John Maynard Keynes and Frank Ramsey: Probability logic
There was another respect in which Peirce linked together quantitative induction and hypothetic inference, for with regard to both he insisted on the importance of what he called 'predesignation'. Consider, for example, Michael Faraday's first law of electrolysis, which states that when an electric current passes through an electrolytic solution for a certain period of time, the mass of the material separated by the passage of the current is proportional to the strength of the current. We can, of course, collect experimental evidence relevant to this law. We examine, in effect, a sample of electrolytic solutions and find that, in each case, material is separated by the passage of an electric current in accordance with the law. In the light of this evidence we conclude that it is probable that the law is true. But, Peirce claimed, it is essential to the soundness of this probable argument that we begin our examination of electrolytic solutions knowing what characteristic we are concerned with, namely their capacity to deposit material in accordance with Faraday's law. We must, that is, specify or 'predesignate' the characteristic identified in the law beforehand. For suppose we do not do this, but instead simply examine and perform experiments with electrolytic solutions, looking for some undesignated characteristic which they all have in common. We might, if we are particularly lucky, notice that they all have the characteristic identified in Faraday's law. But there will be an indefinite number of other characteristics common to all the electrolytic solutions in the sample, no matter how large the sample. In most cases, their sharing the characteristic is no more than a fortuitous coincidence, and it would be a mistake to use quantitative induction to conclude that all electrolytic solutions have that characteristic. They might, for example, all have been experimentally examined on days other than Sundays. Or they might all have been experimentally examined in Faraday's laboratory in the Royal Institution. But an inductive conclusion based on these and other 'artificial' characteristics would be false. So, if we predesignate no characteristic of a sample, quantitative induction from the sample to a population is illegitimate.