The cyclic logic of paradox

Here are several paradoxes presented as logical cycles.

Some of these paradoxes are from the book “Change Principles of Problem Formation and Problem Resolution” by Watzlawick, Weakland and Fisch.

Do let me know if you can see ways of presenting this more clearly.

On this page:

The liar paradox

Epimenides the Cretan says that all the Cretans are liars, but Epimenides is himself a Cretan; therefore, he is himself a liar. Here is a formulation of this paradox shown as a loop.

When Larry says he is lying, this sets up a logical paradox.

(1) Larry is NOT lying	———->	(2) “I am lying”
^ l l		l l v
(4) “I am lying”	<———–	(3) Larry is lying

Assume “Larry is NOT lying”, as at node 1, i.e., what he says is right.
- When you hear him say, “I am lying”, at node 2, you assume what he says is correct, and you conclude that Larry is lying.
- You are now assuming that “Larry is lying” and at node 3.
Assume that “Larry is lying”, as at node 3, i.e., that what he says is wrong.
- When you hear him say “I am lying” at node 4, you now assume that what he says is wrong and conclude that “Larry is NOT lying”.
- You now assume that “Larry is NOT lying” and are back at node 1.
- This closes the logical loop and leaves you in an infinite spin of uncertainty.

The logic forms a cycle, an unchanging system in which the listener’s conclusion endlessly oscillates. This paradox can be a mind teaser but becomes clearer when viewed as a cycle, as in the diagram.

A similar paradoxical statement is “This statement is false”

Paradox: Be spontaneous

If a teacher tells an improvisation student, Sam, to be spontaneous, this creates a paradox. (See Watzlawick et al, p 64)

I am not sure about this one.

(1) Sam is acting as instructed	———->	(2) Sam is not being spontaneous
^ l l		l l v
(4) Sam is being spontaneous	<———–	(3) Sam is not acting as instructed

When a person is spontaneous, they act governed by their own impulses and not controlled by external influences. If you say to me, “Be spontaneous”, then you trap me in a paradox

(1) When “Sam is acting as instructed”, following the instruction to be spontaneous, he is being controlled by external influences, and so
(2) “Sam is not being spontaneous”. When “Sam is not spontaneous”,
(3) “Sam is not acting as instructed” and so not being controlled by an external, so
(4) “Sam is being spontaneous”, so (1) “Sam is acting as instructed.”

If Sam follows the instruction, then he is not following the instruction. And if he is not following the instruction, then he is following the instruction.

This situation is a no-win situation. The instruction catches Sam in a paradox, and he can neither follow nor not follow the instruction.

If this were true, then the situation would be unsatisfactory for Sam and the instructor, but I think that “being spontaneous” is not as simple as this.

The barber’s paradox

The barber is the “one who shaves all those, and those only, who do not shave themselves”. The question is, does the barber shave himself?

The barber shaves men who do not shave themselves

(1) The barber shaves himself	———->	(2) barber shaves men who do not shave themselves
^ l l		l l v
(4) barber shaves men who do not shave themselves	<———–	(3) The barber does not shave himself

Assume that the barber shaves himself.
Applying the paradox, “the barber shaves all those, and those only, who do not shave themselves.”
So, the barber does not shave himself
Applying the paradox again, “the barber shaves all those, and those only, who do not shave themselves”, so now, it seems that the barber does shave himself, and we are back at the first assumption of step 1.

Paradox: Do not follow my instruction

The instruction, “Do not follow my instruction”, is also a paradox.

(1) Sam follows the instruction	———->	(2) Instruction: Do not follow my instruction
^ l l		l l v
(4) Instruction: Do not follow my instruction	<———–	(3) Sam does not follow the instruction

Paradox: I want you to want to study & not follow orders

Let’s set the scene with two paragraphs from Watzlawick.

“A mother and son become caught in a paradox when the mother says: I want my son to learn to do things and I want him to do things – but I want him to really want to do them. I mean, he could follow orders blindly and not want to. … I cannot agree with ordering him to do it – even though if he were left entirely alone, he would never do his homework. Without telling them, any kid’s room would end up knee-deep in clothes and toys.” (Watzlawick et al., p 62)

“She wants her son to comply with what she demands of him, not because she demands it, but spontaneously, of his own will. She insists, “I want you to want to study” (ibid, p 64)

The mother wants (1) her son to study and (2) not to follow her orders.

This is a no-win situation for the mother. She wants her son to study and believes that he will not want to study and she does not want him to obey her.

If he does not do his homework, she does not like this.
If he does his homework, she does not like it because she will believe that he is just obeying her.

I’m not sure that this is a paradox. The mother has set up a situation where the son cannot please both of her demands because she is sure that he does not want to do his homework.

Watzlawick could be saying this is a “do not follow my orders” paradox.

(1) Son follows his mother’s wishes	———->	(2) Instruction: Do not follow my instruction
^ l l		l l v
(4) Instruction: Do not follow my instruction	<———–	(3) Son is not following his mother’s wishes

The paradox of a real man

A woman says to a man, “I was a fool to marry you. I thought I could train you to become a real man.” (See Watzlawick et al., p 65)

(1) Man acts like a real man	———->	(2) Man is following his training
^ l l		l l v
(4) Man is NOT following his training	<———–	(3) Man is not acting like a real man

Say (1) the man acts like a real man,
then he is (2) following his training, so
(3) he is not acting like a real man, so
(4) he is not following his training, acting as an independent person, and (1) acting like a real man.

Success as paradox

“One of the most dangerous experiences human beings can have is success … because you tend to become quite superstitious and repetitious. … and decide that [everyone] ought to do that, when in fact that’s only one of a myriad of ways of getting the same result.”
(Frogs into Princes: Bandler & Grinder, p 23)

When you view success in this way, success is paradoxical as success tends to lead to narrowing and failure.

A paradox in gambling

Fred’s situation was paradoxical like this, with his success leading to failure. His success at feeling powerful at the casino led him to return to the casino, which compounded his powerlessness – repeatedly. When you focus narrowly on Fred’s winning streaks, then his gambling boosted his feeling of power. However, when you focus on the whole picture, then his gambling stripped him of power.

(2) Gambling to feel powerful	———->	(3) Gambling losses
^ l l		l l v
(1) Feeling powerless	<———–	(4) Big problems

Updated 4 March 2021