Latin plurals when talking about fallacies

Solution 1:

If you want to go by the Latin, argumentum ad ignorantiam pluralises as argumenta ad ignorantiam (arguments to ignorance), and similarly reductio ad absurdum pluralises as reductiones ad absurdum (reductions to absurdity) – the point is that ad ignorantiam and ad absurdum (and, for that matter, the principii in petitio principii) serve as adjectival phrases, and are thus indeclinable in Latin.

Solution 2:

The short answer is

ad hominem arguments

or

arguments ad hominem

or

argumenta ad hominem

in that order of popularity, because there are no stated rules.

To explain, first the Latin.

The plural of the stand alone 'argumentum' in English follows that in Latin:

argumenta

The plural of 'argumentum ad ...' in Latin is

argumenta ad ...

the noun is properly (for Latin) the thing pluralized.

Now let's turn to English. A foreign phrase is often declined by the borrowers in the know exactly as in the original language. Depending on the language, the later users of the phrase may or may not be proficient in the grammar of the original, and usually it gets analyzed in as natural way as possible in English.

The plural of 'argumentum' alone given in dictionaries is the same as in Latin, namely:

argumenta

That is for the word by itself.

In this example 'argumentum' is easily recognizable in English as 'argument', so the phrase is often given in mixed English/Latin as 'argument ad hominem' or 'an ad hominem argument'. There the plural is given as expected only affecting the noun:

ad ... arguments

or

arguments ad ...

or the proper Latin way

argumenta ad ...

the English/Latin mix becoming more popular recently for ad hominem and ad populum.

Also, sometimes the qualifier is given as the name of the argument type, e.g. "He used an ad hominem against me", and so there the plural is given as:

ad hominems

but again a plural only ever seems to have appeared for 'ad hominem'. but this never seems to appear ever in a plural form like 'argumentum ad hominems' (pluralizing the entire Latin phrase as though it were a single thing).

The latter support for the plural is only an argument de facto (by the questionable ngrams) rather than de jure, since dictionaries and style guides seem not to consider the possibility.

Solution 3:

I wouldn’t try. You can instead say, if you must, 'The text contains many instances of argumentum ad ignorantiam.'