(3) The major premiss may be an imperfect induction, based on evidence that does not include the conclusion. As an example, we may take the reasoning involved in testing the nature of a given substance in practical chemistry. In a reasoning of this kind our immediate starting point is general knowledge of the properties of chemical substances. This knowledge has been inductively obtained, but it is impossible that it should in the slightest degree depend on any antecedent acquaintance with the properties of the particular substance which is now to be investigated for the first time. Or, again, we may take astronomical inferences based on the law of universal gravitation. That law is an induction based on particular observations, but it implies an infinite number of facts that form no part of the evidence on which it is accepted as true; and many of these facts are in the first instance brought to our notice as inferences from the law, not as data leading up to it. If it is affirmed that, in cases such as these, the major premisses cannot legitimately be established independently of the conclusions syllogistically derived from them, then 429 the validity of imperfect induction as a process of arriving at knowledge must be denied.
If asked to meet the argument contained in the preceding paragraph, Mill would doubtless refer to his doctrine of the function of the major premiss in a syllogism. The real proof of the conclusion of a syllogism, he would say, is to be found, not in the major premiss itself, but in the evidence on which the major premiss is based: the major premiss is nothing more than a memorandum of evidence from which the conclusion might be directly obtained: the intervention of the major premiss is often convenient, but it is not an essential link in the passage from the ultimate data to the conclusion. In reply, it may be said that there is at any rate a shifting of the ground here, and that Mill’s doctrine, even if accepted, fails to justify the charge that every syllogism involves petitio principii ; for it is admitted that the conclusion does not itself constitute any part of the data from which the major premiss is obtained. We must, however, go further and reject the doctrine on the ground that there are at any rate some cases in which the general law expressed by the major premiss is an absolutely necessary link in the argument. Thus, to take but one illustration, there are many consequences of the law of universal gravitation which it would be quite impossible to infer directly from the evidence lying behind that law without the intervention of the law itself.
Having regard then to instances such as those adduced above, we must reject the view that syllogistic reasoning essentially involves petitio principii, in the sense of circulus in probando. Any plausibility that the opposed view may possess depends upon some confusion between the statement that every syllogism is guilty of petitio principii in the above sense and the statement that in every syllogism the premisses presuppose the conclusion in the sense that they could not be true unless the conclusion were true.
The latter statement is applicable not only to syllogistic, but to all demonstrative, inference. The question may indeed be raised whether it is not applicable to all valid inference whatsoever. It is in fact one horn of the dilemma referred to in section [377].
430 At any rate it is a misuse of language to speak of a reasoning as involving petitio principii on this ground. By petitio principii is always understood a certain form of fallacy. But in making explicit what to begin with is merely implicit there is nothing that can by any stretch of language be termed fallacious. To say that all deductive science is nothing but a huge petitio principii is clearly an absurdity. The most that can be said is that in all demonstrative reasoning (so-called) there is really no inference from premisses but only the interpretation of premisses. So far as this is a mere question of language, it may suffice to note the paradoxical conclusions to which it leads; for example, that in the whole of Euclid there is no such thing as inference or proof. So far as it is not a mere question of language, it turns on points that we have already discussed, for instance, the possibility of there being an advance in knowledge subjectively considered although from the objective standpoint the conclusions reached contain nothing new. It is unnecessary to repeat the discussion with special reference to the syllogism.
CHAPTER X.
EXAMPLES OF ARGUMENTS AND FALLACIES.
382. In how many different moods may the argument implied in the following proposition be stated?
“No one can maintain that all persecution is justifiable who admits that persecution is sometimes ineffective.”
How would the formal correctness of the reasoning be affected by reading “deny” for “maintain”? [V.]
383. No one can maintain that all republics secure good government who bears in mind that good government is inconsistent with a licentious press.
What premisses must be supplied to express the above reasoning in Ferio, Festino and Ferison respectively? [V.]