The emergence of an old problem: if there’s a problem with a reductio, what do you call it?

I’ve been attempting to finish a midterm in one of my classes before July 4th rolls around.  I was delighted tonight to realize that my opinion of one of the arguments I was to assess was to argue against the effectiveness of what I took to be a reductio ad absurdum.

I remember first learning what a reductio was while reading one of Plato’s dialogues.  I can’t remember exactly which one, probably The Theaetetus.  In any event, I came to the familiar question of how exactly to name my opposition to this particualr reductio.  Since a reductio ad absurdum is deductively invalid by definition, I could say “and this is inconsistent because…” The function of the argument WAS to be invalid and thus not sound.

I can’t discuss the specifics, but needless to say, it was entertaining to see a familiar problem arise in a quite distinct context or discourse.

Here are a few legitimate sources of information on reductio ad absurdum’s:

A reductio ad absurdum argument reported by Aristotle suggests that the atomists argued from the assumption that, if a magnitude is infinitely divisible, nothing prevents it actually having been divided at every point. The atomist then asks what would remain: if the answer is some extended particles, such as dust, then the hypothesized division has not yet been completed. If the answer is nothing or points, then the question is how an extended magnitude could be composed from what does not have extension


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