Category: Plato

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

Now on to negative assertions and Plato

My interpretation of Plato’s doctrine of negative assertions (or “not-being) in the Sophist at (roughly) 257e


Plato’s doctrine of negative assertions:


Stranger: May we not say that the existence of the not-beautiful is constituted by its being marked off from a single definite kind among existing things and again set in contrast with something that exists?

Theaetetus: Yes.

Stranger: So it appears that the not-beautiful is an instance of something that exists being set in contrast to something that exists.

Theaetetus: Perfectly.

Stranger: What then? On this showing has the not-beautiful any less claim than the beautiful to be a thing that exists?

Theaetetus: Just as much

Stranger: And we must also put the not-just on the same footing as the just with respect to the fact that the one exists no less than the other.



The existence of the not-A (the form not-A?) is constituted

(a) by its being separated from a single (definite) Form among existing things (particulars)


(b) by its being separated from something that exists (form or particular??)


If and only if not-A then (p) A is distinguishable from a single definite form F among existing F-particulars and (q) A is distinguishable from other non-F particulars and/or non-F forms