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SCIENCE 



[N. S. Vol. XXXVIII. No. 982 



standing of the logic of scientific method? 

 I venture still to add these few summary 

 comments as I close. 



Inductive scientific generalizations, in 

 the logically simplest cases, depend upon 

 what Mr. Charles Peiree has defined as the 

 method of taking a "fair sample" of a 

 chosen type of facts. Thus one who sam- 

 ples, to use Mr. Peiree 's typical example, 

 a cargo of wheat, by taking samples from 

 various parts of the cargo, carefully select- 

 ing the samples so that they shall not tend 

 to represent one part of the cargo only, but 

 any part chosen at random, employs essen- 

 tially the same inductive method which, as 

 I gather from inquiry, Virchow used in 

 reaching the main fundamental generaliza- 

 tions of his cellular pathology. Samples 

 chosen for investigation from a great va- 

 riety of growths show, both in the case of 

 normal and in the case of morbid tissues, 

 that in the observed samples there is suffi- 

 cient evidence of the origin of each cell 

 from a previous cell, and evidence too that 

 the tissue is formed of generations of cells 

 whose beginnings, both in the normal and 

 in the morbid growths, lead back to parent 

 cells of certain definable types. This out- 

 come of observation, repeatedly confirmed 

 by samples fairly chosen, that is, by sam- 

 ples chosen from various organisms, from 

 various tissues, and chosen not merely to 

 illustrate the theory, but to represent as 

 well as may be all sorts of growths — this, 

 I say, leads to the probable assertion that 

 this kind of origin of tissues is universal, 

 and that one is dealing with a genuine law 

 of nature. The probability of such a gen- 

 eralization can be tested in a more or less 

 exact way, as Peiree has shown, by the 

 principles of the mathematical theory of 

 probabilities. Inductions of this type we 

 may call statistical inductions. They pre- 

 suppose nothing at the outset as to what 

 laws are present in the world of the facts 



which are to be sampled. The technique 

 of induction here consists wholly in learn- 

 ing, (1) how to take fair samples of the 

 facts in question, and (2) how to observe 

 these facts accurately and adequately. 

 This kind of induction seems to be espe- 

 cially prominent in the organic sciences. 

 Its logical theory is reducible to the gen- 

 eral theory of probability, since fair sam- 

 ples, chosen at random from a collection of 

 objects, tend to agree in their constitution 

 with the average constitution of the whole 

 collection. 



But now, as you well know, a great deal 

 of scientific work consists of the forming 

 and testing of hypotheses. In such cases 

 the inductive process is more complex. 

 Peiree defines it first as the process of 

 taking a fair sample from amongst the 

 totality of those consequences which will 

 be true if the hypothesis to be tested is 

 true, and secondly as the process of 

 observing how far these chosen con- 

 sequences agree with experience. If a 

 given hypothesis, in case it is true, de- 

 mands, as often happens, countless conse- 

 quences, you of course can not test all of 

 these consequences, to see if every one of 

 them is true. But you select a fair sample 

 from amongst these consequences, and test 

 each of these selected consequences of the 

 hypothesis. If they agree with experience, 

 the hypothesis is thereby rendered in some 

 degree probable. The technique of induc- 

 tion now involves at least four distinct 

 processes: (1) The choice of a good hypoth- 

 esis; (2) the computation of certain con- 

 sequences, all of which must be true if the 

 hypothesis is true; (3) the choice of a fair 

 sample of these consequences for a test; 

 and (4) the actual test of each of these 

 chosen consequences. So far as you make 

 use of this method of induction, you need 

 what is called training in the theory of 

 your topic, that is, training in the art of 



