Digital Companion to C. S. Peirce
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1895 | Short Logic | EP 2:11-12

Reasoning is the process by which we attain a belief which we regard as the result of previous knowledge. [—]

Argumentation is the expression of a reasoning.

1905 | Issues of Pragmaticism | EP 2:348

… For this theory requires that in reasoning we should be conscious, not only of the conclusion, and of our deliberate approval of it, but also of its being the result of the premises from which it does result, and furthermore that the inference is one of a possible class of inferences which conform to one guiding principle. Now in fact we find a well-marked class of mental operations, clearly of a different nature from any others which do possess just these properties. They alone deserve to be called reasonings; and if the reasoner is conscious, even vaguely, of what his guiding principle is, his reasoning should be called a logical argumentation.

1908 | A Neglected Argument for the Reality of God (O) | CP 6.456

An “Argumentation” is an Argument proceeding upon definitely formulated premisses.