ScienceWeek

HISTORY OF SCIENCE: ON TESTING HYPOTHESES

The following points are made by Peter Lipton (Science 2005 307:219):

1) In the case of "accommodation", a hypothesis is constructed to fit an observation that has already been made. In the case of "prediction", the hypothesis, though it may already be partially based on an existing data set, is formulated before the empirical claim in question is deduced and verified by observation. Well-supported hypotheses often have both accommodations and successful predictions to their credit. Most people, however, appear to be more impressed by predictions than by accommodations.

2) Edmond Halley (1656-1742) was able to account for the observed comets of 1531, 1607, and 1682 as a single object with a perturbed elliptical orbit. Natural philosophers took some notice when he published his views in the Philosophical Transactions in 1705, but it was only when his prediction of the return of the comet in 1758 was confirmed that the entire European intellectual world embraced Halley's Comet. The single prediction appears to have been far more impressive than the three accommodations [1].

3) Was this reaction rational? It is surprisingly difficult to establish an advantage thesis: to show that predictions tend to provide stronger support than accommodations. The content of the hypothesis, of the statements needed to link the hypothesis to the observation, of background beliefs, and of the observation itself may all be unaffected by the question of whether the observation was accommodated or predicted, and these seem to be the only factors that can affect the degree to which a hypothesis is supported by evidence. The difference between accommodation and prediction seems merely one of timing. Some observations are more reliable and more telling than others, but the date when they were made seems to be irrelevant [2 5].

4) To make the case against the advantage thesis more vivid, consider a fictitious case of twin scientists. These twins independently and coincidentally generate the same hypothesis. The only difference between them is that one twin accommodates an observation that the other predicts. If there really were an advantage to prediction, we ought to say that the predictor has more reason to believe the hypothesis than the accommodator, though they share hypothesis, data, and background beliefs. This is counterintuitive, but things get worse. Suppose that the twins meet and discover their situation. It seems clear that they should leave the meeting with a common degree of confidence in the hypothesis they share. If they came to the meeting with different degrees of rational confidence in their hypothesis, at least one of them ought to leave with a revised view. But what level should they settle on: the higher one of the predictor, the lower one of the accommodator, or somewhere in between?

5) There seems no way to answer the question. Moreover, if there is a relevant difference between prediction and accommodation, then the twin who should revise her view after she meets her sibling must not revise simply because she knew all along that someone like her twin might have existed. If revision were in order merely because of this possibility, then the difference between accommodation and prediction would vanish. Whenever data are accommodated, we know that there might have been someone who produced the hypothesis earlier and predicted the data instead. But how can the question of whether there actually is such a person make any difference to our justified confidence in the hypothesis? Any adequate defense of the putative difference between prediction and accommodation will have to explain how an actual meeting could be different from a hypothetical meeting. Those who reject the distinction seem to be on firm ground when they maintain that no such explanation is possible.

6) In summary: Observations that fit a hypothesis may be made before or after the hypothesis is formulated. Can that difference be relevant to the amount of support that the observations provide for the hypothesis? Philosophers of science and statisticians are both divided on this question, but there is an argument that predictions ought to count more than accommodations because of the risk of "fudging" that accommodations run and predictions avoid.

References (abridged):

1. M. Grosser, in Dictionary of Scientific Biography, C. C. Gillispie, Ed. (Scribner's, New York, 1970), vol. I, pp. 53 54

2. J. S. Mill, A System of Logic (Longmans, London, ed. 8, 1904), III, xiv, 6

3. J. M. Keynes, Collected Writings of John Maynard Keynes Vol. VIII: A Treatise on Probability (Macmillan, London, 1973)

4. P. Horwich, Probability and Evidence (Cambridge Univ. Press, Cambridge, 1982), pp. 108 117

5. G. Schlesinger, Australas. J. Philos. 65, 33 (1987)

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