Safety, Strength, Simplicity Nelson Goodman Philosophy of Science, Vol. 28, No. 2. (Apr., 1961), pp. 150-151. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28196104%2928%3A2%3C150%3ASSS%3E2.0.CO%3B2-Z Philosophy of Science is currently published by The University of Chicago Press.
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http://www.jstor.org Fri May 18 08:41:02 2007
SAFETY, STRENGTH, SIMPLICITY
NELSON GOODMAN
When the evidence leaves us with a choice among hypotheses of unequal strength, how is the choice to be made ? Caution would counsel us to choose the weakest, the hypothesis that asserts the least, since it is the least likely to fail us later. But the principle of maximum safety quickly reduces to absurdity; for it always dictates the choice of a hypothesis that does not go beyond the evidence at all. The very opposite proposal has been advanced by Popper1: that the strongest hypothesis not falsified by the evidence should be chosen. But for every hypothesis strong enough to go beyond the evidence, there is an equally strong conflicting hypothesis based upon the same evidence. This is easily shown. Suppose our evidence tells us just that every examined A is a B, and suppose hypothesis HI affirms in addition that every (or even some one) other A is a B. Then hypothesis H,, affirming that every examined A is a B and that every (or the particular one) other A is not a B, likewise conforms to the stated evidence. Hence strength is indifferent as between any projection and its opposite. And to exclude every hypothesis that conflicts with another equally strong one unviolated by the evidence would be, once more, to exclude every hypothesis that goes beyond the evidence at all. Thus although both safety and strength are desirable features of a theory, they are by themselves incompetent criteria for choice. Another and controlling factor, simplicity, must be taken into account. Simplicity has sometimes been mistakenly identified with safety or with strength, but is readily shown to be distinct from both. Suppose we have examined many and widely distributed specimens of maple trees and found them all to be deciduous, and suppose this constitutes our entire evidence. Since we still will not have examined specimens from every small locality, our evidence may then leave us with a choice between the following two hypotheses:
(I) All maples, except perhaps those in Eagleville, are deciduous. (2) All maples are deciduous. T h e second is clearly both the stronger and the simpler. We would incorporate
(2) in our theory, and retreat to (1) only if further evidence indicated that (2) is false. Insertion of the ad hot exceptive clause both weakens and complicates the hypothesis. Cases like this, where the preferable hypothesis is the simpler and stronger one, give plausibility to the view that strength is the measure of simplicity and is the cardinal principle of choice. But exactly comparable 1 In The Logic of Scientific Discovery (London, 1959-from Chapters VI and VII.
150
the German of 1935), especially
SAFETY, STREXGTEI, SIMPLICITY
151
cases point to the opposite conclusion. The stated evidence also leaves unfalsified the hypothesis: (3) All maples whatsoever, and all sassafras trees in Eagleville, are deciduous. Now (3) is stronger than (2) but is less simple and acceptable. T h e expansion made in (3) is as unwelcome as the exception made in (1). Hypothesis (2), although it lies between (1) and (3) in safety and strength, is simpler than and preferable to either. This shows that neither safety nor strength is the measure of simplicity, and that simplicity takes precedence over both as a factor in the choice of hypotheses. The delicate problem of balancing safety and strength against each other is significant only as between hypotheses of equal simplicity. If neither safety nor strength determines simplicity, what does ? Formulation of general standards for comparing the simplicity of hypotheses is a difficult and neglected task. Here brevity is no reliable test; for since we can always, by a calculated selection of vocabulary, translate any hypothesis into one of minimal length, the simplicity of the vocabulary must also be appraised. I am inclined to think that the standards of simplicity for hypotheses derive from our classificatory habits as disclosed in our language, and that the relative entrenchment of predicates underlies our judgment of relative simplicity; but spelling this out takes some pains. Merely, to reject unfamiliar predicates vrrholesale in favor of familiar ones would be to disallow the introduction of needed new terms into scientific language. Furthermore, we must ordinarily decide not merely which of two hypotheses is the simpler but which one makes for the simpler total theory. I have discussed these matters in Fact, Fiction, and Forecast2; and the criteria of projectibility I have outlined there in terms of entrenchment is perhaps essentially a simplicity criterion. But the whole matter wants more study. What is evident is that adequate canons of induction must incorporate criteria of simplicity that cannot be given solely in terms of strength or safety.
Warvard University Press, 1955; see especially Chapter IV.
