How representative is the sample

Suppose you live near the North Pole, and every bear you've ever seen is white. So you argue:

P1) Every observed bear is white.

C) All bears are white.

Formally, this argument is just like the one about the guppies. But, whereas the guppy-inference seemed to be correct, this one seems not to be. Only a small minority of bears are white (Polar Bears, and perhaps the occasional albino). The difference is that, whereas the guppy-arguer can reasonably assume that the sample of observed guppies was representative of the total population of guppies, the bear-arguer cannot. That is, the guppy-arguer can reasonably assume that the sample of guppies was relevantly similar to the total population, but the bear-arguer cannot. Polar bears are only one of many species of bears, and if you know anything about zoology and adaptation, you know that a trait like colour, though somewhat likely to be similar across a single species, is not nearly so likely to be similar across different species, even within the same genus. Further, you can reasonably assume that mammals living in non-snowy regions are much less likely to be white than ones living in perpetual snow. Being a different species, which lives in a completely different climate, is certainly a relevant difference when drawing inductive inferences about colour with respect to classes of mammals, even if the species is a closely related one.

How do you know whether a sample is representative of the total population, i.e. relevantly similar to it? There is no simple rule for this; our estimate of relevant similarity must be based upon our knowledge of the subject-matter in question. For example, we drew upon some basic biology in criticising the bear-inference.

In general, the larger and more representative the sample used for a given generalisation, the more inductively forceful, or the stronger the inductive inference. An inductive inference that is not forceful - one whose premise does not really support its conclusion - is a weak one. For example, suppose someone argues, 'My brother is a fool. Therefore, probably, all boys are fools.' That is a very weak inductive inference; it is totally unwarranted. The bear-arguer's inference is not quite as bad as that, but it is also very weak. Also, from a given sample, an inference to a generalisation about most of the totality is a stronger one than an inference to a generalisation about all of the totality, since obviously the latter is less certain.

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