What Justifies an A Priori Concept Like Infinity?

[brainstorm]

Categorical distinctions are usually made a priori to the categories being operationalized and compared/contrasted. So, for example, sociological research that compares social classes makes an a priori assumption that individuals cannot be identified with more than one social class. As such, the results will reproduce the mutual exclusion of classes, only because the distinction and assumption was brought in at the beginning of research.

A priori assumptions and premises can only be (in)validated on the basis of philosophical reason. You can't say that because certain categories generate good analytical results that the categories are automatically valid, imo. That could be part of your reasoning as to the validity of the categories, but you still have to explore all issues that come into play. Otherwise your a prioris are going to influence your results without any kind of rigorous basis for them, which would undermine the validity of your research generally, I think.

 

[Pythagorean]

It would be a comforting thought to think so, but the half-*** example I provided in the OP(Infinity as a limiting concept) baffles me. That we can know our own limits without empirical evidence!
How do you explain such a thing??

In terms of observations, I think the general idea is that if it's bigger than you can "perceive" (i.e. significant detection in a system) it's not much different from infinity. For instance, if I have current in a wire, and I place a charge next to it, as the particle gets closer and closer to the wire, it's as if the wire were infinite because, in terms of the field interactions, if you were looking at the wire from the electrons perspective, the wire would seem to go forever in both directions.

If you pull the particle farther and farther away from the wire, the particle can "see" the whole wire at once (just as if you backed away from the broad side of a barn, at a certain point you can get the whole barn in your view).