a single cognition of any kind concept I 



a single necessary and universal cognition judgment V 



a single necessary {cognition} universal syllogism I 



where the derivative phrases determine the primitive phrase 

 in relation to all and only the fundamental distinctions of 

 thought, that is to say, the fundamental logical principles 

 of the agreement of thought with itself ; and where the vari- 

 able recognized in the primitive can be replaced by its limit 

 recognized according to a different mode in every single 

 derivative. This primitive logic, as the formula deserves to 

 be called, demonstrates that the accepted logical determina- 

 tion of thought is not a logical division but a logical trans- 

 formation, and renders necessary, at least as a problem, the 

 invention or discovery of a series of three derivative logics 

 which shall by degrees extend the application of every single 

 differential moment of the primitive logic as far as possible, 

 that is to say, over the whole domain whether of a single 

 cognition or of thought. From the fact that the primitive 

 application of the third differential moment appears in the 

 deduced formula of Science {function} Analysis as the dif- 

 ferentiation of the identity of function in an integrated 

 equation, I infer that the rest of the third derivative logic 

 will appear in the deduction of the corresponding work as 

 the integration of the difference of function in a series of 

 differential equations ; and from the nature and position 

 of the third derivative moment I conclude that this third 

 derivative logic, considered as if it had all appeared, is the 

 only logic that deserves to be called definitive. 



GEORGE ASHTON BLACK 

 New York, 621 W. 113th Street 

 April 28, 1905 



