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Is a catch-22 a specific subtype of circular logic? How are they different? Also, is the catch-22 paradox known by any other names?

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maybe 'vicious circle'? –  Mozibur Ullah Jan 2 '13 at 15:07

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up vote 6 down vote accepted

I think that Catch-22s (Catches-22?) are different from paradoxes, contradictions, or circular reasoning, though they do resemble these things, and are interesting for this reason.

It seems to me that a Catch-22 consists essentially of:

  1. a desideratum D: something that one would like to accomplish

  2. a necessary condition N for accomplishing D. This may often also be a sufficient condition (modulo some actions which one assumes are easy), but often it is something which must be satisfied before D can be accomplished.

  3. a sequence of necessary conditions N1, N2, ... , Nn where N = N1, where for each j < n, the condition Nj+1 is a necessary condition for Nj, and where either

    • D or some Nj is a necessary condition for Nn, and each of the necessary conditions must be satisfied before each one which depends on it (a chronological Catch-22); or

    • D or some Nj is the logical negation of Nn (a logical Catch-22).

The similarity to circular reasoning is, I think, in the cycle of conditions.

The classic example is drawn from the novel Catch-22, with respect to Orr being allowed not to fly anymore in the Allied campaign in Italy during WWII. Without commenting on whether or not these premises are valid propositions in themselves, the structure of that Catch-22 is as follows: Orr will only be relieved of pilot duty if he is crazy; but if he were crazy, he wouldn't request to be relieved of pilot duty. We may analyse this by:

  • D = Orr relieved of pilot duty

  • N1 = Orr is crazy

  • N2 = Orr doesn't request to be relieved of pilot duty

  • N3 = Orr not relieved of pilot duty

As D ⇒ N1 ⇒ N2 ⇒ N3 ≡ ¬D, we have a logical Catch-22.

The other, "chronological" Catch-22 involving a cycle of preconditions is actually a special case of a logical Catch-22; albeit one which is more commonly found in practise, for instance in bureaucratic situations involving approval or identification. The "logical" contradiction in this case arises from the need for the temporal ordering: if a condition Nj is initially not satisfied, and if for some time t the condition Nj can only be satisfied if (through a cycle of preconditions) it is also satisfied at some earlier time t − t', and if we suppose that there is some lower limit to the amount of time required to satisfy each subsequent condition given that its preconditions have been satisfied, then we can conclude that Nj and any condition depending on it will never be satisfied, by induction. This chronological Catch-22 differs from circular reasoning in that we do not suppose that we can actually achieve any of the preconditions; in fact we conclude that we can achieve none of them.

The logical status of a Catch-22 is therefore a reductio ad absurdum which demonstrates that the desideratum D cannot be achieved, because a logical contradiction would be required to achieve it. The only reason to confuse this with an actual contradiction or circular reasoning is if you assume that it is possible to achieve; but that is merely a bad assumption. The emotional power of a Catch-22 is when the desideratum D is more obviously compelling than one or more of the preconditions Nj, so that although D is impossible (and so 'technically' absurd), it is the logical structure which renders D impossible which seems absurd instead. This usually arises because the logical structure of the Catch-22 is established by some entity — again, usually a bureaucracy — whose priorities are more strongly aligned with the logical structure that it has created than with the desideratum D. The absurdity then comes from a clash of priorities between the agent trying to achieve the desideratum D, and the agent or more general setting which they find themselves in which is not very sympathetic to their priorities.

† This can also be used to capture a more complicated and Byzantine collection of preconditions which together form a set of necessary conditions, by taking the disjunction of preconditions and tracing them backwards until the collection of preconditions converge on a fixed set.

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This is an excellent answer. Thank you :) Setting aside the "absurd" logical structure, would the chicken-and-egg problem qualify as a catch-22 if you desire either a chicken or an egg? –  coleopterist Jan 7 '13 at 13:10
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If you require that the chicken arise only from other chickens (ie. not through a gradual process of mutation from chicken-like creatures), and you suppose that initially you have no chickens or chicken embryos (ie. you forbid an infinite causal regress of chickens and reject a special creation event of either chickens or their eggs), then yes: it would be what I've described as a chronological Catch-22, and is absurd due to the conflict of requirements of priority. –  Niel de Beaudrap Jan 7 '13 at 13:23

Catch-22 refers to a logical dilemma in which both outcomes are either equal or undesirable, rendering it unsolvable. It's not circular logic, but a logical complication of the inevitable outcome(s) of a set of premises.

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How would you distinguish a Catch-22 from other dilemmas? –  Niel de Beaudrap Dec 31 '12 at 14:11
    
I think it's an entirely literary distinction. Heller wasn't a logician, but a writer. –  SAHornickel Dec 31 '12 at 14:20
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True, though "dilemma" has passed into English quite some time ago for a situation in which all possible outcomes have undesirable features (at the very least, incurring a hefty opportunity cost). Only for a Catch-22, there aren't any outcomes per se; only rules which systematically prevent something from being possible without directly forbidding it. –  Niel de Beaudrap Dec 31 '12 at 14:45
    
I like to think of these sorts of dilemmas as a boolean function which returns either true or false. In Heller's instance, the question is "can I be excused from service by reason of insanity?" That the rules governing the outcome always return false is, I think, irrelevant. In taking the square root of a negative number, we get an imaginary number. Likewise, that we can imagine an alternate outcome to the dilemma that cannot, in all reason, exist, makes the value of "true" somewhat an imaginary answer. –  SAHornickel Dec 31 '12 at 19:31
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The imaginary truth value should be manifest in my clarification of the unity of true and false. Truth is a property. Either a premise contains truth or it does not. If a premise is false, it must mean that the truth is absent. So "false" refers not to itself, but to the logical construct "not true." So both "true" and "false" refer to the same object: "truth." So when Orr gets his answer of "false" he is actually getting "not true." The imaginary answer is just the inverse. It exists by nature, because the answer must be evaluated on the absence of truth, even if "true" cannot exist by rule. –  SAHornickel Dec 31 '12 at 20:31

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