Others are telling me, not to even try, because it’s surely impossible and I will suffer some great misfortune, if I try.
No one is telling Thomas that he will suffer any great misfortune if he tries, beyond the misfortune of almost certainly wasting his time.
Thomas, you made a similar claim earlier and I explicitly rejected it and reiterated that if you choose to go looking for mathematical contradictions I wish you well. Why are you telling untruths about other people? I think that’s rude.
Now, what if we have countably infinite amount of space dimensions. How many (rational) points are there?
Continuum-many, because e.g. any sequence of 0s and 1s corresponds to an integer (hence rational) point in aleph0-dimensional space. And you can put a side-1/2 cube around each of them to get continuum-many disjoint hypercubes in that space. The cardinality of the space itself is continuum^aleph0 = continuum, so in this case you have as many disjoint hypercubes as points.
(None of this is difficult, controversial, contradictory, or indicative of any sort of inconsistency.)
Aleph-zero dimensions give you aleph-one (=continuum) rational points. And also aleph-one hypercubes.
Since those two numbers are equal, this is not a way to reproduce a paradox in such a space.
Fine, no problem, just another rock with no snake under it. In other words, the ZF has survived another test, as it has survived one billion or so tests before.
As long as you believe, the Yablo’s paradox has nothing to do with the ZF, that it is completely isolated from the ZF, then we have no case against ZF, whatsoever.
Well, I don’t, you guys do believe that the semantics Yablo used, cannot be used against the ZF.
I think that this is a correct and honest description of our disagreement.
No one is telling Thomas that he will suffer any great misfortune if he tries, beyond the misfortune of almost certainly wasting his time.
Thomas, you made a similar claim earlier and I explicitly rejected it and reiterated that if you choose to go looking for mathematical contradictions I wish you well. Why are you telling untruths about other people? I think that’s rude.
Continuum-many, because e.g. any sequence of 0s and 1s corresponds to an integer (hence rational) point in aleph0-dimensional space. And you can put a side-1/2 cube around each of them to get continuum-many disjoint hypercubes in that space. The cardinality of the space itself is continuum^aleph0 = continuum, so in this case you have as many disjoint hypercubes as points.
(None of this is difficult, controversial, contradictory, or indicative of any sort of inconsistency.)
Let us stick to the essentials here.
Aleph-zero dimensions give you aleph-one (=continuum) rational points. And also aleph-one hypercubes.
Since those two numbers are equal, this is not a way to reproduce a paradox in such a space.
Fine, no problem, just another rock with no snake under it. In other words, the ZF has survived another test, as it has survived one billion or so tests before.
As long as you believe, the Yablo’s paradox has nothing to do with the ZF, that it is completely isolated from the ZF, then we have no case against ZF, whatsoever.
Well, I don’t, you guys do believe that the semantics Yablo used, cannot be used against the ZF.
I think that this is a correct and honest description of our disagreement.