LATIN DICTIONARYLexicon Latīnum
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“argue” in Latin

The English word argue itself goes back to Latin arguō, through arguere.

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

argue
to discuss a question: agere rem or de re (general term): disputare, disserere de aliqua re (of learned discussions: disserere, mostly of a continuous discourse): sermonem habere de re (discuss it in conversation): disceptare aliquid or de aliqua re (with a view to the settlement of a dispute): to argue at great length, multis verbis disputare: to argue on the other side, contra disputare: to argue on both sides of a question, in utramque partem: on opposite sides, in contrarias partes.
Produce arguments, argumentari (with neuter pronoun or dependent clause): docere argumentis: firmare, confinnare argumentis: efficere or evincere velle (to wish to establish an opinion).
Accuse, arguere (with genitive, ablative de, accusative with infinitive, or ut). [Vid: ACCUSE.]
Prove, infer (transitively), probare: evincere, ostendere, declarare.

Quick answer

What is the Latin word for argue?
The usual Latin words for “argue” are disputō, argūmentor, firmō; also efficiō, arguō, īnferō. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.