(cf. Delome; see also Argumentation, Rhema, Dicent)

"An "Argument" is any process of thought reasonably tending to produce a definite belief." ('A Neglected Argument for the Reality of God', CP 6.456, 1908)

" defined an argument as a sign which separately monstrates what its intended interpretant is, and a proposition as a sign which separately indicates [what] its object is." ('New Elements', EP 2: 308, 1904)

"I [...] define an argument as a sign which is represented in its signified interpretant not as a Sign of the interpretant (the conclusion) [for that would be to urge or submit it] but as if it were a Sign of the Interpretant or perhaps as if it were a Sign of the state of the universe to which it refers, in which the premisses are taken for granted." (A Letter to Lady Welby, SS 34, 1904)

"An Argument is a Sign which, for its Interpretant, is a sign of law. Or we may say [...] that an Argument is a Sign which is understood to represent its Object in its character as Sign." ('A Syllabus of Certain Topics of Logic', EP 2:292, 1903)

"An Argument is a sign whose interpretant represents its object as being an ulterior sign through a law, namely, the law that the passage from all such premisses to such conclusions tends to the truth. Manifestly, then, its object must be general; that is, the Argument must be a Symbol. As a Symbol it must, further, be a Legisign. Its Replica is a Dicent Sinsign." ('A Syllabus of Certain Topics of Logic', EP 2:296, 1903)

"An Argument is a sign which distinctly represents the Interpretant, called its Conclusion, which it is intended to determine." ('Minute Logic', CP 2.95, 1902)

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Abbreviations (CP, EP, etc.) and sources; see here