DEDUCTIVE TESTING 345 



perties and relations, must follow. Thus, given that my cook has 

 certain properties (e.g. the will and the ability), given the existence 

 of food in the house, given a multitude of other things, it follows 

 necessarily that my housemaid will presently summon me to 

 breakfast. Here, I do not know all the conditions as perfectly as 

 in geometry, but, if I did and could think as adequately about a 

 matter so complicated, I could be just as sure in the one case as 

 in the other. The important point is that in this case also I have 

 reached the expectation that I shall be summoned to breakfast 

 otherwise than by an induction from a simple enumeration of 

 instances of former like events. I could have ignored the qualities 

 of the cook and the other things concerned and reached the 

 expectation by remembering that I have been so summoned for a 

 long series of mornings. But, as a fact, I did not do so. It is 

 when we think in terms of cause and effect that the need for test- 

 ing our thinking by making a deductive appeal to reality arises. 

 Such a testing is necessary even in the mathematics in which the 

 conditions are relatively simple and clearly defined, and the 

 chances of error are correspondingly slight. Thus, when we 

 multiply one number by another (e.g. 123 by 345), we are able to 

 make sure that the product, the conclusion to which we have led 

 by our reasoning, is correct only by some such test as is furnished 

 by dividing it by one of the factors and then ascertaining whether 

 the quotient agrees with the other factor. The more difficult the 

 problem, the more complex the conditions or the more prolonged 

 the chain of reasoning, the more necessary it is to apply tests ; 

 as in biology, where the conditions are often exceedingly complex 

 and so obscure that it is often difficult to separate essentials 

 from non-essentials, real causes and effects from accidental 

 accompaniments. 



582. In science, as in everyday life, we endeavour to deduce 

 effects from causes, or causes from effects, and so link up our 

 knowledge in uniformities, which, though based ultimately on 

 results obtained by simple enumeration, are other, and additional, 

 and as superior to them as a temple to its foundations. All the 

 sciences in which we have succeeded best in this endeavour are the 

 most ' scientific/ the most deductive, the most completely knit into 

 compacted wholes. 1 Mathematics and physics are examples. 

 Zoology and botany formerly rested on a simple enumeration of 

 likenesses, differences, co-existences, and sequences. Doubt- 

 less they had practical uses and satisfied scientific workers of that 

 1 See J. S. Mill, Logical!, iv. 4. 



