Modus Barbara, Modus Celarent, and Modus Darii are names of valid syllogisms in the medieval taxonomy of valid syllogisms. I'm wondering how to say: "Moduses Barbara, Celarent, and Darii." As far as I'm capable, "Modi Barbara, Celarent, et Darii" is all that I can come up with.

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For those unfamiliar with this terminology, this question refers to medieval mnemonic names for syllogisms, mostly drawn from Aristotelian logic. All valid syllogisms, along with their names, are available here.

The names "Barbara," "Celarent," and "Darii" (as well as the fourth first figure mood which you seem to have left out: "Ferio") are obviously indeclinable, since their vowels refer to the four types of propositions: A, E, I, and O (universal/particular affirmation/negation).

If you wish to translate your phrase as-is, you are correct to add the terms in apposition after modi. I found one precedent for this construction in a logic manual:

Non minus contorta vulgo est argumentandi ratio, si syllogismi tertiae figurae, qui sunt in modis Disamis atque Bocardo ad primam figuram reducuntur.

I therefore think your translation is correct:

Modi Barbara, Celarent, et Darii

This is a little awkward. If you can reword, it might be easier to understand if you separated them out a little:

Hi sunt modi primae figurae: Barbara, Celarent, Darii, et Ferio. Modus Barbara est...etc.

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