(_c_) _Mere_ counting or “enumeration” only helps you in induction by comparison with some other numerical result, and, if imperfect, only to the extent of suggesting that there {153} is a common cause or there is not a common cause. _E.g._ if you throw a six with one die fifty times running, you infer that the die is probably loaded. This is because you compare the result with that which you expect if the die is fair, viz. a six once in every six throws. You infer that there is a special cause favouring one side. The principle is that ignorance is impartial. If you know no reason for one case more than another, you take them as equal fractions of reality; if results are not equal fractions of reality, you infer a special reason favouring one case. [1] Pure counting cannot help you in Induction in any way but this. _Perfect Induction_ simply means that the total is limited and the limit is reached; you have counted 100 per cent, of the possible cases, and the chance becomes certainty. The result is a mere collective judgment. [1] See Lecture IX, p. 144, note. _System_ (_d_) The principle of scientific system is quite a different thing. Essentially, it has nothing to do with number or with a generalised conclusion. It is merely this, “What is once true is always true, and what is not true never was true.” The aim of scientific induction is to find out “What _is_ true,” _i.e._ what is consistent with the given system. We never doubt this principle; if we did we could have no science. If observation contradicts our best-established scientific laws, and we cannot suppose an error in the observation, we must infer that the law was wrongly, _i.e._ untruly stated. Therefore, as Mill says, one case is enough, _if_ you can find the truth about it. People object that you cannot make a whole science out of one case, and therefore you must have a number of instances. That is a {154} _practical_ point to be borne in mind, but it has no real scientific meaning. “Instance” cannot be defined except as one observation, which is a purely accidental limitation. The point is, that you use your instances not by counting cases of given terms, but by ascertaining what the terms really are (_i.e._ modifying them), and what is their real connection. This is the simple secret of Mill’s struggle to base scientific Induction, on Induction by simple Enumeration; the latter is not the evidence, but the beginning of eliciting the evidence--so that the Scientific Induction is far more certain than that on which Mill bases it. Aristotle’s statement is the clearest and profoundest that has ever been made. [1]