THEORIES CONCERNING AXIOMS. 309 



yet what we call divisibility may be an attribute only of our 

 sensations of sight and touch, and not of their uncognizable 

 cause. Divisibility may not be predicable at all, in any intel- 

 ligible sense, of Things in themselves, nor therefore of Matter 

 in itself; and the assumed necessity of being either infinitely 

 or finitely divisible, may be an inapplicable alternative. 



On this question I am happy to have the full concurrence 

 of Mr. Herbert Spencer, from whose paper in the Fortnightly 

 Review I extract the following passage. The germ of an idea 

 identical with that of Mr. Spencer may be found in the present 

 chapter, about a page back, but in Mr. Spencer it is not an 

 undeveloped thought, but a philosophical theory. 



" When remembering a certain thing as in a certain place, 

 the place and the thing are mentally represented together ; 

 while to think of the non-existence of the thing in that place, 

 implies a consciousness in which the place is represented, but 

 not the thing. Similarly, if instead of thinking of an object 

 as colourless, we think of its having colour, the change con- 

 sists in the addition to the concept of an element that was 

 before absent from it the object cannot be thought of first as 

 red and then as not red, without one component of the thought 

 being totally expelled from the mind by another. The law of 

 the Excluded Middle, then, is simply a generalization of the 

 universal experience that some mental states are directly de- 

 structive of other states. It formulates a certain absolutely 

 constant law, that the appearance of any positive mode of con- 

 sciousness cannot occur without excluding a correlative negative 

 mode ; and that the negative mode cannot occur without ex- 

 cluding the correlative positive mode : the antithesis of positive 

 and negative being, indeed, merely an expression of this ex- 

 perience. Hence it follows that if consciousness is not in one 

 of the two modes it must be in the other."* 



I must here close this supplementary chapter, and with it 

 the Second Book. The theory of Induction, in the most com- 

 prehensive sense of the term, will form the subject of the Third. 



* For further considerations respecting the axioms of Contradiction and 

 Excluded Middle, see the twenty-first chapter of An Examination of Sir Wil- 

 liam Hamilton's Philosophy. 



