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July 7th, 2019 (Permalink)

Rule of Argumentation 61: Defend your position!

This is how arguments usually start: someone makes an affirmative claim that someone else either denies or at least doubts and challenges. If you are the person making a claim and someone challenges it, the burden is on you to defend that claim. If you cannot or do not wish to defend it, then you should withdraw it2.

You may be familiar with the notion of burden of proof in the Anglo-American legal system. In a criminal case, the burden of proof is on the prosecution to prove the defendant's guilt beyond a reasonable doubt. At the very least, the prosecutor must present a prima facie3 case for guilt. If the prosecution succeeds in presenting a prima facie case then the burden of proof switches from the prosecution to the defense. However, if the prosecutor fails to present such a case then the defense wins, that is, the defendant need not even present a case unless the prosecution meets its burden of proof.

Another way of making this same point is that in the Anglo-American legal tradition there is a presumption of innocence, that is, the defendant is presumed innocent until proven guilty. The presumption of innocence is the other side of the burden of proof coin: the burden is on the prosecution and the presumption is in favor of the defendant. If the prosecutor meets the burden with a prima facie case, then the burden and presumption switch: the burden is then on the defense to rebut the prosecution's case sufficiently to show a reasonable doubt of the defendant's guilt.

The notions of burden of proof, presumption, prima facie evidence, and the shifting of the burden of proof can all be extended from the legal realm to argumentation in general. However, it's not obvious who gets the burden and who gets the presumption, that is, who plays the role of the prosecutor and who the defendant?

The answer is that the burden is on the affirmative rather than the negative, that is, on he who affirms as opposed to she who denies. The reason for this is an asymmetry between affirmative claims and denials, namely, that it is much easier to find evidence for an affirmation than a negation4. Moreover, unless they just blurt out claims for no reason, those who introduce a claim should be able to produce some evidence to support it. In contrast, you may be skeptical of a claim without having studied or considered the matter enough to present evidence against it.

The burden of proof is not all or nothing, but comes in degrees. If you assert a plausible claim then the burden of proof will be light, whereas an implausible claim places a heavy burden on you. This is the basis for the familiar saying that extraordinary claims require extraordinary evidence5.

Logical fallacies that result from attempts to evade the burden of proof include6:

So, the burden of this rule is that if you make an affirmative claim, be prepared to defend it. If, in contrast, you are the challenger and the proponent of the challenged claim makes a prima facie case, then accept the burden of proof. It is now up to you to either make a case against the claim, or to accept it.

Next Month: Rule 7


  1. Previous entries in this series:
    1. Rule of Argumentation 1: Appeal to reason!, 12/14/2018.
    2. Rule of Argumentation 2: Be ready to be wrong!, 1/26/2019.
    3. Rule of Argumentation 3: Focus on claims and arguments!, 2/13/2019.
    4. Rule of Argumentation 4: Be as definite as possible!, 3/8/2019.
    5. Rule of Argumentation 5: Be as precise as necessary!, 5/29/2019.
  2. As with all the rules discussed in this series, this is a rule of thumb, that is, a rule that has exceptions. For this rule, common sense is an exception. For instance, a person who asserts that every living thing eventually dies does not bear the burden. Instead, those who challenge such a claim must make a prima facie case against it, and only then does the burden shift to the claimant.
  3. Latin for "at first sight". See: Eugene Ehrlich, Amo, Amas, Amat and More: How to Use Latin to Your Own Advantage and to the Astonishment of Others (1985). A prima facie case for a claim is one that is sufficiently strong to prove the claim unless successfully rebutted.
  4. It is often said that you can't prove a negative, which is over-stated but a good rule of thumb. For an explanation of how much truth there is in this saying, see: Logical Literacy: "You can't prove a negative.", 3/14/2015.
  5. Popularized by the astronomer Carl Sagan, see: Broca's Brain: Reflections on the Romance of Science (1980), p. 73.
  6. For more on each fallacy, see the entries under the names of the fallacies available from the drop-down menu in the navigation pane to your left.

July 4th, 2019 (Permalink)

An Independence Day Puzzle at the Logicians' Club

In July of 2019, the Logicians' Club* held its monthly meeting on the fourth. To celebrate the holiday, the members played a game. On this day, its three regular members were in attendance: Mrs. A, Miss B, and Mr. C. It was the latter who suggested the game and organized it for the other two members to play. They met in a private room of the tavern where the club meetings were held.

"Fellow logicians," Mr. C began impressively after clearing his throat, "I have here a bag of patriotic hats," he said, holding up a large opaque bag. "Two of the hats are red, two are blue, but only one is white." He reached into the bag, pulled out a white hat and placed it on his own head.

"In a few minutes," he continued, "I will turn out the lights and pull two hats out of the bag. Then I will place a hat on each of your heads. When I turn the light back on, both of you will be able to see the color of the other's hat, but you won't be able to see your own. I will ask each of you to guess the color of your own hat by whispering in my ear so that the other player won't know your guess. If at least one of you is right, you will both win a prize which you can share.

"Now, I'm going to step out of the room for a few minutes and allow you time to confer. It won't be cheating if you agree between you on a strategy for playing the game. Remember two things: first, only one of you has to guess the color of her hat correctly in order to win the prize―it doesn't matter whether the other player's guess is incorrect; second, if you win you will share the prize, so this is not a competitive game. Good luck!" And he left the room.

Is there a strategy that the two logicians can use to ensure that they win the prize? If so, what is that strategy?

* For other meetings of the club, see:

(Added 7/9/2019) An anonymous reader wrote in wondering whether Mr. C could have taken the white hat that he put on his own head and put it on one of the two players when the lights were out. Of course, he could have, but rest assured that he didn't.

(Added 7/5/2019) Thanks to Lawrence Mayes for pointing out a loophole in the description of the game which has now been closed by amending this sentence.

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