About qualitative superiority

[Popcaliana]

I am currently confused... Why is it that an inaccessible cardinal is considered to only have a quantitative superiority over finite numbers, rather than a qualitative one?
As you know, an inaccessible cardinal cannot be reached by any operation using any cardinal number below it; there is an absolute, insurmountable wall between inaccessible cardinal and what is below it. How is this different from qualitative superiority?
It was explained that this is a quantitative difference because a 1-dimensional line segment can be raised to an inaccessible dimension by performing an operation using the inaccessible cardinal itself. However, isn't this the exact same situation as a non-1-A character being raised to 1-A level by a 1-A character?

 

[Berga14]

raised to an inaccessible dimension by performing an operation using the inaccessible cardinal itself. However, isn't this the exact same situation as a non-1-A character being raised to 1-A level by a 1-A character?

The first one is still about quantity though. The difference between 2 cardinals in the end is just an uncountable quantity.

 

[FriendOfTheTeaParty]

I am currently confused... Why is it that an inaccessible cardinal is considered to only have a quantitative superiority over finite numbers, rather than a qualitative one?
As you know, an inaccessible cardinal cannot be reached by any operation using any cardinal number below it; there is an absolute, insurmountable wall between inaccessible cardinal and what is below it. How is this different from qualitative superiority?
It was explained that this is a quantitative difference because a 1-dimensional line segment can be raised to an inaccessible dimension by performing an operation using the inaccessible cardinal itself. However, isn't this the exact same situation as a non-1-A character being raised to 1-A level by a 1-A character?

It's still pretty quantitative. Qualitative isn't only not being to be reached up by numerical additions, but it's also about being utterly indivisible to the previous layer of existence. While with an inaccessible cardinal you can still "divide" or point out lower quantitative stuff from it like a "1" or a "2" as a subset of its composition. So it's still beholden to lower quantities.

Also it's not the same as being raised to 1-A because the process is fundamentally alien to a quantitative nature. There's still composition between the lower quantity and the inaccessible, while there's no overlap in composition between a non 1-A and the 1-A when being raised to such a level.