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.No contradiction isinvolved in the conjunction of the premisses of an induction with thenegative of its conclusion.(2) It does not follow nor is it true that it is proper to describe as accidental or miraculous the states of affairs to which we are or wish tobe able to make causal inference.We apply these adjectives to what isunusual or irregular or to what is not explained by any or any knowncausal law and not to states of affairs for which a deductive metaphysicianfails to find a demonstration. Contingent is not synonymous with miraculous or with fortuitous.(3) Scientists general propositions are neither commands nor signals,statements or recommendations of habits.They are truths or falsehoods.(4) In neither of the usual senses of hypothesis is it true either thatall the general propositions of science and ordinary experience or all theirsingular and general propositions are mere hypotheses.For in some sense of established some singular and general proposi-tions are established.And there is a contradiction in describing aproposition as a hypothesis (i.e.conjectural proposition) but established. 138 COLLECTED PAPERS: VOLUME 2Some general propositions are established to be the explanations of othersalready known to be true.These are called laws and not hypotheses.And some non-general propositions are known to be true.These are called matters of fact or facts and not hypotheses.I might here do a little terminological sorting.In one sense of hypothesisany proposition, singular or general, which is only conjectured to be true,is a hypothesis.In another sense, a proposition is a hypothesis which issuch that if true it would be the explanation of some other acceptedproposition or range of accepted propositions.A protasis or antecedentfrom which would follow certain apodoses or consequents, themselvestaken to be true, is said to be a possible explanation of those consequents.It is said actually to be their explanation when it is itself taken to be true.And then we say, not if , but because.In this sense a hypothesis is aconjectured protasis.Such a conjectured protasis is usually a more generalproposition than the propositions which it explains or would explain, butthis is not always the case, as for example in history and detection.These two uses overlap.For a conjectured protasis is a case of a con-jectured proposition and usually a conjectured proposition is conjecturedas a possible explanation of something else which is not conjectural.In neither use is hypothesis equivalent to hypothetical propositionwhere this is a title for an if-then proposition.An if-then propositionneed not be conjectural and need not be as a whole a protasis to somefurther apodoses, though of course an if-then proposition can be eitheror both.But in the second use a hypothesis is always a protasis in an if-then proposition and in its first use it is usually so.It is worth while to make these points.For a law-proposition, that is,a general proposition which explains or would explain a range of lessgeneral accepted propositions (1) is an if-then proposition, i.e.a variableor open hypothetical; (2) it is often itself conjectural and not establishedand (3) (by definition) it is an explanation or a possible explanation of arange of other propositions which are known or taken to be true.On the other hand I have qualms about one of Miss MacDonald sprofessed detections of English idiom-nuance.To call a law-proposition established and to call it known do not seem to me to be the samething: and though commonsense may say that we know certain law-propositions, I think that this is either false or else a boastful misuse of the CHAPTER 10: INDUCTION AND HYPOTHESIS 139word.What we do, perhaps, often know is that a law-proposition is sowell established that it would be foolish to collect further evidence for itor to re-scrutinize our present evidence for it.We are often sure andwarranted in being sure of a law-proposition.But to be sure is not thesame as to know.There is no contradiction in saying that Newton was sureof so and so and was justified in being sure of it, and yet was mistaken; butthere is a contradiction in saying that he knew it and was wrong.However, even so, I agree with Miss MacDonald that we should beobliterating real and important distinctions if we followed the prescrip-tions of some logicians and called all propositions alike conjecturalor problematic , or all alike merely more or less probable.There is adifference between the propositions which we should naturally expresswith is , was and will be and those which we should naturally expresswith may be , might have been , probably and very, very probably
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