The cyclic logic of paradox

Here, I investigate the meaning of paradox and whether client Zed’s situation is paradoxical.

Some family therapists have focused on paradox. I present several paradoxes as logical cycles, including some raised in “Change Principles of Problem Formation and Problem Resolution” by Watzlawick, Weakland and Fisch.

On this page:

Paradox definition

A paradox is:

A seemingly absurd or self-contradictory statement which is or may be true, for example:
- The science of quantum mechanics posits that light is both a particle and a wave, and
- The statement “the solution is the problem”.
A statement which, despite sound, or apparently sound, reasoning from acceptable premises, leads to a conclusion that seems logically unacceptable or self-contradictory, for example, “the liar paradox”.
A person or thing that combines contradictory features or qualities.
A statement that conflicts with common belief.

Initially, I thought that a paradox only included statements like the logical paradox, “This statement is false”. Now, I see that it also includes a situation that combines contradictory features.

Paradox: “This statement is false”

Let’s consider a classic example of a logical paradox and how that works. Epimenides the Cretan says that all the Cretans are liars. A simpler form of this paradox is, “This statement is false”.

(1) Tentatively assume “this statement is true”.		(2) “This statement is false”.

(4) “This statement is false”.		(3) Tentatively assume “this statement is false”.

Start by tentatively assuming that “this statement is true” (node 1). The statement is “This statement is false” (node 2), so if it is true, you tentatively must assume that “this statement is false”, which is node 3.
Now tentatively assume that this statement is false (node 3). The statement is “This statement is false” (node 4), so if it is false, you must tentatively assume that “this statement is true”, which brings you back to node 1.

There are only two alternatives: either the statement is true or it is false. Having considered both, we find that (1) if it is true, it is false; and (2) if it is false, it is true. So, the logic forms a cycle, an unchanging system in which your conclusion endlessly oscillates between “this statement is true” and “this statement is false”. This is precisely what makes this a logical paradox and a mind teaser. For me, the diagram makes it clearer.

A similar paradox is, “I am lying”.

A slightly more complicated paradox is “I always lie”, which I discuss below. It is more complicated as there are three alternatives here: (1) I always lie, (2) I’m always truthful, and (3) I sometimes lie.

Paradox: Do not follow my order.

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

(1) Try to follow the order.		(2) “Do not follow my order”.

(4) “Do not follow my order”.		(3) Try not to follow the order.

Start by trying to follow the order at node 1. The order is “Do not follow my order” (node 2), so to follow the order, you must try not to follow it (node 3).
Now try not following the order (node 3). The order again says “Do not follow my order” (node 4), so to NOT follow the order, you must try to follow it, which brings you back to node 1.

Paradox: I want you to want to study

Watzlawick illustrates a paradox with the example of a mother and son.

“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)

I struggle to get my head around this situation.

I can see it as a paradox because the mother is combining contradictory wants. She wants him to study and to really want to study. She rejects both blind obedience and coercion, yet she is convinced that, if left alone, he will not study at all.

The mother issues a command that logically undermines itself. Whatever he does, he fails on one level of the message, as she will not accept that he has met her requirements when he:

does not study,
studies because he is told to, and so is being obedient,
studies and wants to, but she does not believe he really wants it. Here, he would be meeting her ideal, but not because of her demand, as you cannot produce want by demand.

I can also see this as a double bind: the son receives two incompatible injunctions: to study and to want to study spontaneously, with no acceptable way to satisfy both simultaneously. Here, the paradox does not lie merely in the mother’s conflicting wishes, but in the structure of her communication: the demand to freely want something is a paradox and impossible to follow.

Wanting is free only if it is not commanded, but here it is commanded. The demand means that the wanting is forced.

Success as a 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 this way, it becomes paradoxical: success tends to lead to the failure of becoming narrow-minded.

Client Zed: A gambling paradox

Problem gambling client Zed generated a paradoxical situation for himself.

During the fictional counselling session with my client Zed, I identified a self-reinforcing feedback cycle.

This diagram shows the dynamic driving this client’s problem gambling.

Towards the end of the session, I summed it up, saying to him:

There is a cycle here: (1) the more you gamble to feel respected, while on winning streaks, (2) the more money you lose and the less respect you get at home and at work, so (3) the more you need respect, and (4) this throws you back to gamble more. This vicious cycle is making your life very difficult.

The method for generating and using the cyclic intervention is critical: the page describing the example counselling session details this.

Zed’s life became paradoxical because:

His solution was his problem, and
His success at feeling respected led to his failure to gain respect.

The cyclic cobweb diagram we generated during the session succinctly expressed this paradox in a way Zed could understand and value.

Gambling creates other paradoxes.

Some gamblers value their relationships with venue staff who chat with them and offer them free drinks. So, they gamble to foster friendship, while often alienating family and others.
Some people gamble to escape from tensions at home, but commonly, gambling losses will exacerbate those home tensions.
Some people gamble because they feel a gambling venue is a safe place to be, not like in a pub or on the street; however, as gambling becomes a problem, the venue becomes a dangerous place for them.

Clients’ paradoxes can challenge a counsellor

One client with a gambling problem told me that after leaving our counselling sessions, she went straight to the pokies. One way of looking at this is that she was saying that the solution of counselling had become a problem.

Another client said, “I have to keep gambling. It’s the only way I can get back to square one.” One way of looking at this was that this problem gambler was telling me that gambling was his only solution.

Looking back, I don’t think I handled either situation well. The crazy, spinning logic of these paradoxes seemed unassailable and caught me in the client’s despair. I needed to find better ways to stay curious and to hear how trapped they felt.

Mathematics cannot prove every truth

Logical paradoxes like “this statement is false” are self-referential and contain a negative. If they are true, they are false; and if they are false, they are true.

In the 1930s, the mathematician Kurt Gödel constructed this kind of self-reference within a mathematical system. Stated in English, it’s like, “This statement of number theory does not have any proof”. He showed that any mathematical system defined by a set of axioms contains true statements that mathematics cannot prove. Mathematics has intrinsic limits: it cannot prove every truth.

(Douglas Hofstadter: Godel, Escher, Bach: An Eternal Golden Braid, p 18)

When climate-change deniers demand “proof” that climate change is real, they are exploiting a misunderstanding of how knowledge works. Science does not deliver mathematical certainty; it delivers overwhelming evidence and the best available explanations. Demanding proof in this way is not scepticism; it is a logical error and an impossible demand often used to avoid accepting the evidence.

See my page on Convergence: The basis for scientific confidence.

More paradoxes

If you want more paradoxes, here are some.

“I always lie”

Another form of the Epimenides paradox is when Larry says, “I always lie”. (Let’s label the liar Larry.)

This is slightly more complex than “This statement is false”, the first example above. This is because there are not two, but three alternatives here: (1) I always lie, (2) I always tell the truth, and (3) sometimes I lie, and sometimes I do not.

Here is this paradox shown as a cycle.

(1) You assume Larry is telling the truth.		(2) He says, “I always lie”.

(4) He says, “I always lie”.		(3) You assume he always lies.

Start by assuming that Larry is telling the truth (node 1). If what he says is true, then his statement at node 2, “I always lie”, must be true. But if “I always lie” is true, then Larry must always be lying, which takes us to node 3.
Now assume instead that Larry always lies (node 3), meaning that any statement he makes is false. So, his statement at node 4, again, “I always lie”, must be false. But if “I always lie” is false, then he does not always lie, and at least sometimes tells the truth. Taking his statement as one of his truthful statements returns us to node 1.

Assuming that Larry is telling the truth leads you to think he always lies. Assuming he always lies leads you to think he could be telling the truth. The result is uncertainty.

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.” (Watzlawick et al., p 65)

(1) Man acts like a real man.		(2) Man is following his training.

(4) Man is NOT following his training.		(3) Man is not acting like a real man.

Say the man acts like a real man (node 1), then
He is following his training (node 2), so
He is not acting like a real man (node 3), but as
He is not following his training and is acting independently (node 4),
He is acting like a real man (node 1).

This woman has set up a no-win situation for herself and the man.

Paradox: Be spontaneous

When a teacher tells an improvisation student, Sam, to be spontaneous, this creates a paradox. (Watzlawick et al, p 64-68)

(1) Sam is acting as instructed, being spontaneous.		(2) Judgement: Sam is not being spontaneous because he is acting as instructed.

(4) Judgement: Sam is being spontaneous, doing his own thing.		(3) Sam is not acting as instructed

When a person is spontaneous, they act guided by their own impulses rather than controlled by external influences. If you say to me, “Be spontaneous”, then you trap me in a paradox.

When Sam is acting as instructed and trying to be spontaneous (node 1), he is following the instruction to be spontaneous, controlled by external influences (node 2), and so Sam is not improvising and is not acting as instructed (node 3).
When Sam is not acting as instructed (node 3), he is doing his own thing (node 4), and so is acting as instructed and being spontaneous (node 1).

This situation is a no-win situation for both people. The instruction traps Sam in a paradox: he can neither follow it nor not follow it.

More simply, the order “Be spontaneous” can be seen as paradoxical, as (1) if you are spontaneous, then you are following an order, and that is not spontaneous. However, (2) if you are not spontaneous, you are doing your own thing, and so being spontaneous.

The barber’s paradox

The barber in a small village has a rule:

He shaves all and only those men who do not shave themselves.”

A key question arises: Does the barber shave himself? The barber’s paradox shows that the barber’s rule about who he shaves breaks down when it comes to whether he shaves himself. Mathematicians pondered this because it demonstrated difficulties with set theory.

(1) Assume the barber shaves himself		(2) Rule: He shaves … only those men who do not shave themselves

(4) Rule: He shaves all … those men who do not shave themselves		(3) Assume: The barber does not shave himself

If he shaves himself, he breaks his rule, as “he shaves … only men who do not shave themselves”, so he should not shave himself.
However, if he does NOT shave himself, well again, he breaks his rule as “he shaves all … those men who do not shave themselves”, so he should shave himself.

The rule is faulty as it does not guide the barber for all men.

The introduction to my counselling pages includes:

Links to the other counselling pages, including those describing how this approach relates to other counselling practices and theories, see the top of the introduction page
References for all the counselling pages, at the end of the introduction page.

First loaded 2020: Updated 8 Feb 2026