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Digital Companion to C. S. Peirce
‘Theorematic Reasoning’ (pub. 06.01.13-12:18). Quote in M. Bergman & S. Paavola (Eds.), The Commens Dictionary: Peirce's Terms in His Own Words. New Edition. Retrieved from http://www.commens.org/dictionary/entry/quote-carnegie-institution-correspondence-7.
Term: 
Theorematic Reasoning
Quote: 

Imagine, for example, an endless succession of objects. [—] Yet this proof will rest on some proposition which is simply self evident. But as long as one only has the idea of simple endless series, one may think forever, and not discover the theorem, until something suggests that other idea to the mind. What I call the theorematic reasoning in mathematics consists in so introducing a foreign idea, using it, and finally deducing a conclusion from which it is eliminated.

Source: 
Peirce, C. S. (1902). Carnegie Institution Correspondence. L [R] 75.
References: 
NEM 4:42
Date of Quote: 
1902
URL: 

http://www.commens.org/dictionary/entry/quote-carnegie-institution-correspondence-7