3.2 What it is not for

It isn't suitable for proving invalidity of some supposition. I might say ``at daytime, it isn't night; and now it's daytime, so now it's also night'' and you may pass some time trying the rules of natural deduction, but obtaining nothing useful. After some time, you will intuitively discover that the reasoning might not be valid, and it's then when another methods -not natural deduction- should be tried in order to prove invalidity. They are explained later.

So, natural deduction only serves for proving validity, but not invalidity. What a pity, isn't it?

Neither does it serve to provide a good answer to the question ``What would happen if...?''. When we are to prove the validity of $A\vdash B$, we must think of things that would happen if $A$ happened, and if we discover that one of these things is $B$, then we have finished. But we will never be able to give a complete and finite list of all those things.