[mrkeen]

The system works according to its defined rules.

In one system, a set can contain itself, in another system it can't.

So it doesn't really make sense to ask 'can it?'

If you allow sets to contain themselves, you also have to talk about sets which do not contain themselves, which yields Russell's paradox.

If you disallow sets (or types) from containing themselves then you can't construct Russell's paradox, which is why it follows.

[Koshkin]

> In one system, a set can contain itself

But doesn't this lead to a contradiction (or to making the system of little use)?