276 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



the extensive variations in certain other quantities, and the 

 measured values of the latter become the measured values 

 of the former. For example, heat intensities are measured 

 by variations in the length of a column of mercury, weight 

 intensities by the distortions in a coil spring, and electricity 

 intensities by the spatial deflection of a coil in a magnetic 

 field. Similarly, though much more crudely, the intelligence 

 of an individual may be measured by counting the number 

 of questions of a certain kind which he is able to answer 

 correctly, and pleasures may be measured by the amount 

 of money required to produce them. Finally, measurement 

 of intensive quantities which have no extensive correlates 

 involves an application of the principle of order; the quan- 

 tities to be measured are arranged in a series by virtue of 

 some ordering relation; one member of the series is then 

 selected more or less arbitrarily as the standard element 

 and given a number, such as 1 or 0; finally, the remaining 

 members of the series are numbered, and values are as- 

 signed to them in terms of their distance in the series from 

 the standard element. This is essentially the way in which 

 hardness and specific gravity are measured, and it is com- 

 monly employed in the measurement of various commercial 

 products such as the coarseness of sandpaper, the quality of 

 coal, and the delicacy of canned fruits and meats. 



quantity: scientific content 



Scientific quantity is measured value. Hence the field 

 of scientific quantity is the field of numbers. But this 

 statement requires clarification. Measuring and counting 

 are both activities of attaching numbers to events, and they 

 should not be confused. In the first place, number is prop- 

 erly an attribute only of pluralities, hence always applies 

 to classes or aggregates; measured value, on the other hand, 

 applies to a single event by virtue of its position in a series. 

 Number, therefore, applies not to the simple events them- 

 selves but to the aggregate in which they occur; measured 

 value, however, applies directly to the simple events them- 



