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Monty Pythons' Joke About the "Piranha Brothers"

Updated on January 15, 2015

The Joke: 2:55-3:37

Do you Understand the Joke About the Piranha Brothers' Operations?

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The Text of the Joke about the Piranha Brothers' Operations

Monty Python, Flying Circus, Episode 14, "The Piranha Brothers."

"When the Piranhas left school they were called up but were found by an Army Board to be too unstable even for National Service. Denied the opportunity to use their talents in the service of their country, they began to operate what they called 'The Operation'. They would select a victim and then threaten to beat him up if he paid the so-called protection money. Four months later they started another operation which the called 'The Other Operation'. In this racket they selected another victim and threatened not to beat him up if hedidn't pay them. One month later they hit upon 'The Other Other Operation'. In this the victim was threatened that if he didn't pay them, they would beat him up. This for the Piranha brothers was the turning point."

Is This Funny? Deductive Reasoning and Formal Fallacies.

The Piranha brothers are clearly daft - this is what comes across and makes us laugh when we hear about the two failed attempts they made before they accidentally hit the right concept for their extortion operation. For some reason, it is detectable that their logic is wrong but the joke is also on the average person - without this being readily understood. For starters, ask for an analytical, detailed presentation of the error the unintelligent brothers committed with the first two operations - and let's see if anyone can lay out a clear account. Even worse, the logical flaws of which the Piranha brothers are cuplable, are perpetrated by scores of intelligent people on a regular basis. It so happens that the specific examples of those logical flaws - the examples we have in this joke - are easy to see through. But other instances are not so transparent and the average person ordinarily falls for them - even though those are instances of the exactly same type of errors we have in the joke.

Let us start again. Something is wrong with the reasoning of the two brutish brothers in the joke; this is what makes us laugh, but what exactly is wrong? How should we put it? We can't say "no one who is not extremely unintelligent can expect to make money on this basis;" this begs the question as to what the flaw in the Piranhas' reasoning is exaclty. Notice, "begging the question" here does not mean "raising a question" but it refers to a characteristic logical error that is related to circular reasoning: the brothers do this because they are unintelligent and what proves that they are unintelligent is that they do this. We are still not accounting for what it is that makes what they a patent case of flawed thinking.

In the first operation they devised, the advertisement was that they would beat those who paid the extortion money. It is easy to see that the reasoning is wrong. If you don't want to be beaten, then you don't gain anything by paying up because, according to the advertisement, you will be beaten up anyway. As explained earlier, this is an example of a type of logical error; this particular instance of the error type is easy to detect for being fallacious but this is not generally the case. Consider the following argument and try to decide if it is a good argument or not. [What do we mean by "good?" That the truth of the premises guarantee that the conclusion is true. The premises are put down: accepting them as true, if the argument is logically correct, compels us to accept the conclusion as true too. In other words, if the argument is good or logically correct, there is no logically possible way that the premises are true but the conclusion is not true.]

  1. If you diet, you are in good shape exercise.
  2. But you are not in good shape.
  3. Therefore, you have dieted.

Can you tell if this is a good argument or not? If it is good, or if it is not good, can you tell why it is, or it is not, good?

Here comes the kicker: it might come as a big surprise that the argument you have just reflected on has exactly the same abstract type or logical form as the argument underpinning the ad of the Piranha's first operation. It might be surprising even to hear that there is an argument (a proof) in the reasoning of the Piranhas - but there is, and here it is.

  1. If you pay, you are to be beaten up. [This is the motto or advertisement or concept for the first operation.]
  2. But you surely don't want to be beaten up -- you are not to be beaten up as far as your wishes go.
  3. /.. Therefore, you [ought to] pay.

Like the preceding argument, on which you were invited to reflect, this one has a characteristic logical form. Every deductive argument does. To extract the logical form take "not" and "if-then" as the fixed (logically key) words and treat the rest as variable or placeholders. Here is the form.

  1. If p, then q.
  2. Not q.
  3. /.. Therefore, p.

This is indeed an invalid argument form. Any argument that has this logical form fails the logical test: an argument with this form can possibly have all true premises and a false conclusion. This may be or may not be obvious. In the case of the Piranhas joke, it comes across that there is something logically wrong. But this doesn't have to be the case. The test is to extract or detect the logical form of a deductive argument and then to inquire whether this form is valid or not. If the logical form of an argument is invalid - as in this case - we have what we call a Formal Fallacy (this can only happen with deductive arguments, which are the arguments with characteristic logical forms.) We don't have to bother about whether the argument actually happens to have true premises. Even if it is, since it is invalid, it cannot guarantee a true conclusion. The conclusion itself may actually be true but not thanks to the argument - it can happen coincidentally. The argument is invalid: it does not prove its conclusion even if the premises are true.

It is not even clear to the average person that there is an argument - a proof - involved in the joke we have been contemplating. Check the reconstruction above. Premise 2 (that "surely, you don't want to be beaten up") is not stated explicitly, it is assumed. The argument has what Aristotle called, thousands of year ago, an enthymematic presentation.

In the Second Operation, the Piranha Brothers offer not to beat the target up if he doesn't pay them. Let us reconstruct the full argument - once again, we have an enthymeme here - and extract its logical form. The 2nd premise (the assumption that the target does not want to be beaten up, is the same in all operations...) The conclusion is also the same - it expresses the brothers' expectation "you ought to pay" which is to be derived from the motto or advertisement and the psychological truth (the 2nd premise about not wanting to be beaten up) as premises.

  1. If you don't pay, you are not to be beaten up.
  2. You surely don't want to be beaten up -- you are not to be beaten up as far as your wishes go.
  3. /.. Therefore, you [ought to] pay.

The logical form follows. [Notice how we "cut" around the key logical particles, so-called logical constants, "not" and "if--then." Words like these determine the logic of a language!]

  1. If not-p, then not-q.
  2. Not-q.
  3. /.. Therefore, p.

This is an invalid argument form. It is possible to produce counterexamples to this form. A counterexample is an argument that has this logical form and clearly has all true premises and a false conclusion. This shows that it is logically possible that this form takes true premises in but throws a false conclusion out. So, the truth of the premises does not guarantee the truth of the conclusion. The form is invalid or formally fallacious.

Finally, the hapless criminals "turn the corner" when they accidentally hit on a motto for their operation, which yields an argument with - finally - a valid argument form. In this case they threaten to beat up the prospective victim was threatened that if he doesn't pay them. Here, reconstruction of the argument leads us to a logical form that is valid. It is logically impossible to have any argument of this logical form, which has true premises but a false conclusion. [Now, if an argument has this logical form, it is valid; it is logically correct in the sense that it has a correct logical form or structure - one that guarantees that, IF you put true premises, then the conclusion - the NEW sentence you get out - is guaranteed to be true. A valid argument can have premises that happen to be false. It is still VALID! IF the premises were true, the conclusion would have to be true. A valid argument with false premises is called unsound. It is a bad argument but the flaw here is not logical - it has to do not with what logical form the argument has but with how the world works. Use this as an opportunity to reflect on the following statement: deductive reasoning has nothing to do with the actual world works - it depends only on how certain particles ("not," "and," if--then," "either--or," "all," "some,"...) are defined and, hence, it depends on what logical form the argument has; nothing to do with factual information...]

  1. If you don't pay, you are to be beaten up.
  2. But you surely don't want to be beaten up -- you are not to be beaten up as far as your wishes go.
  3. /.. Therefore, you [ought to] pay.

Here is the logical form:

  1. If not-p, then q.
  2. Not-q.
  3. /.. Therefore, p.

This is a valid argument form. I can also show you how the conclusion can be derived from the premmises by applying certain rules of inference (those rules have standard names); the rules of inference are valid in standard deductive reasoning; so, moving from premises to conclusion deductively, step by step, we apply valid rules of inferences: this takes us to a conclusion that is validly supported by the premises.

  1. If not-p, then q. [Premise 1]
  2. Not-q. [Premise 2]
  3. Not-not-p. [From 1 and 2: by the rule Modus Tollens.]
  4. p. [From 4: by the rule Double Negation Elimination.]



Is It Objective?

The reason the joke about the Piranha Brothers comes across as funny (it should be funny if it is a successful joke) has to do with logic, as we saw. It is not guaranteed that we can detect logical errors or flaws (fallacies affecting arguments or inconsistency of sets of sentences/theories). Even with the Piranhas joke, the average person cannot give specifics about what causes the anomaly. The Piranhas, presumed unintelligent, reason wrongly - this much we get. They take as valid what are invalid (incorrect) argument-forms.

Would this joke come across as funny in other cultures? If nothing else besides the logic is the source of the joke, the joke should work only for speakers whose language has the same logic! Don't you think so? You might hear sometimes that what is "logical" depends on the culture - even on the person. "Logical" in this sentence must have a different meaning from the one we are discussing here. For instance, "it is illogical to spend your money without saving" means something else - it is not about what arguments work or if a theory is inconsistent. If the logic is indeed different in some other language, the Piranhas joke should not work there! Assuming the only joke here is because of violation of logical form, if the joke works with the natives (in translation, if need be), then they are playing by the same logic as we are. So, next time someone tells you that EVERYTHING is relative and even logic varies from one culture (or, better, linguistic community) to another, now you know what to say: Perhaps, but this must be shown! Would, for instance, the Piranhas joke fail to work among the natives.

There are consequences to this, of course. Logic orders us - it has normative force. Like the Piranha brothers, putting down an argument that has an invalid logical form means that we are wrong - objectively! Even if no one notices, we are still wrong. If our favorite people, or our favorite culture for that matter, evidently play the same logic game but get it wrong - that's it, they get it wrong; appealing to tolerance is irrelevant here.

Now that we understand that correctness (validity) of deductive arguments is a matter of logical form, here are some patterns or structures (argument forms) that are valid - and some notoriously invalid logical forms - of the standard logic of statements. Check the symbols used - explained below - and the representation of the argument forms in those symbols.

Valid Argument Forms

Valid Argument Forms.  Their names (from top to bottom): Modus Ponens; Modus Tollens; Disjunctive Syllogism.
Valid Argument Forms. Their names (from top to bottom): Modus Ponens; Modus Tollens; Disjunctive Syllogism.
Valid Argument Forms.  Their names (from top to bottom): Constructive Dilemma or Arguing by Cases; Chain or Hypothetical Syllogism; Double Negation.
Valid Argument Forms. Their names (from top to bottom): Constructive Dilemma or Arguing by Cases; Chain or Hypothetical Syllogism; Double Negation.
Valid Argument Forms.  Their names (from top to bottom): Simplification or Conjunction Elimination; Contraposition.
Valid Argument Forms. Their names (from top to bottom): Simplification or Conjunction Elimination; Contraposition.
Conjunction Introduction; DeMorgan's Laws; Importation.
Conjunction Introduction; DeMorgan's Laws; Importation.
In light of this, revisit the DeMorgan's laws above. Those laws actually work in both directions: from left to right (as indicated) but also from right to left. This means that we have logical equivalence of the phrases on the two sides.
In light of this, revisit the DeMorgan's laws above. Those laws actually work in both directions: from left to right (as indicated) but also from right to left. This means that we have logical equivalence of the phrases on the two sides.

Invalid Argument Forms (Formal or Deductive Fallacies

Invalid Argument Forms. Their names, from top to bottom: Denying the Antecedent; Affirming the Consequent; Converse Fallacy.
Invalid Argument Forms. Their names, from top to bottom: Denying the Antecedent; Affirming the Consequent; Converse Fallacy.

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