The problem with classes is to decide whether they are real (ie, can be found) or abstractions (ie, are invented by us in our minds), because this decision is fundamental to our entrance to logic (ie, what we assume, and thereby also what we conclude). Without one of these decisions, we can’t enter logic. Among us (humans) about one third has decided the former, about one third has decided the latter and about one third hasn’t (can’t) decide.
For example, consider the classes “glasses” and “vases”, and the question “What is the difference between them”? Now, the question is whether this question concerns FINDING the difference between them, or FINDING OUT what we mean the difference is? Is there a way to find out whether a particular thing is a glass or a vase, or does the question refer to where we draw the line between them, ie, is there a line between them or do we draw this line?
These two possibilities are mutually exclusive, ie, contradictory, meaning that logical reasoning originating from one of them is totally inconsistent with logical reasoning originating from the other. It means that one third of us (humans) think that one third of us is totally stupid, and vice versa, whereas the remaining third isn’t consistent. This fundamental problem thus splits us (rational humans) up into two camps that simply can’t communicate. Rationality thus comes with a splitting seed, like also (other) beliefs do.
So, is there a way to decide which of these two entrances to logic is correct, or true. Well, the answer can be found in the logical end of them, since the assumption that classes are real ends in paradox (Russell’s paradox), whereas the assumption that they are our inventions ends in ambiguity, because it means that only the latter isn’t contradictory. It means that only this alternative can be correct (or true), because only it does not contradict itself. This does not mean that it is correct (or true), but just that only it out of the alternatives we have can be correct (or true). The possibility that nothing can be correct (or true) remains, but this possibility is actually included in this alternative.
The conclusion of this logical reasoning is thus that only the assumption that classes aren’t real can consistently embrace the possibility that nothing can be correct (or true). (In practice, this may mean that there are two correct conclusions. Just not one, but several.)