A hidden assumption

doronshadmi said:
Dear jsfisher,

There is no use to explain color to a blind man.
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Ah! you have met Christophera, then?

It was nice talking to you. I have learned a lot.

Have a nice life.
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Please tell me you are not running away. You made some claims...I asked you to support your accusations...And now you run away??

Wow. So, you really do make wild, unsupportable accusations about other people. When confronted, you dodge and weave, then eventually just run away.

Do you know what we call people like that? People that make false accusations, then hide? We call them....Liars.

Yes, you are now no longer just a suspected liar. You have demonstrated a profound ability to lie intentionally. Well done!!

Doronshadmi, you are a liar.
 
jsfisher said:
Silence and simplicity are not synonyms.
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You are absolutely right. Silence is used here as some analogy, and any definition is nothing but some analogy.

No analogy is Simplicity itself, because any analogy is more complex than Simplicity itself.

In other words Simplicity itself is naturally undefined, but used as the best point of view of any definition.

If you are blind to Simplicity itself as naturally undefined, and try to define it, it means that your abstract ability holds only if X is defined, but then you do not get X itself but only some analogy (definition) of it.

Since your abstract ability is blind to X itself, there is no use to continue our dialog about X, unless you directly get it without using any analogy.

You wrote:"Silence and simplicity are not synonyms"

Now understand what you wrote, and then we continue our dialog, if you wish.

As long as you claim that Cardinality is a complete thing, you actually say that some definition (some analogy) is synonym to completeness (totality) itself.

"Silence and simplicity are not synonyms" exactly because Simplicity itself is undefined (and undefined is not some definition, at the moment that you directly get Simplicity itself).
 
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doronshadmi said:
Now understand what you wrote, and then we continue our dialog, if you wish.
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Are you going to continue to dodge any responsibility for a false accusation you made? You alleged I had made contradictory statements. I challenged you to provide evidence, but instead you change the subject.

Either support your accusation, or retract it.

It is not possible to conduct a meaningful dialog with an openly dishonest person.
 
jsfisher said:
Are you going to continue to dodge any responsibility for a false accusation you made? You alleged I had made contradictory statements. I challenged you to provide evidence, but instead you change the subject.

Either support your accusation, or retract it.

It is not possible to conduct a meaningful dialog with an openly dishonest person.
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Does Cardinality is complete as Cantor claim (because if not, then Aleph0 idea does not hold)?

If your answer is "yes", then you make a contradictory statement, because no definition (analogy) is the thing itself.

If your answer by "no", then you supprort my theory and contradict your own claim that my theory is wrong.

If your answer is not yes and not no, then you are using the undefind, but then no premise or conclusion are distinguished from each other.
 
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doronshadmi said:
Does Cardinality is complete as Cantor claim (because if not, then Aleph0 idea does not hold)?
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Cantor made no such claim.

Your question is therefore unanswerable.

Define what you mean by "complete" in non-circular terms, and the question may become answerable. But probably not, because you don't understand the word "cardinality," either.

If your answer is not yes and not no, then you are using the undefind, but then no premise or conclusion are distinguished from each other.
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No, premises and conclusions can be distinguished from each other if they are well-defined (which "complete as Cantor claimed") is not.
 
doronshadmi said:
Does Cardinality is complete as Cantor claim (because if not, then Aleph0 idea does not hold)?

If your answer is "yes", then you make a contradictory statement, because no definition (analogy) is the thing itself.
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A hypothetical future event is not evidence for a past event.

Support your accusation or retract it.
 
jsfisher said:
I think I have read all of his .PDF files. They get very repetitive after a while, but they do skip around in the most bizarre ways. I've also tracked down many of this posts in other fora.
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awww, you're missing George, aren't you :)
 
nathan said:
awww, you're missing George, aren't you :)
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I miss ChristopherA and DavidJayJordan, too. And now add Becomingagodo to the list. But you are right, George was my favorite, and I do miss him.

;)
 
drkitten said:
Cantor made no such claim.
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Really?

"Cantor introduced into mathematics the notion of a completed set, so that the integers, for example, could be considered together as a set in themselves, and so as a completed infinite magnitude. Only by conceiving of the integers as a whole entity, (as a Ding für sich) could Cantor define the first transfinite number, which he denoted by a lower case omega (ω), in contradistinction to the familiar sideways eight infinity symbol (∞), which had only meant unbounded." ( www.asa3.org/asa/PSCF/1993/PSCF3-93Hedman.html )

"Cantor is quoted as saying:

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type."
( www.en.wikipedia.org/wiki/Absolute_Infinite )
 
doronshadmi said:
Really?

"Cantor introduced into mathematics the notion of a completed set, so that the integers, for example, could be considered together as a set in themselves, and so as a completed infinite magnitude.
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Yes.

"Completeness" is not the same as "a completed set."

Since "cardinality" is not a set, it is neither a "completed set" nor is it an "uncompleted set."


You might as well ask if "red" plays offense or defense. No, it doesn't. "Red" is a color, and colors don't play football.

Oh, and your very citation gives you the lie, if you understand the notation. The set of all integers is indeed a lower case omega (ω), but that's not the "cardinality" of the set of all integers. Cantor was very clear -- and for good reason -- about distinguishing between sets and their cardinality. The number ω is an ordinal number (the so-called first limit ordinal), and it has a cardinality of aleph-0 (which I can't figure out how to type). But other ordinals also have that same cardinality, for example ω+ω.

So, no, cardinality is not a set. (And I was right. You don't understand "complete," and even if you did, you don't understand "cardinality.")

I repeat, "Cantor never made such a claim."

You don't understand what Cantor said. Why should I believe you when you say you're fixing his math, when you don't even understand what you're fixing?
 
doronshadmi said:
Time is not involved here.

Now please answer to http://www.internationalskeptics.com/forums/showpost.php?p=3633810&postcount=725 .
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My answer is exactly the text you quoted in the above referenced post:

Are you going to continue to dodge any responsibility for a false accusation you made? You alleged I had made contradictory statements. I challenged you to provide evidence, but instead you change the subject.

Either support your accusation, or retract it.

It is not possible to conduct a meaningful dialog with an openly dishonest person.​
 
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jsfisher said:
My answer is exactly the text you quoted in the above referenced post:

Are you going to continue to dodge any responsibility for a false accusation you made? You alleged I had made contradictory statements. I challenged you to provide evidence, but instead you change the subject.

Either support your accusation, or retract it.

It is not possible to conduct a meaningful dialog with an openly dishonest person.​
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At the moment that you answer to http://www.internationalskeptics.com/forums/showpost.php?p=3633810&postcount=725 you will get the exact answer to your question.

So please do it and see for yoursef how you contradict yourself, no matter what answer you provide.
 
doronshadmi said:
You do not need more than that.
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Unfortunately, I don't. That paper demonstrates pretty conclusively that you have no idea how transfinite mathematics works and that you've learned to parrot a few symbol strings but have no idea what they actually mean.

I had hoped that you could provide evidence against the obvious conclusion and in support of the idea that you had even a marginal understanding of Cantor's theories.

By your own admission, you have none.

This time please reply to the second part of http://www.internationalskeptics.com/forums/showpost.php...&postcount=734 .
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You mean this?

Contor's notion of a complete set means that the set of all things of some common property has an exact magnitude(a complete thing) which he called cardinal number.
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Easily responded to. I don't believe you know what any of the words in that phrase mean, either.
 
doronshadmi said:
At the moment that you answer to http://www.internationalskeptics.com/forums/showpost.php?p=3633810&postcount=725 you will get the exact answer to your question.

So please do it and see for yoursef how you contradict yourself, no matter what answer you provide.
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So, your statement that I had made (meaning in the past made) a contradictory statement, in doron's world of misunderstanding and gibberish really means that I will make (in the future) a contradictory statement?

Is this more of that 5 year-old reasoning you embrace? No wonder you understand so very little.

By the way, drkitten already provided a perfectly correct response to your bogus question.
 
jsfisher said:
So, your statement that I had made (meaning in the past made) a contradictory statement, in doron's world of misunderstanding and gibberish really means that I will make (in the future) a contradictory statement?

Is this more of that 5 year-old reasoning you embrace? No wonder you understand so very little.

By the way, drkitten already provided a perfectly correct response to your bogus question.
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jsfisher,

You have no choice but to agree with at least one of the 3 options:

1. Yes

2. No

3. Not any of the above options.

In all cases you contradict yourself, so time is not involved here.
 
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drkitten said:
Unfortunately, I don't. That paper demonstrates pretty conclusively that you have no idea how transfinite mathematics works and that you've learned to parrot a few symbol strings but have no idea what they actually mean.

I had hoped that you could provide evidence against the obvious conclusion and in support of the idea that you had even a marginal understanding of Cantor's theories.

By your own admission, you have none.



You mean this?



Easily responded to. I don't believe you know what any of the words in that phrase mean, either.
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Here it is again:

Contor's notion of a complete set means that the set of all things of some common property has an exact magnitude(a complete thing) which he called cardinal number.

Now please show how a complete set exists without a complete (exact) cardinal.

If you claim that aleph0 is not an exact (complete) value, then Cantor's transfinite system does not hold.
 
doronshadmi said:
Contor's notion of a complete set means that the set of all things of some common property has an exact magnitude(a complete thing) which he called cardinal number.
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Showing me a set of words that you don't understand a second time will not make you understand them.


Now please show how a complete set exists without a complete (exact) cardinal.
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Domain error.

Once again, you have produced a question that cannot be answered because you are using words in ways incongruent to their meanings.


If you claim that aleph0 is not an exact (complete) value,
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Exact and complete are not synonyms. There is no such thing as a "complete" value, because completeness is a property of sets, not of numbers.
 
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drkitten said:
There is no such thing as a "complete" value, because completeness is a property of sets, not of numbers.
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Value is a general concept which is also related to cardinal numbers, where in the case of cardinal number the value is called magnitude.

The completeness of a set and its magnitude are inseparable (the completeness of a set is measured by the value of its cardinal ( http://en.wikipedia.org/wiki/Cardinal_number )), so please stop your zigzag and show that aleph0 is separable of the set of Natural numbers.

Futhermore, by using Dedekind's notion of 1-to-1 mapping Cantor proved that any unbounded subset of N has the same cardinality as N. It can be done only if |N| is inseparable of N (where N is complete).

If you cannot do that, then your claims do not hold water.
 
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doronshadmi said:
Value is a general concept which is also related to cardinal numbers, where in the case of cardinal number the value is called magnitude.

The completeness of a set and its magnitude are inseparable (the completeness of a set is measured by the value of its cardinal ( http://en.wikipedia.org/wiki/Cardinal_number )), so please stop your zigzag and show that aleph0 is separable of the set of Natural numbers.

Futhermore, by using Dedekind's notion of 1-to-1 mapping Cantor proved that any unbounded subset of N has the same cardinality as N. It can be done only if |N| is inseparable of N (where N is complete).
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More words that you demonstrably don't understand.


If you cannot do that, then your claims do not hold water.
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I should put a laughing dog here. You haven't presented a well-founded conjecture that can be proven or disproven. The words you used are not meaningful in the combination that you use them.

And my claims therefore don't hold water. How rich....
 
drkitten said:
And my claims therefore don't hold water. How rich....
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Hmmm, just out of interest, other than the statement that doron understands very few of the words he uses, what claims did you make, drkitten?
 
jsfisher said:
Hmmm, just out of interest, other than the statement that doron understands very few of the words he uses, what claims did you make, drkitten?
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Well, last night I claimed -- correctly -- that Colonel Mustard did it in the conservatory with the lead pipe. Or maybe in the ballroom with Miss Scarlet; I don't remember exactly. It was late and I had been drinking a bit. I'm afraid that some kittens just can't hold their lighter fluid.

Tonight I'm sticking to wood stain.
 
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drkitten said:
No, thank you. My spoon is broken.
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Yes I know. It is permanently broken all along the dialog.
drkitten said:
You haven't presented a well-founded conjecture that can be proven or disproven.
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I did better than that.

I provided the simplest state that actually enables us to present some well-founded conjecture that can be proven or disproven.

This simplest state is used by you as a hidden assumption of any premise and conclusion.

Please carefully follow:

http://www.internationalskeptics.com/forums/showpost.php?p=3628609&postcount=707

http://www.internationalskeptics.com/forums/showpost.php?p=3630543&postcount=717

http://www.internationalskeptics.com/forums/showpost.php?p=3633592&postcount=723

if you wish to avoid the hidden assumption.
 
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doronshadmi said:
I provided the simplest state that actually enables us to present some well-founded conjecture that can be proven or disproven.
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You claimed that the simplest state is silence ... but you're not showing any evidence of that.
 
nathan said:
So, when you wrote 'The completeness of a researchable thing is exactly its restriction.' you were not describing a researchable thing? Is that what you are now saying?
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A researchable thing cannot be both researchable AND complete.

If you force completeness on a researchable thing you are actually limiting it.

The incompleteness of a researchable thing is actually its natural ability to be developed both from within and from without, without any limitation.

The thing that is naturally not changed under any manipulation is simplicity at its self state, but then it is both invariant and non-researchable and it is the best point of view of any researchable thing, which is naturally a never ending developing thing, that is not restricted by any limitation like a completed development.
 
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doronshadmi said:
Since when you are talkin' to youself (and you are also correct, in ths case)?
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Goodness, I haven't heard that particular comeback since I left the elementary school playground. Is that the best you can do for substantive comment?

I'm afraid, Doron, that it's obvious to anyone with a passing knowledge of the field that you are very badly abusing notation and terminology. That in and of itself is not necessarily bad --- but it's also obvious that you have no idea THAT you are doing it, or in what regard your terminology differs from the standard. You've been urged to produce clear definitions for your concepts since this first page of this thread, and have systematically avoided doing so. When I start holding your feet to the fire about "no, that's not what that word means; no, those words are not synonymous; no, that adjective cannot be applied to that word," you not only fail to correct your terminology to re-express the question, but you get hostile.

Infantilely so, in this case.

Your puerile response is the best possible demonstration I could have hoped for that you really don't understand any of the concepts you're slinging around.
 
doronshadmi said:
Please explain us how (for example) |N| is not related to N.
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What exactly do you mean by "not related"? Are you expecting |N| to be a member of N? It isn't, nor should it be expected to be. Aleph-null isn't a natural number.

Also please explain us why 1+|N|=|N|+1 and why 1+ω≠ω+1?
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"Us" don't need that explained; you are the only one lost at sea. It would be very difficult explaining it to you because you understand neither cardinal nor ordinal numbers. And helping you understand much of anything has proven very difficult because you have your kindergarten perception filters permanently enabled.
 
drkitten said:
Goodness, I haven't heard that particular comeback since I left the elementary school playground. Is that the best you can do for substantive comment?

I'm afraid, Doron, that it's obvious to anyone with a passing knowledge of the field that you are very badly abusing notation and terminology. That in and of itself is not necessarily bad --- but it's also obvious that you have no idea THAT you are doing it, or in what regard your terminology differs from the standard. You've been urged to produce clear definitions for your concepts since this first page of this thread, and have systematically avoided doing so. When I start holding your feet to the fire about "no, that's not what that word means; no, those words are not synonymous; no, that adjective cannot be applied to that word," you not only fail to correct your terminology to re-express the question, but you get hostile.

Infantilely so, in this case.

Your puerile response is the best possible demonstration I could have hoped for that you really don't understand any of the concepts you're slinging around.
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You will do anything in order not to answer to http://www.internationalskeptics.com/forums/showpost.php?p=3635569&postcount=747, isn't it?
 
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