1 92 SCIENTIFIC METHOD IN PHILOSOPHY 



greater than its part. But the word " greater " is one 

 which is capable of many meanings ; for our purpose, we 

 must substitute the less ambiguous phrase " containing a 

 greater number of terms." In this sense, it is not self- 

 contradictory for whole and part to be equal ; it is the 

 realisation of this fact which has made the modern theory 

 of infinity possible. 



There is an interesting discussion of the reflexiveness 

 of infinite wholes in the first of Galileo's Dialogues on 

 Motion. I quote from a translation published in 1730. 1 

 The personages in the dialogue are Salviati, Sagredo, and 

 Simplicius, and they reason as follows : 



" Simp. Here already arises a Doubt which I think is 

 not to be resolv'd ; and that is this : Since 'tis plain that 

 one Line is given greater than another, and since both 

 contain infinite Points, we must surely necessarily infer, 

 that we have found in the same Species something greater 

 than Infinite, since the Infinity of Points of the greater 

 Line exceeds the Infinity of Points of the lesser. But 

 now, to assign an Infinite greater than an Infinite, is what 

 I can't possibly conceive. 



" Salv. These are some of those Difficulties which 

 arise from Discourses which our finite Understanding 

 makes about Infinites, by ascribing to them Attributes 

 which we give to Things finite and terminate, which I 

 think most improper, because those Attributes of Majority, 

 Minority, and Equality, agree not with Infinities, of which 

 we can't say that one is greater than, less than, or equal 

 to another. For Proof whereof I have something come 



1 Mathematical Discourses concerning two new sciences relating to 

 mechanics and local motion, in four dialogues. By Galileo Galilei, 

 Chief Philosopher and Mathematician to the Grand Duke of Tuscany. 

 Done into English from the Italian, by Tho. Weston, late Master, and 

 now published by John Weston, present Master, of the Academy at 

 Greenwich. See pp. 46 ff. 



