Version: v1, Published online: 1998

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## 2. Inference to the best explanation and enumerative induction

Inference to the best explanation is *ampliative*. The conclusion one reaches is not a mere summary of the data on hand – one comes to believe something further which explains the data. We also recognize a pattern of ampliative inference called ‘enumerative induction’. This is the extrapolation of observed regularities to universal generalizations or to conclusions about particular unobserved cases. Thus, given that every calico cat you have observed has been female, you may infer that the next calico cat you see will be female. This conclusion certainly goes beyond the data you possess, so enumerative induction is ampliative.

With these points in hand, we can consider a further response to the challenge raised in the previous section: (4) There is indeed no logical connection between the satisfaction of explanatory criteria and truth, but this gap does not impair the legitimacy of inference to the best explanation. For, arguably, no pattern of ampliative inference can be shown antecedently to lead to true conclusions (see Induction, epistemic issues in). If the lack of such a guarantee were to make a pattern of ampliative inference illegitimate, it would be improper for us to rely on enumerative induction. Since this result is absurd, there can be no force to the demand that explanatory goodness be demonstrably associated with truth.

However, not all patterns of ampliative inference are reasonable or acceptable. Hence, (4) as such does not establish that inference to the best explanation, in particular, has anything to recommend it. The outcome would be more telling if inference to the best explanation could be more closely linked with enumerative induction. Proceeding along these lines, Gilbert Harman has argued forcefully that all enumerative induction really *is* inference to the best explanation (at least implicitly). If so, the legitimacy we accord to induction cannot be wholly denied to inference to the best explanation.

A difficulty for this view is that we seem to make inductive inferences that in no way serve to explain what has been observed. For example, you might notice that there have been fewer people in the supermarket on Tuesdays than on other days. You conclude by induction that Tuesday is in general the least crowded day at the market. Yet, you may have no explanation at all for what you have observed, no idea why the store has had fewer customers on Tuesdays. It is therefore difficult to see how inference to the best explanation enters into your inductive reasoning. This objection follows Ennis (1968).

Still, there is something suggestive about the notion that inference to the best explanation is of a piece with enumerative induction. Suppose that inference to the best explanation favours simple hypotheses. The inductive extrapolation of observed regularities to other times and places also displays a methodological preference for certain kinds of uniformity or simplicity. This point is highlighted by various cases which can equally well be treated as instances of explanatory inference or of enumerative induction. Suppose you are trying to determine the functional dependence of two quantities, *X* and *Y*, and you have collected data points like (1,1), (2.5, 2.5), (4,4), and (5,5). It would be natural and reasonable to suppose that the function is *X* = *Y*, representable as a straight line passing through the data points. Reaching the conclusion *X* = *Y* can be thought of as a simple extrapolation from the data given, that is, as an example of enumerative induction. There are, however, indefinitely many wavier curves that pass through the given data points – for example, the graph of the function *Y* = sin (2 π *X*) + *X*. The choice of a straight line to connect the points is sometimes cited as a paradigm of inference to the best explanation; one is opting for the simplest hypothesis (in this case, the simplest curve or function) that accounts for the data (see Simplicity (in scientific theories). If curve-fitting cases provide reason to think that enumerative induction and inference to the best explanation really merge or overlap, a critic will be unable to accept one wholeheartedly while rejecting the other across the board.

Vogel, Jonathan. Inference to the best explanation and enumerative induction. Inference to the best explanation, 1998, doi:10.4324/9780415249126-P025-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/inference-to-the-best-explanation/v-1/sections/inference-to-the-best-explanation-and-enumerative-induction.

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