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What, if anything, is the elided noun in the phrase a fortiori?

A curious variant and a curious translation

I had been assuming that the full phrase is a fortiori ratione, "with stronger reason", but this answer by @Johann Ramminger just sent me to the following passage from Ockham's Dialogus, part 3, tract 2, book 2, translated here by John Scott, including collations from numerous manuscripts:

Quotation with collations from Dialogus,
part 3, tract 2, book 2, pointing out "Ex quo concluditur quod multo fortius…" in three manuscripts

Three of the manuscripts have the variant concluditur quod multo fortius…distincta est in place of per consequens a fortiori. The translator appears to have favored the variant: "It is much more the case that…is distinct." So, the variant and translation seem to take a fortiori to mean that the conclusion is itself stronger, rather than that the conclusion is established with a stronger basis. This suggests that there is actually no elided noun in a fortiori—that the adjective is meant substantively, the phrase perhaps meaning "with greater strength".

Reasoning and evidence?

My first thought is that the above reading is simply a mistake. The reasoning is typical a fortiori: since a king's power does not derive from the pope's, neither can an emperor's, since an emperor's power includes and surpasses that of a king. The subject matter primes such a mistake, since the subject matter is an explicit comparison of (legal) powers.

But I could be wrong. What textual evidence do we have that a fortiori is short for a fortiori ratione—or whatever it's short for, if anything?

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