The Commens Dictionary

Quote from ‘On the Logic of Drawing History from Ancient Documents Especially from Testimonies (Logic of History)’

Quote: 

This appears to be in harmony with Kant’s view of deduction, namely, that it merely explicates what is implicitly asserted in the premisses. This is what is called a half-truth. Deductions are of two kinds, which I call corollarial and theorematic. The corollarial are those reasonings by which all corollaries and the majority of what are called theorems are deduced; the theorematic are those by which the major theorems are deduced. If you take the thesis of a corollary, – i.e. the proposition to be proved, and carefully analyze its meaning, by substituting for each term its definition, you will find that its truth follows, in a straightforward manner, from previous propositions similarly analyzed. But when it comes to proving a major theorem, you will very often find you have need of a lemma, which is a demonstrable proposition about something outside the subject of inquiry; and even if a lemma does not have to be demonstrated, it is necessary to introduce the definition of something which the thesis of the theorem does not contemplate.

Date: 
1901
References: 
CP 7.204
Citation: 
‘Deduction’ (pub. 02.02.13-09:40). 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-logic-drawing-history-ancient-documents-especially-testimonies-logic-histor-8.
Posted: 
Feb 02, 2013, 09:40 by Sami Paavola
Last revised: 
Jan 07, 2014, 01:00 by Commens Admin