378 



MEMOIRS OF THE AMERICAN ACADEMY 



Conclusion. 



If the question is asked, What are the axiomatic principles of this branch of 



deducible from others? I reply that whatever rank 



gned to the laws of 



contradiction and excluded middle belongs equally to the interpretations of all the 



t> 



quations given under the head of "Application of the Algebraic Sigi 



relating to backward involution, and the principle 



ex- 



Logic," together with those relating to 



pressed by equations (95), (96), (122), (142), (156), (25), (26), (14), (15), (169), (170) 



But these axioms are mere substitutes for definitions of the universal logical 



and 



far 



the 



be defined, all axioms may be dispensed 



th 



The 



fundamental principles of formal logic are not properly axioms, but definitions and 

 divisions ; and the only facts which it contains relate to the identity of the concep- 

 tions resulting from those processes with certain familiar ones. 



