8

I've seen this used enough times that there's probably a formal name for it, but I don't know what it is. For example, from Catch-22:

"I think I'm going crazy."

"Only a sane person is capable of doubting their own sanity. Therefore, you're just fine."

Or, conversely:

"Of course I'm not a witch! There's no such thing as witches!"

"Only a witch would say that! Burn her!"

Is there a formal name for this type of argument?

  • Reductio ad absurdum? (proof by contradiction) – Florin Andrei Jul 14 '11 at 19:13
  • No, this is a completely different concept. – Mason Wheeler Jul 14 '11 at 19:56
  • Not to sound glib, but doesn't that make the proposition trivially true? – Ryder Jul 30 '12 at 19:39
5

It's a "Catch-22" paradox!

The Catch-22 paradox is that behaving a certain way because of some desire is a sure way to not get what you desire. If you want to be declared insane in order to be discharged, you can't act insane as only sane men can act insane. But if you don't exhibit signs of being insane, you will not be discharged. The same analysis works for the witch paradox.

One point of Catch-22 is to illuminate the dysfunction of the US Army and bureaucracy in general. The continual use of paradox accomplished that goal in my opinion.

The point isn't to prove the original statement, but to demonstrate a particular type of absurdity. Another example that I've seen professionally is that in order to get a job that requires a security clearance, you need to already have clearance, but you can't get clearance until you have a job that requires it. In the entertainment industry, blockbuster movies require a lead actor who is a "name", but the only way to become a "name" is to star in a blockbuster movie. The usual solution to these conundrums is to fudge the rules a bit: interim security clearances are granted to people who start jobs that require clearances and actors can star in blockbusters if they are particularly well received in smaller roles.

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    A no-win situation or circular logic might also be ways to characterize these sorts of paradoxes. – Joseph Weissman Jul 14 '11 at 23:00
  • I think that the comparison of Catch-22 to the Paradox of the Liar is not sound. The Liar sentence is true iff and only if it is false and thus a sign of a deep problem. Heller's Catch-22 is resoluble quite easily: "You think you are crazy, but you are wrong about that." – vanden Jul 15 '11 at 5:48
  • @vanden: I wasn't sure if the asker knew about paradox in general, so I gave the first example that came to mind. I don't mean it to be an instance of Catch-22 or to compare them directly. Perhaps it would be best to remove that section altogether. – Jon Ericson Jul 15 '11 at 16:52
  • @Jon: While I take your point, my claim wasn't restricted to the Liar. Paradoxes in general are not so easily resolved as the apparent tension in the Catch-22 case. (I am here using 'paradox' in a technical rather than idiomatic sense.) – vanden Jul 15 '11 at 19:15
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    @vanden: It's a bureaucratic paradox. ;-) I've updated the answer to downplay the concept of paradox in order to emphasize the concept of conundrum and absurdity. Perhaps that satisfies your objection... – Jon Ericson Jul 15 '11 at 19:20
0

I'm not sure if this fits the pattern you're looking for, and I realize that this may a bit controversial, but there is the saying (not exactly a rule of inference) that:

The exception proves the rule.

I've always taken this very informal almost joking statement to mean that one has a general rule in mind, one sees an exception to the rule, but the circumstances of the exception are so rare that it implies that rule probably is pretty accurate in most circumstances. If forced to formalize and pedanticize this I would say it's a Bayesian confirmation by improbable data.

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    "The exception proves the rule" is one of the most upsetting idioms in English. It has come to be understood as the absurd view that a counter-example proves a generalization ("All mammals give birth to live young." "What about the platypus?" "See, I told you!"). en.wikipedia.org/wiki/Exception_that_proves_the_rule provides a good discussion of one sensible meaning (the existence of the exception proves that the rule exists to be excepted). I've also encountered the claim that it relies on archaic sense of 'prove' meaning "to test and find wanting" but can find no ready url. – vanden Jul 15 '11 at 5:54

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