A couple of weeks ago, I wrote here about Diogenes Laertius' work on the "lives and opinions" of the classical philosophers.
I will continue that discussion now.
In book six, our Diogenes gets around to someone else of the same name, Diogenes of Sinope [the cynic].
I am fascinated by the proximity of the following two sentences.
A man once proved to him syllogistically that he had horns, so he put his hand to his forehead and said 'I do not see them.' And in a similar manner he applied to one who had been asserting that there is no such thing as motion, by getting up and walking away.
This little passage confirms the point I made in the earlier post about Diogenes L's utter lack of creative impulse. No pausing to explain, no over-arching narrative. Just one damned thing after another.
More important I have no idea who our Diogenes was mentioning in the first of those sentences, i.e. what argument Diogenes of Sinope had encountered. Was there any standard sophistical argument for proving that someone has horns? The only possible context that comes to my mind [inspired by the specification in our author's passage that the proof was "syllogistic"] is that this could have arisen out of an explanation of the distinction between a valid argument and a sound one. A valid argument draws the conclusion required by its premises but, since this definition does NOT require that the premises be true for 'validity,' it allows that they can be false.
Thus: all men have horns. You are a man. Therefore, you have horns.
That is valid, though of course not sound.
Was Diogenes complaining about someone who had simply been making this fair distinction? I don't know. Diogenes of L. doesn't tell us anything more about the "proof that he had horns". Just for the fun visual, I've included the conventional Venn diagram of such a syllogism above. You is the central green circle. Men is the middle term -- the red circle. Possessors of horns is the outer circle.
[See postscript for another thought.]
And the use of the word "see" rather than "feel" in the context of the perceptual response to the paradox is odd. The cynic puts his hand to his forehead presumably so that he can FEEL the horns or their absence, which of course he cannot SEE.
Then of course, our author passes immediately to the refutation of Zeno's paradoxes of motion. He doesn't say that specifically because he in this book (not a slave to chronology) hasn't come to Zeno of Elea yet when our Diogenes is talking about the cynical namesake. But the statement of the ambulando response is straightforward. One can move, so something about the proof of motion's impossibility must be wrong.
Here too the cynic, generally painted as the hero of this little story, just misses the point.
POSTSCRIPT
Diogenes Laertius circles back to the issue of a proof that "you" have horns much later in the book. Apparently this was a sophism associated with the Stoic philosopher Chrysippus.
Our Diogenes says, in his usual one-damn-thing-after-another tone: "Another [syllogism] was: if you have not lost a thing you have it; but you have not lost horns. Therefore you have horns."
So presumably we are to understand that THIS is the argument to which Diogenes of Sinope was replying by feeling his own forehead. My first impression was not entirely wrong. Yes, Chrysippus created a syllogism with a false major premise, and a blatantly false conclusion as well. A valid argument though not a sound one.
The Stoics love this conditional style of syllogism, "If A then B; and A; thus B." Somewhat different from the categorical style of my earlier example. Connected to this, the false major premise was somewhat more plausible sounding than the one I thought up, above. So we can understand how it may have helped Chrysippus develop a reputation as a dialectician not to take lightly.
We can also sympathise somewhat with the cynic's ambulando-esque reply.
Comments
Post a Comment