PERFORMANCE OE LOGICAL INFERENCE. 
501 
itself ; the second, known as the Law of Contradiction, states that a thing cannot at the 
same time and place combine contradictory or opposite attributes ; whatever A and B 
may be it is certain that A cannot be both B and not B. This law, then, excludes from 
real, or even conceivable existence, any combination of opposite attributes. 
The third law, commonly known as the Law of Excluded Middle, but which I prefer 
to call by the simpler title of the Law of Duality, asserts that every thing must either 
possess any given attribute or must not possess it. A must either be B or not B. It 
enables us to predict anterior to all particular experience the alternatives which may be 
asserted of any object. When united, these laws give us the all-sufficient means of 
analyzing the results of any assertion : the Law of Duality developes for us the classes 
of objects which may exist ; the Law of Identity allows us to substitute for any name 
or term that which is asserted or known to be identical with it ; while the Law of Con- 
tradiction directs us to exclude any class or alternative which is thus found to involve 
self-contradiction. 
14. To illustrate this by the simplest possible instance, suppose we have given the 
assertion that 
A metal is an element , 
and it is required to arrive at the description of the class of compound or not-elementary 
bodies so far as affected by this assertion. The process of thought is as follows : — 
By the Law of Duality I develope the class not-element into two possible parts, those 
which are metal and those which are not metal, thus — 
What is not element is either metal or not-metal. 
The given premise, however, enables me to assert that what is 7iietal is element ; so that 
if I allowed the first of these alternatives to stand there would be a not-element which 
is yet an element. The law of contradiction directs me to exclude this alternative from 
further consideration, and there remains the inference, commonly known as the contra- 
positive of the premise, that 
What is not element is not metal. 
Though this is a case of the utmost simplicity, the process is capable of repeated appli- 
cation ad infinitum , and logical problems of any degree of complication can thus be 
solved by the direct use of the most fundamental Laws of Thought. 
15. To take an instance involving three instead of two terms, let the premises be- — 
Iron is a metal (1) 
Metal is element .... (2) 
We can, by the Law of Duality, develope any of these terms into four possible combi- 
nations. Thus 
Iron is metal, element ; . . . (a) 
or metal, not-element ; . . ({3) 
or not-metal, element ; . . (y) 
or not-metal, not-element . (b ) 
