On Wednesday, December 4, 2013 6:56:15 AM UTC-7, WM wrote: > Am Mittwoch, 4. Dezember 2013 10:13:59 UTC+1 schrieb Zeit Geist:
> > Remember, before we write a Proof, we must first formalize the statement. This allows to understand clearly what the Natural Language statement actually means. > > No. Every formal particle has to be defined in normal language. Every composition of formal particles can be defined in normal language too. The language does not matter at all. But normal language often exhibits nonsensical approaches in formal language like the confusion of all and every. >
WRONG. We must use Formal Language to avoid accident confusion and intentional charades.
But fine. Never mind the Symbolic Language, which I'm now sure you don't understand. In English, you Second Conclusion says "There Exists a Line equal to d." It's Existential in any Language.
And again, ALL Gives Us EVERY. Do you need the Proof again?
> > Now, please tell me whose Methods the Quantifier Confusion resides in? > > For every n in |N: The FIS d_1, d_2, ..., d_n is in the remaining part of the (rationals-complete) list > > You agree. >
> d_1, d_2, d_3, ... is in the remaining part of the list. > > You do not agree. >
I don't agree.
> That means that d has the power to deviate from all entries of the list that none of the strings d_1, d_2, ..., d_n has. You see? >
What are you trying to say here?
Are you saying:
That can d can be unequal from all entries of the list, but all the F(IS(d_n) can't. ?
If so, this is the case.
BTW, I find that a strange way phrase things. Numbers, and other Mathematical Objects, usually aren't referred to as having "powers" but as having "properties".
> So you have "proved" that d contains more than all d_n, (which is the same as to contain more than all strings d_1, ..., d_n). You don't call the difference d_oo, but you "proved" that it exists. >
Why does "d contain more than all d_n" mean? More what?
There is no d_oo, and never said or "proved" there is. All decimal places of d are of finite index.
> The quantifier confusion is this: > > "For every natural index there is a larger one" > > has been inverted to > > "there is an index oo larger than every natural". >
You are severely mistaken. That is not what was done here.
Throw you distractions as much as you want, but the facts remains you have made a huge Logical error.
You claimed that two pairs of Sentences ( each pair consisting of a Premise and a Conclusion) have the SAME Logical Structure.
However, the First Conclusion is a Universal Statement and the Second Conclusion is an Existential Statement.
How do you claim the pairs have the Same Logical Structure when the Conclusions differs in Logical Structure.
You claim, my (our) Methods can prove Both Conclusions using exactly parallel proofs. But, that's wrong, because the Conclusions are not of parallels forms.
If they were of Parallel forms, then you could use the my methods of the First Proof to construct a proof of Second set of Statements.
But they aren't Parallel forms. You are wrong!
Do you see why the Second Conclusion,
"conclude for all n: d_1, d_2, ... is in the remaining part of the list."
is actually an Existential Statement. Even though, in the English, it starts with "for all"?
Your Analysis of the Assertion of the Statement is Incorrect.