Covering generalisations

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In the politician case, the connecting premise was a generalisation (review the discussion of generalisations in Chapter 1 if you are not clear about what a generalisation is). Connecting premises are usually generalisations. But in the inflation case the connecting premise we used was a conditional (see Chapter 2). This is also common. However, there is an important relationship between conditionals and generalisations that must be appreciated. Consider the following propositions:

(a) If Betty is a Siamese cat, then she has blue eyes.

(b) All Siamese cats have blue eyes.

(a) is a conditional, (b) is a generalisation. The special relationship in which they stand is that (b) is a covering generalisation for (a). (We can also say that (a) is an instance of (b), as is common in logic.) Note that (a) may be inferred from (b); the argument from (b) to (a) would be valid. But covering generalisations need not be hard generalisations: 'If Jane's cat is Siamese then its eyes are blue' is an instance of 'All Siamese cats have blue eyes', but it is also an instance of 'Most Siamese cats have blue eyes'.

There is one further aspect to the relationship between covering generalisations and their instances that should be appreciated. Another way to express the proposition expressed by the generalisation (b) is this:

(c) If something is a Siamese cat, then it has blue eyes.

Or we could say, 'Whatever X may be, if X is a Siamese cat, then X has blue eyes'. This is exactly like (a), except we use the indefinite pronoun instead of the name 'Betty'; this makes the conditional statement into a generalisation. In other words, generalisations of the 'All A are B' sort are themselves conditionals, except they are generalised, (b) and (c) are generalised forms of (a).

The same goes for generalisations of the form 'No A are B', as in 'No ungulates are carnivores'. This says, in effect, that all ungulates are non-carnivores. So it could be expressed as 'If something is an ungulate, then it is not a carnivore'.

Very often, when people assert conditionals, they do so on the basis of some covering generalisation. It is important to be aware of this when reconstructing arguments. Suppose you are given the inflation argument, but without a connecting premise:

P1) Consumer confidence is increasing.

C) Inflation will increase.

Suppose you reply to the arguer by saying that you just have no idea whether or not PI constitutes a reason to infer C, that inflation is going to increase. You point out that the argument, at any rate, is certainly not valid as it stands, and is not inductively forceful. Suppose that the arguer now tries to satisfy you with:

P1) Consumer confidence is increasing.

P2) If consumer confidence is increasing, then inflation will increase.

C) Inflation will increase.

Does this really improve the argument? It makes it valid all right. But this doesn't really help you. All that P2 says is that if PI is true then so is C. You have already said that you have no idea whether PI constitutes a reason to infer C. The arguer is not going to convince you merely by asserting P2; to do so is merely to assert that PI is a good reason to infer C. So the new version is not really an advance on the first version; although you cannot deny that the new version of the argument is valid, you can't really say whether the argument is sound, even if you grant that the arguer does know that PI is true.

Suppose, however, that you wished to find out whether or not to believe P2. P2 says that if consumer confidence is now increasing (which it is), then inflation will increase. So the only way to find out whether P2 is true would be to look into the future to see whether inflation does increase. But that you cannot do. So what do you do? What you need is to find out whether, in general, increases in consumer confidence bring about increases in inflation. And that you can find out, by doing some statistical research (consumer confidence is defined in terms of how much people buy, and how much they borrow in order to buy). So what you really need to know, and what it is possible to find out, is whether the following covering generalisation is true:

Whenever consumer confidence increases, inflation increases.

Probably it isn't, but the corresponding soft generalisation might well be true:

Usually, when consumer confidence increases, inflation increases.

This could be established by inductive inference from a survey of past cases in which consumer confidence increased.

So: the arguer giving the inflation argument gives a conditional premise rather than a generalisation, but if the arguer believes the conditional, he or she probably does so on the basis of believing the corresponding covering generalisation. Since that is what the arguer is assuming at bottom, that is what should be included in the reconstruction of the argument. If we do not do this, then our analysis of a given argument may be superficial. Indeed, it is easy to reconstruct an argument as valid in a completely superficial way, if we do not take pains to discover what connecting premises an arguer is relying on at bottom. For example, the following argument might have been given in 1914:

P1) If the Archduke Ferdinand has been assassinated, then a general war involving all the European powers will soon break out.

P2) The Archduke Ferdinand has been assassinated.

C) A general war involving all the European powers will soon break out.

The practice of argument reconstruction

Now in fact this argument would have been sound, but someone ignorant of the political situation in Europe at the time would have needed a lot of explanation in order to see why they should accept PI. PI is a connecting premise which ensures validity, but it hardly begins to tell us why the arguer thinks that a single assassination will lead to a general war involving several countries. In reconstructing, we should try to bring out as much of this as we can.

Finally, you should take care to distinguish the relationship we have just been discussing between conditionals and generalisations from the following sorts of cases:

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