DESCRIPTION AND INTERPRETATION 503 



which facts are gathered ought to make a difference in the kind of 

 thinking by means of which they are welded into sciences. There 

 is, however, a difference between sciences which is more important 

 in that to it is due a vast difference in the thinking by which they 

 are created. Some sciences are founded on a multitude of facts, 

 and some on a very few. The mathematical sciences are examples 

 of the latter class. Thus, " All the inductions involved in all 

 geometry are comprised in those simple ones, the formulae of 

 which are the Axioms, and a few of the so-called Definitions. 

 The remainder of the science is made up of the processes em- 

 ployed for bringing unforeseen cases within these inductions ; or 

 (in syllogistic language) for proving the minors necessary to 

 complete the syllogisms ; the majors being the definitions and 

 the axioms. In those definitions and axioms are laid down the 

 whole of the marks, by an artful combination of which it has been 

 found possible to discover and prove all that is proved in geometry. 

 The marks being so few, and the inductions which furnish them 

 being so obvious and familiar; the connecting of several of them 

 together, which constitutes Deductions or Trains of Reasoning, 

 forms the whole difficulty of the science, and, with a trifling excep- 

 tion, its whole bulk; and hence Geometry is a Deductive Science." 1 

 The definitions are precise descriptions. The axioms are laws. 

 We have defined a law as a description of a uniformity in the 

 sequence of phenomena, and we saw that it is usually possible 

 to deduce necessary consequences from it about sequences of 

 phenomena, 



820. Physics in all its branches and throughout its whole vast 

 extent is another science that has been developed from a few 

 essential facts which have been welded into laws from which the 

 rest of the science has been deduced. Relatively speaking, very 

 little mere recollection is needed by the mathematician or the 

 physicist. His * knowledge,' however toilsomely acquired, con- 

 sists mainly in a special skill in thinking about sequences. 



821. Astronomy is a science which is founded on an immense 

 number of facts. Thus there are millions of stars, only a few of 

 which the astronomer has named and attempts to recollect. If 

 he merely classified his facts according to co-existences and re- 

 semblances, for example if he classified the heavenly bodies accord- 

 ing to their apparent magnitudes, luminosities, and positions relative 

 to one another, astronomy would be a very incomplete science, and 

 the best astronomer would be a powerful photographic camera. 



1 J. S. Mill, Logic, ii. iv. 4. 



