6 THE PRINCIPLES OF SCIENCE. [chap. 



soft; but at the same time and place an attribute cannot be 

 both present and absent. Aristotle truly described this 

 law as the first of all axioms — one of which we need not 

 seek for any demonstration. All truths cannot be proved, 

 otherwise there would be an endless chain of demonstration ; 

 and it is in self-evident truths like this that we find the 

 simplest foundations. 



The third of these laws completes the other two. It 

 asserts that at every step there are two possible alter- 

 natives — presence or absence, affirmation or negation. 

 Hence I propose to name this law the Law of Duality, for 

 it gives to all the formuliTe of reasoning a dual character. It 

 asserts also that between presence and absence, existence 

 and non-existence, affirmation and negation, there is no 

 third alternative. As Aristotle said, there can be no mean 

 between opposite assertions : we must either affirm or 

 deny. Hence the inconvenient name by which it has been 

 known — The Law of Excluded Middle. 



It may be allowed that these laws are not three indepen- 

 dent and distinct laws ; they rather express three different 

 aspects of the same truth, and each law doubtless pre- 

 supposes and implies the other two. But it has not 

 hitherto been found possible to state these gharacters of 

 identity and difference in less than the threefold formula. 

 The reader may perhaps desire some information as to the 

 mode in which these laws have been stated, or the 

 way in which they have been regarded, by philosophers 

 in different a2;es of the world. Abundant information 

 on this and many other points of logical history will be 

 found in Ueberweg's *%s^em of Logic, of which an excellent 

 translation has been published by Professor T. M. Lindsay 

 (see pp. 228-281). 



The Nature of the Laws of Identity and Difference. 



I must at least allude to the profoundly difficult ques- 

 tion concerning the nature and authority of these Laws of 

 Identity and Difference. Are they Laws of Thought or 

 Laws of Things ? Do they belong to mind or to material 

 nature ? On the one hand it may be said that science is a 

 purely mental existence, and must therefore conform to the 

 laws of that which formed it. Science is in the mind and 



