(1) I have found that such an object has always been attended with such an effect.
(2) I foresee that other objects which are in appearance similar, will be attended with similar effects.
He goes on: “I shall allow, if you please, that the one proposition may justly be inferred from the other; I know in fact that it always is inferred. But if you insist that the inference is made by a chain of reasoning, I desire you to produce that chain of reasoning. The connection between these propositions is not intuitive. There is required a medium which may enable the mind to draw such an inference, if, indeed, it be drawn by reasoning and argument. What the medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it who assert that it exists, and is the origin of all our conclusions concerning matters of fact.”
If we regard the matter more closely we may say with certainty: This medium exists not as a substance but as a transition. When I speak in the proposition of “such an object,” I already have “similar” in mind, inasmuch as there is nothing absolutely like anything else, and when I say in the first proposition, “such an object,” I have already passed into the assertion made in the second proposition.
Suppose that we take these propositions concretely:
(1) I have discovered that bread made of corn has a nourishing effect.
(2) I foresee that other apparently similar objects, e.g., wheat, will have a like effect.
I could not make various experiments with the same corn in case (1). I could handle corn taken as such from one point of view, or considered as such from another, i.e., I could only experiment with very similar objects. I can therefore make these experiments with corn from progressively remoter starting points, or soils, and finally with corn from Barbary and East Africa, so that there can no longer be any question of identity but only of similarity. And finally I can compare two harvests of corn which have less similarity than certain species of corn and certain species of wheat. I am therefore entitled to speak of identical or similar in the first proposition as much as in the second. One proposition has led into another and the connection between them has been discovered.
The criminological importance of this “connection” lies in the fact that the correctness of our inferences depends upon its discovery. We work continuously with these two Humian propositions, and we always make our assertion, first, that some things are related as cause and effect, and we join the present case to that because we consider it similar. If it is really similar, and the connection of the first and the second proposition are actually correct, the truth of the inference is attained. We need not count the unexplained wonders of numerical relations in the result. D’Alembert asserts: “It seems as if there were some law of nature which more frequently prevents the occurrence of regular than irregular combinations; those of the first kind are mathematically, but not physically, more probable. When we see that high numbers are thrown with some one die, we are immediately inclined to call that die false.” And John Stuart Mill adds, that d’Alembert should have set the problem in the form of asking whether he would believe in the die if, after having examined it and found it right, somebody announced that ten sixes had been cast with it.
We may go still further and assert that we are generally inclined to consider an inference wrong which indicates that accidental matters have occurred in regular numerical relation. Who believes the hunter’s story that he has shot 100 hares in the past week, or the gambler’s that he has won 1000 dollars; or the sick man’s, that he was sick ten times? It will be supposed at the very least that each is merely indicating an approximately round sum. Ninety-six hares, 987 dollars, and eleven illnesses will sound more probable. And this goes so far that during examinations, witnesses are shy of naming such “improbable ratios,” if they at all care to have their testimony believed. Then again, many judges are in no wise slow to jump at such a number and to demand an “accurate statement,” or even immediately to decide that the witness is talking only “about.” How deep-rooted such views are is indicated by the circumstance that bankers and other merchants of lottery tickets find that tickets with “pretty numbers” are difficult to sell. A ticket of series 1000, number 100 is altogether unsalable, for such a number “can not possibly be sold.” Then again, if one has to count up a column of accidental figures and the sum is 1000, the correctness of the sum is always doubted.