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# Similarity, likelihood and uncertainty

The theory of similarity highlights important features of plausible judgement under uncertainty. This is because judgement under uncertainty is essentially judgement about the likelihood that some future event will be 'similar' to some past event (of which it is considered to be a repetition). A first important feature common to similarity and likelihood is the inherent ranking structure of the corresponding judgements. This characteristic was clearly pointed out by John Maynard Keynes, when he wrote:

[T]he so-called magnitudes or degrees of knowledge or probability, in virtue of, which one is greater and the other less, really arise out of an order in which it is possible to place them [...] When, therefore, we say that one probability is greater than another, this precisely means that the degree of our rational belief in the first case lies between certainty and the degree of our rational belief in the second case.

(TP, p. 37)

Indeed '[probability is, so far as measurement is concerned, closely analogous to similarity' (TP, p. 30). With both probability and similarity we can say that greater proximity of features increases the likelihood that any given event or object will belong to a certain category (see Keynes, TP, p. 30.). However,

we cannot in these cases measure the increase; we can say that the presence of certain peculiar marks in a picture increases the probability that the artist of whom those marks are known to be characteristic painted it, but we cannot say that the presence of these marks makes it two or three or any other number of times more probable than it would have been without them. We can say that one thing is more like a second object that it is like a third; but there will very seldom be any meaning in saying that it is twice as like.

(TP, p. 30)

As we have seen, similarity judgements presuppose a fine decomposition of characteristics in order to highlight the different orders of similarity relevant for the case in view, and a more 'synthetic' ability aimed at assessing overall similarity on the strength of the various assessments of partial similarity. In the case of likelihood, its reasonable assessment presupposes a fine decomposition of characteristics so as to highlight the different 'orders of likelihood' relevant for the case in view, that is, the different scenarios relevant to the analysis of whether a certain event is likely to be repeated over time. As with similarity, there is no immediate connection between partial likelihood and overall likelihood. The former is bound to a particular order of likelihood (that is, to a particular set of conditions making a certain event more or less likely); the latter presupposes the ability to move beyond likelihood on each specific dimension so as to assess the similarity of future to past events from a more general point of view. In short, evaluation of likelihood is a special similarity judgement made with reference to future outcomes.

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