Читать книгу This is Philosophy of Science - Franz-Peter Griesmaier - Страница 14

The simplest example of an inductive inference is that of inferring something about an entire population from observing only some of its members. Recall the earlier example involving koalas: I inferred from having observed 20 of them munch exclusively on eucalyptus leaves that all members of the species Phascolarctos cinereus (that’s the koala’s scientific name) feed on eucalyptus leaves. Of course, such inferences are not restricted to biological populations. We might conclude that all igneous rocks are black, after we have seen many lava fields and observed that all of those were black. We can characterize the nature of statistical inferences in the following way:

A statistical inference is an inference from the observed frequency of a property in a sample to the claim that the same frequency holds for the population from which the sample was taken, within a certain margin of error.

Here is an example in explicit form:

Premise 1:	The frequency of red marbles in a sample of 200 balls drawn from an urn was 49%.
Premise 2:	The urn contains exactly 1,000 marbles which are either red or black.
Conclusion:	The frequency of red balls in the urn is 50%, with a margin of error of ± 2%.

Obviously, SI is an inference from the observed (the sample) to the unobserved (the population). Suppose you randomly picked up the first one hundred plants in a meadow and every one of them was a grass. You might well infer that every plant in the field was a grass. As we all know, beliefs (or hypotheses) based on SI can turn out false. Not all igneous rocks are black, and it’s unlikely that all plants in a meadow are grasses, although koalas seem to invariably eat eucalyptus. Often, this is due to sampling problems, which can never be fully eliminated (maybe all the tall plants that are easily accessed are grasses, but some small, ground-hugging plants are broad-leaved species). But even if the sampling doesn’t involve any bias, evidence from samples provides only defeasible reasons for beliefs about the relevant population, as the deviation of election results from predictions based on sampling (called polling) clearly demonstrates. There is much more to be said about SI, some of which you’ll find in later chapters.