Yes, and in fact the ancient Greek term, of those who invented the thing, was neither ("illogical" or "not a ratio").
It was "alogos" (later "arritos"), with the meaning "inexpressible", "which cannot be spelt out" - in the sense that you can never fully write out e.g. the square root of two the way you can a natural or a rational number like 2/3 or 1/4.
Unfortunately "alogos" also meant "illogical", so that's where the confusion stems...
Well, maybe the point is that "illogical" should mean inexpressible and the whole issue is the wrong connotations of it.
Which the author explains near the end of the article.
Re:Calculus Is Deeply Irrational
by richardwhiuk on Tuesday August 20, 2019 @01:20PM
(#20749463)
But uses to drive traffic in a deeply unappealing way.
Re:Calculus Is Deeply Irrational
by hcarvalhoalves on Tuesday August 20, 2019 @12:59PM
(#20749188)
"Illogical" is a synonym of "Irrational" because...
> Greek mathematicians termed this ratio of incommensurable magnitudes alogos, or inexpressible.
Looks like the intention of the author was to play with that word game in order to get an appealing title, but even for people familiar with the topic it can have the "not logical" meaning first.
“Not logical”, which by definition does not apply to math.
“Not a ratio”, e.g., a number that cannot be written as the division (ratio) of two whole numbers.
It should be no surprise to anyone, that calculus deals with the latter, but the title would allude to the article dealing with the former.