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Digital Companion to C. S. Peirce
Complete Argument
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1867 | On the Natural Classification of Arguments | W 2:24

…every argument has, as portion of its leading principle, a certain principle which cannot be eliminated from its leading principle. Such a principle may be termed a logical principle.

An argument whose leading principle contains nothing which can be eliminated is termed a complete, in opposition to an incomplete, rhetorical, or enthymematic argument.

In 1893, Peirce modified the last part of this quote as follows: "Since it can never be requisite that a fact stated should also be implied in order to justify a conclusion, every logical principle considered as an assertion will be found to be quite empty. The only thing it really enunciates is a rule of inference; considered as expressing truth, it is nothing." (CP 2.467)

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1880 | On the Algebra of Logic | W 4:167; CP 3.166

…a leading principle, which contains no fact not implied or observable in the premisses, is termed a logical principle, and the argument it governs is termed a complete, in contradistinction to an incomplete, argument, or enthymeme.

Citation
‘Complete Argument’. Term 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/term/complete-argument/page, 29.03.2023.
See also
Logical Principle | Argument | Immediate Inference