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But this argument, though valid, is probably not sound, since P2 is probably false. Yet the original argument is surely a good argument, in some sense. The truth of the premise would be a good reason for expecting the conclusion to be true; one would be surprised to find it was false. Certainly if you had to bet on whether or not the conclusion is true, then, given no relevant information except for PI, you would bet that it is true, not that it was false. You would reasonably infer the truth of C from PI rather than its falsity.

However, we must notice something very important about the inference from PI to C. A logician would not be in a position to recognise the forcefulness of this argument as we have written it so far. For in order to recognise it, one has to know certain facts about Inverness - the facts which make it different from, say, a hot place around which they grow cotton like Cairo. The logician, as noted earlier, does not know anything as specific as that. Someone giving the argument is implicitly relying on a proposition which is similar to P2 in the argument given directly above, but which is much more likely to be true - namely, that very few people in Inverness own no items of woollen clothing, which is the same as saying that almost everyone in Inverness owns at least one item of woollen clothing. That is to say, the use of the quantifier 'everyone' would be inappropriate here, but use of the weaker quantifier 'almost everyone' is appropriate. Given what we know about Inverness, we can be almost completely certain that almost everyone in Inverness owns at least one woollen item of clothing. (Recall from Chapter 1 that expressions such as 'most', 'almost all', and 'few' are called 'quantifiers'.) We can represent the argument, then, as follows:

P1) Fiona lives in Inverness.

P2) Almost everyone in Inverness owns at least one item of woollen clothing.

C) Fiona owns at least one woollen item of clothing.

This argument is still not valid, since Fiona still might conceivably be one of those few who do not have any woollen clothing. Still, these premises, just by themselves, do provide a good reason for accepting the conclusion: The logician, knowing nothing but the truth of PI and P2, could happily accept that if the premises are true, then, probably, so is C. We recognise this by calling such an argument inductively forceful (the word 'inductively' is meant to contrast with 'deductively'), and inserting the word 'probably', in parentheses, before the conclusion:

P1) Fiona lives in Inverness.

P2) Almost everyone in Inverness owns at least one item of woollen clothing.

C) (Probably) Fiona owns at least one woollen item of clothing.

The word 'Probably', here, is not to be regarded as part of C. It is not, strictly speaking, part of the argument. What it is, rather, is an indication to the reader that the argument has been judged, by the person doing the reconstruction, to be inductively forceful. If we were to remove it from the above reconstruction, the inductive force of the argument, and its status as not being deductively valid, would be unaffected.

Roughly, then, an inductively forceful argument is one that is not deductively valid - the truth of the premises would not ensure the truth of the conclusion - but whose premises provide good reason to expect the conclusion to be true rather than false. Before we characterise the concept of inductive force more accurately, however, it will be useful to look briefly at the more basic concept of probability.

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