In making this generalisation explicit, we make it explicit exactly what is wrong with the original argument. For we have now represented the argument as a deductively valid one. But in this way we represent the argument as very obviously unsound, owing to the falsity of P2 (PI in each case, is true). The second argument shows this, because it is valid, yet PI is true and C is false. According to the definition of validity, it follows that P2 is false.
The technique just discussed is this: to show that an argument is unsound, make explicit the assumed generalisation upon which it is based, in such a way that the argument becomes deductively valid (or inductively forceful). Then find a true premise and false conclusion which are suitably analogous to the premise and conclusion of the original argument, and substitute them (as we did with PI and C of the above argument).
Sometimes an arguer's assumed, faulty generalisation is perfectly obvious, but they seem not to notice that it is faulty. Here is an example:
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