vii.] INDUCTION. 151 



reasoning upon the subject, can have any validity ; for 

 without experience we are without the basis and materials 

 of knowledge. It is the fundamental postulate accordingly 

 of all inference concerning the future, that there shall be 

 no arbitrary change in the subject of inference ; of the pro- 

 bability or improbability of such a change I conceive that 

 our faculties can give no estimate. 



The other condition of inductive inference that we 

 acquire an approximately complete knowledge of the com- 

 binations in which events do occur, is in some degree 

 within our power. There are branches of science in which 

 phenomena seem to be governed by conditions of a most 

 fixed and general character. We have ground in such 

 cases for believing that the future occurrence of such 

 phenomena can be calculated and predicted. But the 

 whole question now becomes one of probability and im- 

 probability. We seem to leave the region of logic to enter 

 one in which the number of events is the ground of in- 

 ference. We do not really leave the region of logic ; we 

 only leave that where certainty, affirmative or negative, is 

 the result, and the agreement or disagreement of qualities 

 the means of inference. For the future, number and 

 quantity will commonly enter into our processes of reason- 

 ing ; but then I hold that number and quantity are but 

 portions of the great logical domain. I venture to assert 

 that number is wholly logical, both in its fundamental 

 nature and in its developments. Quantity in all its forms 

 is but a development of number. That which is mathe- 

 matical is not the less logical ; if anything it is more 

 logical, in the sense that it presents logical results in a 

 higher degree of complexity and variety. 



Before proceeding then from Perfect to Imperfect In- 

 duction I must devote a portion of this work to treating 

 the logical conditions of number. I shall then employ 

 number to estimate the variety of combinations in which 

 natural phenomena may present themselves, and the pro- 

 bability or improbability of their occurrence under definite 

 circumstances. It is in later parts of the work that I must 

 endeavour to establish the notions which I have set forth 

 upon the subject of Imperfect Induction, as applied in the 

 investigation of Nature, which notions may be thus briefly 

 stated : 



