisher
ETcorngods survivor
- Joined
- Dec 23, 2005
- Messages
- 24,532
So, you have no explanation for your circular reasoning.
jsfisher
ETcorngods survivor
- Joined
- Dec 23, 2005
- Messages
- 24,532
Excellent! We have the full monty! Circular reasoning plus contradiction. Thank you, Doron. You never fail to disappoint.
doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
So you don't get what you read because you refuse to get Cardinality in terms of OM.
Please do not forget that we are talking about philosophical novel notions and not about agreed mathematical terms.
doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
You are hopeless. Bye.
jsfisher
ETcorngods survivor
- Joined
- Dec 23, 2005
- Messages
- 24,532
Not at all. You don't get what you write because you refuse to understand basic Mathematics.
No, we aren't talking about any such thing. You are talking about nonsense, contradiction, and circular reasoning. You are correct about that "not about agreed mathematical terms" part, though. Then again, no one has ever accused you of talking about agreed upon mathematical terms.
The Man
Unbanned zombie poster
No Doron you simply showed that instead of trying to understand or employ that axiom you just made up your own ridiculous and contradictory interpretation.
Cardinality is one of many “agreed mathematical terms” that you don’t get to just redefine (if you could call anything you are doing definitive) at your whim. Ignorance, misinterpretation, misrepresentation, contradiction and insisting that people simply ‘refuse to get’ your great ideas are hardly “philosophical novel notions” (certainly not on this forum).
Leaving so soon, but you just got back from the last time you said that?
jsfisher
ETcorngods survivor
- Joined
- Dec 23, 2005
- Messages
- 24,532
How so? I'm not that one that attempts to establish nonsense through contradiction and circular logic.
Once again: You cannot assume the numbers are defined while trying to define set theory. Numbers are an outcome of set theory.
doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
doronshadmi said:
Pay attention that we do not measure here the cardinal of the members of set A, but we measure here the cardinal of the members of set B, and by doing that we define the measurement unit of the existence of set A, which is not less than cardinal 1. Rough thinkers like The Man cannot get it and I find their roughness very fruitful because I use their inability to get things as a fertilizer to re-check and re-explain my notions in clearer ways.
In this case The Man cannot get the difference between collection and fusion, which helps me here to sharpen my argument about the difference between them, and how they are used under OM framework.
OK, let's return to business.
If we generalize it to "There exists set", then the magnitude of the existence of a Set is at least 1. Following the same reasoning, the magnitude of the existence of Emptiness is 0, where the magnitude of the existence of its opposite, called Fullness, is ∞. In each one of these examples, Set is used to measure the magnitude of the existence of X.
So Set is an existing measurement tool that is used to measure the magnitude of the existence of X, such that |{X}| = the measurement unit of the existence of X, where X is a fusion in the case of Emptiness or Fullness, or X is a collection in the case of A as a member of B.
I am quit sure that The Man will not get also this post.
Last edited:
doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
Jsfisher is another rough thinker that cannot get the difference between fusion and collection (among a lot of other things all along this thread).
In this case he cannot get the difference between:
1) |{X}| = the measurement unit of X existence, where X is a fusion (in the case of Emptiness or Fullness) or X is a collection (in the case of a set).
2) {X} as an existing measurement tool of X, where {X} is a collection, and X is a fusion or a collection.
So |{X}| measures the existence of the members of {X} and does not measure the existence of {X}.
In other words, there is no circularity here because the cardinal measures the existence of the member of {X}, and it does not measure the existence of {X}.
Jsfisher forcing {X} = 1, which is circular.
I am talking about |{X}| = 1 (where X is a fusion -in the case of Emptiness or Fullness- or X is a collection -in the case of a set-), which is not circular, because |{X}| is not {X} .
I am quit sure that jsfisher is not going to get that post.
Last edited:
The Man
Unbanned zombie poster
Is that why your notions stink so badly, too much fertilizer? Funny, your re-explanations just look like you repeating the same old crap.
You claim the minimum value for your “measure of existence of a set” is 1 and your set B has that value because it contains set A. So that is a measure of B and not A, likewise your application of your “measure of existence” is not uniform. You apply it one way that you call “fusion in the case of Emptiness or Fullness” and another you call “collection in the case of A as a member of B”. Nowhere have you applied your “measure of existence of a set” to A as the set in the axiom of the empty set. Your contrived and variable application of your “measure of existence of a set” (particularly considering you apply it to some set B that contains A as opposed to just A itself as the set in the axiom of the empty set) demonstrates that it is nothing more then a way for you to lie to yourself about your misinterpretation and misrepresentation of the axiom of the empty set by requiring a set not to be empty.
As usual, Doron, there is noting to ‘get’ just you stringing together some words and phases that you think sound significant but do not mean what you would like them to mean.
jsfisher
ETcorngods survivor
- Joined
- Dec 23, 2005
- Messages
- 24,532
More words you don't understand, Doron?
Utter rubbish. What you fail to understand is that you cannot simply assume the existence of numbers when attempting to explore the foundations of Mathematics (even in a philosophic sense).
That which you attributed to me, on the other hand, is more proof you have extremely poor reading comprehension, since you made a straw man rather than understand what I'd written.
That is a lie.
You are also quite wrong.
doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
That is true as long a you do not get the difference between collection and fusion.
I you clearly do not get the difference between them.
The Utter rubbish is your mindmade.
Futhermore, you are the one that are using here a straw man .
Last edited:
doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
No, B is an existing measurement tool that measures the existence of its members, whether they are fusions (in the case of Emptiness or Fullness) or collections (in the case of A).
Nothing is circular here as long as you distinguish between the EXISTING measurement tool {X} and |{X}|, where |{X}| is the measurement's result of X (where X is a fusion in the case of Emptiness or Fullness, or X is a collection in the case of A).
Last edited:
jsfisher
ETcorngods survivor
- Joined
- Dec 23, 2005
- Messages
- 24,532
Your continual vocabulary drift to terms du joir changes nothing. What you do or do not get doesn't not alter what is true. The point you don't get had to do with numbers. Numbers are based on set theory, not the other way around. You cannot use them in developing your set notions without engaging in circular reasoning.
You notions universally have been, are now, and (I predict) will continue to be contradictory, ill-defined, and riddled with circular reasoning.
doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
In order to claim that you first have to understand what a Set is.
You don't understand what a Set is as long as you do not distingush between collection and fusion.
And jsfishir, you you do not distingush between collection and fusion.
As long as you don't get that, you continue to use here a straw man.
doronshadmi
Penultimate Amazing
- Joined
- Mar 15, 2008
- Messages
- 13,320
This is exactly what the ZF axiom of the empty set does.
It defines the empty set by the absence of collections where "absence of collections" is exactly the fusion known as Emptiness.
Furthermore, the axiom of the empty set does not determine the existence of the empty set because by the ZF axiom of the empty set:
"There exists set A such that any set (including A, or in other words, A exists independently of the axiom's description) is not a member of A"
Pay attention to the fact that if A exists because of the axiom of the empty set, then we are using a circular reasoning, where A existence depends on A existence (also please pay attention to the fact that if A is not one the things that are not members of A, then A is not empty).
In order to avoid this circularity, A must exist independently of the axiom, which only describes its properties and does not determine its existence.
So "There exists set A" is a fact of existence that does not depend on the description of the ZF axiom of the empty set, and A existence is used to measure "the absence of collections", which is exactly the fusion known as Emptiness.
By tha same reasoning, the existing collection B is used to measure the existence of collection A.
EDIT:
In other words collections are used to measure the existence of both collections or fusions.
On the contrary, fusions cannot be used to measure the existence of collections or fusions, because fusions' existence can be also too weak (in the case of Emptiness) or too strong (in the case of Fullness).
This is exactly the reason of why mathematicians using collection (and not fusion) as a measurment tool.
jsfisher said:
Since cardinality measures the existence of things, it is used here to also measure their absence (as clearly shown above by using the independent existence of the ZF axiom of the empty set from the description of the axiom).
In that case Cardinality as a measurement unit of existence, which can be measured only if there exists a measurement tool.
So as you see nothing is measurable unless there exists at least a measurement tool, and cardinal 1 is simply a measurement unit of such an existence, and not determines its existence.
Number 1 does not determine the existence of a collection exactly as the ZF axiom of the empty set does not determine the existence of the empty set.
Both number 1 or the ZF axiom of the empty set generally do not determine the existence of the things that they describe.
In other words, nothing is circular here.
Last edited:
- Status