Deeper than primes - Continuation

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doronshadmi said:
I agree with you that I wrongly assumed that your professional level of mathematics enables you to understand that {a,b,c,...} or {{},{a,b,c,...},...} are expressions that are used "without loss of generality".
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That's the thing about Mathematics. It requires precision of expression, not just hand-waving and assumption.

Why the scary quotes, by the way?

Back to the actually topic of this latest arc, though, the base question is whether you correctly represented Cantor's Theorem. A really good place to start with something like that, yet another thing you passed over, would be which statement of Cantor's Theorem would you be presenting?

If it is the one involving the cardinality of a set and its power set, then there is a whole preface you need to provide about cardinality. Yet another thing you omitted.
 
jsfisher said:
You are having that much trouble figuring out what part of my post you responded to?
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You wrote that I were (mis-)responding to something, so please direct me to the part of your post that were (mis-)responded by me.
 
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doronshadmi said:
You wrote that I were (mis-)responding to something, so please direct me to the part of your post that were (mis-)responded by me.
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As already pointed out, that would be the text that you quoted from my post to which you responded.
 
doronshadmi said:
The claim that philosophy has no impact on the math, is simply your philosophical point of view, so?
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Here we see what is fundamentally wrong with the line of argumentation of Doron Shadmi; he mixes 'objective' and 'subjective' arguments as he sees fit without any logic to it.

This not only invalidates the rest of his work, it also makes it for him to see the error of his ways nigh impossible.

The reader will find the flaws in Doron Shadmi's reasoning obvious and glaring, that much of luck we have.
 
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jsfisher said:
That's the thing about Mathematics.
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{a,b,c,...} or {{},{a,b,c,...},...} are easily understood as A and P(A) expressions without a loss of generality, unless one insists to deal with notations instead of notions, and probably this is your case.

jsfisher said:
If it is the one involving the cardinality of a set and its power set, then there is a whole preface you need to provide about cardinality. Yet another thing you omitted.
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Not at all. It is the one involving P(A) members that is not paired with any A member, such that both P(A) and A members are inaccessible to the platonic common objective (discovered) level of actual infinity (notated the outer "{" and "}" in both sets).
 
doronshadmi said:
It is the one involving P(A) members that is not paired with any A member, such that both P(A) and A members are inaccessible to the platonic common objective (discovered) level of actual infinity (notated the outer "{" and "}" in both sets).
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So, what is the statement of Cantor's Theorem you had in mind?
 
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doronshadmi said:
{a,b,c,...} or {{},{a,b,c,...},...} are easily understood as A and P(A) expressions without a loss of generality, unless one insists to deal with notations instead of notions, and probably this is your case.
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You need to define your notation rigidly and thoroughly before you can even begin to communicate notions.

So unless one deals with notations, one can not begin to deal with notions.

This is one for the upcoming Doron's errors.
 
jsfisher said:
Edited by full replacement:
So, what is the statement of Cantor's Theorem you had in mind?
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That there is no bijection between P(A) and A members, which is a relative measure that is inaccessible to the absolute level of the platonic common existence of both sets (which is notated by the outer "{" and "}" of {a,b,c,...} or {{},{a,b,c,...},...} that are easily understood as A and P(A) expressions without a loss of generality).

"There exists set X" is only a tautology, where what comes after "such that" is not only a tautology (and in the case of Cantor's Theorem, J's "existence" involved with contradiction, where this contradiction has no impacted on the platonic common level of existence of both P(A) and A, because this common level of existence is only a tautology).
 
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doronshadmi said:
"There exists set X" is only a tautology, where what comes after "such that" is not only a tautology (and in the case of Cantor's Theorem, J's "existence" involved with contradiction, where this contradiction has no impacted on the platonic common level of existence of both P(A) and A, because this common level of existence is only a tautology).
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The irony here being that since tautology has multiple meanings, it fits well. Especially if one notices that Doron's explanations are tautologies...

:big:
 
As long as one does not understand that platonic existence is a discovery that does no need any meaning in order to exist (it is a tautology of existence that does not need any further interpretation or meaning), one wrongly gets this discovery only in terms of subjective invented multiple interpretations and meanings that are not the discovered tautology of existence.
 
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doronshadmi said:
That there is no bijection between P(A) and A members, which is a relative measure that is inaccessible to the absolute level of the platonic common existence of both sets (which is notated by the outer "{" and "}" of {a,b,c,...} or {{},{a,b,c,...},...} that are easily understood as A and P(A) expressions without a loss of generality).
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Wow. That's nothing like the Cantor's Theorem I've ever seen. It just goes all over the place. When you make stuff up, Doron, you really do go all out.

How would you go about proving that, umm, invention?

By the way, Doron, do you realize that a bijection between A and P(A) isn't the same as between the members of A and P(A)? The latter is gibberish.
 
doronshadmi said:
As long as one does not understand that platonic existence is a discovery that does no need any meaning in order to exist (it is a tautology of existence that does not need any further interpretation or meaning), one wrongly gets this discovery only in terms of subjective invented multiple interpretations and meanings that are not the discovered tautology of existence.
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Excellent. You finally admit your invented terminology has no meaning. On this we can all agree.
 
Since there are so many things that doronshamdi misunderstands, let me respond to this post.

doronshadmi said:
The claim that philosophy has no impact on the math, is simply your philosophical point of view, so?
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I believe that you are shifting the burden. You are the one that is claiming philosophy has an impact on math. Too bad you haven't provided any proof of that. Lots of claims, no proof.
 
jsfisher said:
By the way, Doron, do you realize that a bijection between A and P(A) isn't the same as between the members of A and P(A)? The latter is gibberish.
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It is gibberish from your one level reasoning of set, which does not distinguish between the discovered level of A and P(A) (notated by the outer "{" and "}") and the invented level of A and P(A) (notated by their members, and the mapping (which is not bijective, in this case) is done at the invented level of members of these sets).
 
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Little 10 Toes said:
You are the one that is claiming philosophy has an impact on math. Too bad you haven't provided any proof of that. Lots of claims, no proof.
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1. Axioms in the framework of mathematics do not need any proof, otherwise they are not axioms, in the first place.

2. By using philosophical view of these axioms, I explicitly demonstrated that they are derived from using platonic and non-platonic levels, where the existence at the platonic level is only tautology.

Let's take. for example the Axiom Of Infinity:

"There exists a set X (the discovered level of set X) such that (the invented level of set X) the empty set is a member of X and, whenever a set y is a member of X, then S(y) is also a member of X".

More details are given in http://www.internationalskeptics.com/forums/showpost.php?p=10024836&postcount=3762.

So we are going even deeper than the mathematical level of axioms (which do not need any proof, otherwise they are not axioms, in the first place).
 
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doronshadmi said:
As long as one does not understand that platonic existence is a discovery that does no need any meaning in order to exist (it is a tautology of existence that does not need any further interpretation or meaning), one wrongly gets this discovery only in terms of subjective invented multiple interpretations and meanings that are not the discovered tautology of existence.
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This is hilarious without disambiguation of 'tautology'.

I think, because Doron uses the word tautology so often of late, that Doron does not know what tautology actually means...
 
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