Kowalenko, Robert
(2007)
A CurveFitting Approach to Ceteris ParibusLaws.
In: UNSPECIFIED.
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Abstract
Lawlike generalisations hedged with a ceteris paribusclause such as widely in use in psychology, the social and biological sciences, are best construed as incomplete strict laws. These incomplete laws can be “fleshed out” by adding a set of enabling, or completing, conditions to their antecedent. In other words, the logical form of a cplaw, ceteris paribus (A > B), is (A & C > B). The nature of C must be subject to nonad hoc constraints, however, failing which all putative ceteris paribusgeneralisations will be trivially true. Two simple and plausible constraints are that: (i) A and CB be jointly sufficient for the consequent of the law, and (ii) the relevant completer also occur in the antecedents of other lawsin other words, that there be many other lawlike generalisations of the form (D & C > E), (F & C > E), etc. Apparent counterexamples to this proposal can be disarmed by interpreting the epistemology of cplaws as a curvefitting problem, which consists in determining the relevant nomic regularity and plotting the correct curve over a very noisy dataset that contains large numbers of outliers and anomalies. The process of specifiying the content of the ceteris paribusclause that is hedging a lawcandidate is in fact isomorphic with the process of determining which parts of one's data are outlying and anomalous, and which are part of the regularity. I submit that statistical theorems such as the Akaike Information Criterion (AIC) are instrumental in the latter process, and therefore also in the former. AIC states that a lawhypothesis which minimizes both the number of adjustable parameters and error variance (i.e. a hypothesis that achieves an optimal balance between simplicity and adequacy to the data), displays the highest estimated accuracy of prediction of future data from the same distribution. I go on to discuss how AIC in combination with conditions (i) and (ii) illustrates the fundamental difference between a ceteris paribuslaw and a statistical law, and how it yields the distinction between spurious and genuine hedged regularities that is necessary to make cplaws “respectable”. Thus, I show how popular putative problem cases, such as “turtles live long lives”, can be dealt with by the theory. Finally, I utilise work by Lange (2000, 2002) to deflect the criticism that cplaws are, by their very nature incompletable, and hence indeterminate. I conclude that the curvefitting approach provides a very simple, powerful, and yet metaphysically conservative account of ceteris paribuslaws.
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