Can Non-Numerical Methods Effectively Organize Qualitative Data?

[alvin51015]

The best question I can ask at this point is this: is there a way to order things or arrange things of which it is not even possible to use numbers or any form of numerical counting?

 

[micromass]

I think you will really need to be more clear. I have no clue what you mean. Every collection of objects (let's keep it finite) can be counted and thus can be assigned a number.

 

[HallsofIvy]

It is possible to order "un-countable" sets, if that is what you are talking about. For example, the set of all real numbers between 0 and 1 is uncountable and is a subset of the set of all real numbers between 0 and 2 which is a subset of all real numbers between 0 and 3, etc. We can "order by inclusion"- A comes before B if and only if A is a subset of B. Of course, that collection of sets is then countable.

But "ordering" is in fact equivalent to "counting". If a collection of objects can be "well ordered" (given any two objects, A and B, we can determine whether A is before B or B is before A and each object has a unique "next" object) then the collection is "countable".

 

[alvin51015]

Right. Practically it seems that in this universe there is probably no way to do analysis without some form of numerical ordering. The only reason I brought it up was that I imagined a potential non numerical analysis would be the end result as the limit of the level of abstraction approached infinity.