The scope of a generalisation

Consider the following hard generalisations:

1 All cows are herbivores.

2 All black cows are herbivores.

The subjects of these generalisations - what the generalisations are about - are cows and black cows, respectively. Both generalisations are true, and they stand in a special relationship. There are two aspects of this relationship. First, they attribute the same feature to their subjects (that of being herbivores). Second, the subject of the second is a subset of the first (all black cows are cows). Thus we say that the scope of (1) is wider than that of (2) and conversely that the scope of (2) is narrower than that of (1). Note that we can compare generalisations in this way only

Figure 5.1 The scope of a generalisation

when the subject of one is a subset of the subject of the other. We cannot, for example, say that the generalisation 'All lions are carnivores' is narrower than, or wider than, either (1) or (2). Nor can we compare the scope of 'All sheep are herbivores' to that of either (1) or (2).

Figure 5.1 represents the situation expressed by (1) and (2). It can sometimes be important to adjust the scope of a generalisation, making it either narrower or wider. Usually, in reconstructing arguments, we have to narrow them; hardly ever do we have to widen them. Suppose, for example, you are a fervent environmentalist, and believe that radical measures must be taken immediately to protect the environment from air pollution. In particular, you believe that our reliance upon petroleum products - such as petrol for cars - must be halted as soon as possible. So you argue:

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