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Logo design credit goes to: tubbadu
Please state in which country your phrase tends to be used, what the phrase is, and what it should be.
Example:
In America, recently came across "back-petal", instead of back-pedal. Also, still hearing "for all intensive purposes" instead of "for all intents and purposes".
Online in general: using "reductio ad absurdum" as a fallacy.
It's a longstanding logical tool. Here's an example of how it works: let's assume you can use infinity as a number. In that case, we can do:
∞ + 1 = ∞
And:
∞ - ∞ = 0
Agreed? If so, then:
∞ - ∞ + 1 = ∞ - ∞
And therefore:
1 = 0
Which is absurd. If we agree that all the logical steps to get there are correct, then the original premise (that we can use infinity as a number) must be wrong.
It's a great tool for teasing out incorrect assumptions. It has never been on any academic list of fallacies, and the Internet needs to stop saying otherwise. It's possible some other fallacy is being invoked while going through an argument, but it's not reductio ad absurdum.
Well if we're going to be talking about logical fallacies, I feel like the string of arguments that you made there is a category error. Infinity isn't exactly a number, it's more of a philosophical concept than anything else. I would argue that trying to subtract Infinity from Infinity is illogical and kind of silly, but it wouldn't be a reductio ad absurdum as you put it, but instead a category error.
An absurdist argument might be more like, if I have one cat I can trade it for one dog. Therefore infinite cats can be traded for infinite dogs. This is obviously absurd, because infinite cats don't exist, unfortunately.
That's fair.
The way read it they were using it as an example where absurdity makes sense to poke a hole in the logic that infinity can be used as a number.
Or in math you'll talk about approaching infinity, that is just some arbitrarily large number.