June 8, 1883.J 



SCIENCE. 



515 



some 3'ears back, will be glad to find here, in a 

 more elaborate and technical form, the theor}- 

 of induction that was outlined in one of those 

 papers. It is, philosophicallj' considered, the 

 most ingenious account of the subject that we 

 have an3'where read ; but, as said, vs'e still 

 hesitate to accept this account as complete. 

 But space forbids anj' lengthj' statement of 

 our difficulties in this connection. We must 

 be content with few words. 



Mr. Peirce brings the theorj' of induction 

 into direct connection with the general theor}' 

 of probable inference, but does so in a way of 

 his own. He rejects, in the first place, any 

 notion that the occurrence or non-occurrence 

 of an event in the past in any way affects the 

 probability of its occurrence in the future. 

 The doctrine of inverse probabilities, as it has 

 hitherto been applied, Mr. Peirce considers as 

 furnishing no foundation for the theory' of in- 

 duction, and equallj' does he reject our old and 

 trusted friend, the postulate of the uniformity 

 of nature, as the basis of inductive inference. 

 One maj- well ask, remembering Hume, what 

 j-et remains when these faithful allies have 

 failed. But Mr. Peirce's insight finds j'et 

 another resource, — not the probability that a 

 given event will be repeated in the future, but 

 the probability that a given form of inference 

 would, in an}' constitution of the universe 

 whatever, tend in the long-run to lead us to 

 truth rather than to error : this is, for Mr. 

 Peirce, the ground of the true inductive infer- 

 ence. Thus, then, the universe need have no 

 peculiar constitution to render inductive infer- 

 ence valid. 



The inductive inference, then, is to be ex- 

 pressed as one form of probable inference. 

 Simple Probable Deduction is exemplified in 

 the tj'pical syllogism : 



The proportion p of the M's are P's ; 



S is an M ; 



It follows, with a probability p, that S is a 

 P. 

 This means that the conclusion, S is P, would 

 in the long-run, and if S is chosen at random, 

 be true in a proportion, p, of cases. — More 

 complex is Statistical Deduction, of the form: 



The proportion r of the M's are P's ; 



S', S", S'" are a numerous set, taken at 

 random from among the M's : 



Hence, probably and approximately, the 

 proportion r of the S's are P's ; 

 that is, the more M's we choose at random, 

 the more likely it is that the same proportion 

 of P's will appear among the chosen M's as 

 exists among the whole actual number of M's. 

 — But now suppose, that, knowing nothing of 



the real proportion of P's among the M's, we 

 undertake to discover this proportion by sam- 

 pling the M's. Then we have but to employ 

 our previous principle, and saj' that the more 

 M's we choose at random, the more will it be 

 likel}' that the proportion of P's among the 

 chosen M's will equal, and so will reveal, 

 the actual proportion of the P's among all the 

 M's. But now we have induction. We do 

 not assume anj' thing about the constitution of 

 the unknown parts of the class M. We make 

 no postulate of the ' uniformitj' ' of the class 

 M. That I have found one M that is P, or 

 more, makes it no more probable that the next 

 M found will be P. But we conclude only 

 that the conclusion reached in the following 

 syllogism is reached bj' a method or precept 

 that must in the long-run lead us towards 

 truth, and away from error. The tj'pical in- 

 ductive syllogism is : 



S', S", S'", etc., form a numerous set, taken 

 at random from among the M's ; 



S', S", S'", etc., are found to be — the pro- 

 portion p of them — P's : 



Hence, probably and approximatelj', the 

 same proportion, p, of the M's are P's. 



Thus sampling, continued and fair, tends 

 toward truth, and gives us justifiable amplia- 

 tive inferences, whatever the constitution of 

 the things about which we infer. Mr. Peirce 

 applies a similar analysis to the form of induc- 

 tion which he calls hypothesis. 



This is a verj- inadequate sketch of a view 

 that deserves serious attention. Of all attempts 

 at a purely empirical theory of our knowledge 

 of nature, this is one of the most promising. 

 We should be sorry to prejudge it in anj' waj' 

 by adding to our lame exposition hasty criti- 

 cism ; but, when we say that the theory seems 

 to us to fail just at the most important point, 

 we express what, fairlj' or unfairly-, many 

 readers will feel. The most important point 

 lies in the words ' chosen at random.' Mr. 

 Peirce himself, with perfect fairness, suggests 

 some of the difficulties involved in this word. 

 ' Sampling,' he saj-s ' is a real art, well de- 

 serving an extended study b}- itself.' But 

 does not this art depend for its very existence 

 on an a priori assumption about the structure 

 of the universe ? Is not a world of which we 

 know that in it we can choose our S's at ran- 

 dom from among the M's a world of which 

 we already must know a good deal? Mr. 

 Peirce makes one admission about such a 

 world. It is, he tells us, a world in which we 

 must assume that there are no supernatural 

 and malignant powers at work confusing our 

 choice; i.e., making our supposed random 



