We must find alternatives to the petroldriven automobile

Assuming the truth of PI, this is a deductively sound argument. Even if you doubt PI, this is, at any rate, a much better argument than the earlier version; since the new P2 is a narrower generalisation than the old P2, its premises have a better chance of being true. Furthermore, by narrowing the generalisation, the issue is defined more exactly. We now have it explicitly before us that the point at issue is the use of petrol-driven automobiles, not automobiles in general.

Thus, when reconstructing arguments, we should take care not to employ a hard generalisation that is wider in scope than we need, if there is anything doubtful about the wider one that could be eliminated by employing a narrower one. If a narrower (but hard) generalisation will suffice for constructing an argument for the desired conclusion, then we should employ the narrower one. This is not to say we should always choose narrower generalisations whenever possible; for example, it would not improve the argument to rewrite P2 as 'All green petrol-driven automobiles emit carbon monoxide'. For adding the word 'green', besides not making the generalisation any more likely to be true (or at least not appreciably so), renders the argument invalid. The point is that if one generalisation is narrower than another and more likely to be true, then, provided that it is sufficient for obtaining the desired conclusion, the narrower one should be employed.

Note that in some cases there is no natural word or phrase for the class of cases we wish to generalise about. In such cases we have to reduce the scope of a generalisation by explicitly excepting a certain class of what would otherwise be counter-examples. For example, consider the inference 'That is a mammal; therefore it doesn't fly'. The generalisation needed is 'No mammals except bats fly', since 'No mammals fly' is false (and of course we would also need the premise that the creature in question is not a bat; we ignore flying squirrels).

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