What is wrong with this statement?

Consider the following statements:

  1. Non-self cannot be distinguished without self.
  2. Anything distinguishable from self is non-self.
    By combining 1 and 2,
  3. Anything distinguishable from self cannot be distinguished without self must be distinguishable from self.

What is wrong with statement 3?

What’s wrong with it? It doesn’t make any sense!

What would “distinguishable” in general mean? We know what it means for something to be distinguishable from other things, but distinguishable in general? You’ll need to give a more precise definition before we can even judge whether or not there is anything inconsistent about that sentence. It’s only necessary flaw, at the moment, is that it is poorly worded.

The use of the term ‘self’ is arbitrary. Consider:

Anything ‘distinguishable’ must be distinguishable from something else.
Anything ‘distinguishable’ must be distinguishable from other.
Anything ‘distinguishable’ must be distinguishable from pizza.

The problem is with the double-use of the term ‘distinguishable’ - more or less the same thing Twiffy said, if I’m not mistaken.

That seems like an intuitive definition of the term - then, the problem is that the term “distinguishable”, as defined, is inherently self-contradictory. If anything “distinguishable” must be distinguishable from itself, it must be other than itself, which it isn’t, therefore contradiction. So the definition might be intuitively satisfactory, but it’s entirely impractical, so pick a different definition.

how do you define anything but by comparison. It’s hard to properly define anything from yourself.