PRESIDENTIAL ADDRESS. .'^03 



the vicious method of saying that they are perceptions of a bo<ly. Now, the 

 perceptions of a part of a body are among the perceptions -which compose 

 the whole body. Thus two bodies a and 6 are both classes of perceptions ; and 

 /) is part of a when the class which is b is contained in the class which is a. 

 It immediately follows from the logical form of this definition that if b is part 

 of a, and c is part of b, then c is part of a. Thus tlie relation ' whole to 

 p;nt ' is transitive. Again, it will be convenient to allow that a body is part 

 of itself. This is a mere question of how you draw the definition. With this 

 understanding, the relation is reflexive. Finally, if a is part of b, and b is 

 [lart of «, then a and b must be identical. These properties of ' whole and 

 part ' are not fresh assumptions, they follow from the logical form of our 

 definition. 



One assumption has to be made if we assume the ideal infinite divisibility 

 of space. Namely, we assume that every class of perceptions which is an 

 extended body contains other classes of perceptions which are extended bodies 

 diverse from itself. This assumption makes rather a large draft on the theory 

 of ideal perceptions. Geometry vanishes unless in some form you make it. 

 The assumption is not peculiar to my exposition. 



It is then possible to define what we mean by a point. A point is the class 

 of extended objects which, in ordinai-y language, contain that point. The 

 definition, without presupposing the idea of a point, is rather elaborate, and I 

 have not now time for its statement. 



The advantage of introducing points into Geometry is the simplicity of the 

 logical expression of their mutual relations. For science, simplicity of defini- 

 tion is of slight importance, but simplicity of mutual relations is essential. 

 .\nother example of this law is the way physicists and chemists have dissolved 

 the simple idea of an extended body, say of a chair, which a child under- 

 stands, into a bewildering notion of a complex dance of molecules and atoms 

 and electrons and waves of light. They have thereby gained notions with 

 simpler logical relations. 



Space as thus conceived is the exact formulation of the properties of the 

 apparent space of the common-sense world of experience. It is not necessarilj' 

 the best mode of conceiving the space of the physicist. The one essential 

 requisite is that the correspondence between the common-sense world in its 

 space and the physicists' world in its space should be definite and reciprocal. 



I will now break off the exposition of the function of logic in connection 

 with the science of natural phenomena. I have endeavoured to exhibit it as 

 ilie organising principle, analysing the derivation of the concepts from the 

 immediate plienomena, examining the structure of the general propositions 

 which are the assumed laws of nature, establishing their relations to each 

 other in respect to reciprocal implications, deducing the phenomena we may 

 expect under given circumstances. 



Logic, properly used, does not shackle thought. It gives freedom and, 

 above all, boldness. Illogical thought hesitates to draw conclusions, because it 

 never knows either what it means, or what it assumes, or how far it trusts its 

 own assumptions, or what will be the effect of any modification of assumptions. 

 Also the mind untrained in that part of constructive logic which is relevant to 

 the .subject in hand will be ignorant of the sort of conclusions which follow 

 from various sorts of assumptions, and will be correspondingly dull in divinino' 

 the inductive laws. The fundamental training in this "relevant logic is, 

 undoubtedly, to ponder with an active mind over the known facts of the case, 

 directly observed. But where elaborate deductions are possible, this mental 

 activity requires for its full exercise the direct study of the abstract logical 

 relations. This is applied mathematics. 



Neither logic without observation, nor observation without logic, can move 

 one step in the formation of science. We may conceive humanity as engaged 

 in an internecine conflict between youth and age. Youth is not defined by 

 years, but by the creative impulse to make something. The aged are those who, 

 before all things, desire not to make a mistake. Logic is the olive branch 

 from the old to the young, the wand which in the hands of youtli has the magic 

 property of creating science. 



