80 Wisconsin Academy of Sciences^ Arts, and Letters. 



of the painter is paint. The simplest expression of thought 

 is not the syllogism but the logical proposition. Now, it is 

 plain that if the proposition is the formulation — the material 

 representative of thought — if we study it as we study other 

 natural symbols, we will find in it the fundamental Law of 

 Thinking, and ultimately the fundamental Law of all Science : 

 Just as, if it were possible to reduce all elementary substances 

 to one, the chemist would be able to find in that one a con- 

 densed expression of chemical science. 



What then is a proposition? Simply stated, it is the as- 

 sertion of relation between two terms ; or more abstractly, it 

 is the reference of an individual to its species — the assertion of 

 a classification. We find here the same duality which we 

 noticed above. If we give prominence to the individual 

 notion, we consider the proposition in extension ; if we turn 

 our attention to the specific notion we consider the proposition 

 in intention : in the one case referring to the individuals com- 

 posing the class, in the other to the attributes composing the 

 class-type. The first corresponds to induction, the second to 

 deduction. When we study individuals we study physics ; 

 when we study the attributes composing the class- type, we 

 study metaphysics. The Law of Thinking as educed from a 

 study of the proposition is the law of classification. The 

 proposition, considered affirmatively, asserts explicitly agree- 

 ment between certain attributes of two terms ; that is, it asserts 

 a classification. The aim of science is to reach this proposition, 

 to discover and assert the principle of classification — in other 

 words, to formulate metaphysically what nature has presented 

 physically. We must find, then, the first or fundamental 

 law of thinking in this integration or classification. This 

 fundamental law may be subdivided into two species, accord- 

 ing to the two terms of the proposition ; of which the first may 

 be stated thus : " Every possible object of thought is to a cer- 

 tain extent identical with every other "; and as the proposition 

 implicitly states disagreement, the second may be stated thus : 



