What is Science

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I have only to divide the numbers in the second column by 7 in order to arrive at those in the first, or multiply those in the first by 7 in order to arrive at those in the second. That is a definite rule which I can always apply whatever the numbers are ; it is a rule which might always be true, but need not always be true ; whether or no it is true is a matter for experiment to decide. So much is obvious ; but now I want to ask a further and important question. How did we ever come to discove
...r this rule ; what suggested to us to try division or multiplication by 7 : and what is the precise significance of division and multiplication in this connexion ?
THE SOURCE OF NUMERICAL RELATIONS The answer to the first part of this question is given by the discussion on p. 123. Division and multiplication are operations of importance in the counting of objects ; in such counting the relation between 21, 7, 3 (the third of which results from the division of the first by the second) corresponds to a definite relation between the things counted ; it implies that if I divide the 21 objects into 7 groups, each containing the same number of objects, then the number of objects in each of the 7 groups is 3.


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