The Barber Paradox and The Irrationality of Logic

People are often surprised to learn I avoid mathematics exercises and puzzles like

plague. Simply because I worked for nearly 30 years in the computer business

everyone assumes I am a mathematics wizard. I'm actually very good with arithmetic

and logic, algebra, geometry, trigonometry and calculus you can forget, I just can't be

arsed. It's a myth that computer programmers have to be good at maths, for many

branches of business programming it can actually be a drawback. Learn from The

Barber Paradox, one of the most famous thought experiments of 20th century

philosophy usually attributed to Nobel prize winning British mathematician and

philosopher Bertrand Russell demonstrates how mathematical logic is often illogical.

The Barber paradox highlights a fundamental problem in mathematics, exposing

an inconsistency in the basic principles on which mathematics is founded. It seems

strange to many that Russell, a thinker who devoted most of his early career to

finding mathematical truths that provided answers to the great philosophical question

like "Where did we come from?" “how did human consciousness develop?” "Is there

a God?" "Does life have any meaning?" and "Who put the bang in wallah wallah bing

bang?" should then turn to demonstrating the absurdities of mathematical thinking.

In the latter part of his life however, Russell's quest for truth took him in another

direction and one of the results of this is the crazy logic of The Barber Paradox.

Russell's paradox asks us to consider a hypothetical situation:

A certain village has only one barber. He shaves all the people who does not

shave themselves, but no one else.

The question we must answer is "Who shaves the barber?"

However we attempt to answer this question ,

mathematical logic comes up against a logic barrier and gets

into trouble. Suggest the barber shaves himself and we hit

the barrier. The barber shaves only men who do not shave

themselves, so if he shaves himself then he doesn’t shave

himself, which is nonsense.

Trying to escape by saying that the barber does not

shave himself but is shaved by the barber only gets us into a

new set of problems. The barber shaves everyone who does

not shave himself, so if he doesn’t shave himself then he shaves himself, which is

again a logical absurdity. Note here that the paradox depends on very precise wording

in the problem statement, wording that creates a paradox rather than expressing the

question in a straightforward way to avoid ambiguity.

Many students try a clever escape by saying that the barber is a woman. This still

does not answer the paradox according to mathematical logic. If the barber is a

woman, then she either shaves herself (and so is one of the people not shaved by the

barber), or does not shave herself (and so is one of the people shaved by the barber,)

You may note here a typical mathematician's irrationality creeping in, a woman

(unless she is from southern Europe) does not need to shave her face and thus cannot

be part of the logic problem. Seeing the problem from too narrow a perspective rather

than taking a broad view is often an obstacle to finding a good solution.

Both cases, then, are impossible; the barber can neither shave himself thus

belonging to the group that shave themselves and those who are shaved by the barber

Who shaves the barber?

nor not shave himself. Again observe the rigidity of the mathematical mind set. Stuck

in pedantic mathematical perspectives on the logic they fail to see the absudity of the

problem. As Sherlock Holmes said to Watson, "You see but you do not observe." The

whole question is based on the assumption that everybody shaves but we have

already seen that women do not need to shave, that fact is even turned into an absurd

trap to block an escape route from the paradox. And when it comes to women not

shaving, neither do a certain category of men. It is, is it not, an irrational to assume

the barber does not have a beard, the kind of illogical assumption those who claim to

be scientists are always accusing their critics of making.

So there's the answer, a bearded barber. The question ‘Who shaves the barber?’ is

in fact not unanswerable. Like most thought experiments those obsessed with

mathematics try to pass off as "science" it only becomes unanswerable if ridiculously

limiting parameters are imposed in other words the problem can only exist

hypothetically. Are all the people in the village men? Unlikely. Are all the men in the

village clean shaven? Not necessarily. When exposed to the harsh light of critical

analysis in the real world the question is simply nonsensical. Like so much of modern

"science" that only exists in theory or imagination, the paradox is a problem that has

no relevance in the real world.

Let's apply a little more reality to dismissing this particular absurdity of The

Barber Paradox so the mathematically minded can chill out, waste no more time on it

Does the barber look like this.

and concentrate on holding down jobs as shelf stackers and burger flippers.

In life we take on many roles but cannot give our attention to all simultaneously.

My wife and I had two children so one of my roles is a father. Although I have been

my children's father at all time from their birth, when I was at work, while fulfilling

the provider part of a father's role I was principally an Information Technology

consultant. I fitted the role of consultant and the role of hands on Dad around each

other. Now my children are 37 and 33 my father role has receded into the background

and I'm just a guy well past the first flush of middle age who no longer works and

sees his children occasionally, doing the best I can in the role of grandad. I am still

knowledgeable on some aspects of information technology though I am no longer

actively a consultant and fill my time as an internet content creator.

Likewise the barber in the conundrum. While in one sense the barber is always

the barber, in another he is only actively the barber when his shop is open for

business or he is engaged in barbering related activities. At other times he might be a

husband or lover, a father, bathroom tenor, mountain biker, poet, and so on. All these

titles we could give him are not mutually exclusive.

Only in the warped world of theoretical science could the kids Dad, the

undiscovered opera star, shave himself while he is not engaged in being the barber,

then go off and open the shop thus becoming the barber for the day. Mathematical

minds will complain here that I cheated. OK, try this, my car will not start. I am not a

mechanic but I have tools and know how to strip down and rebuild an engine. There

is either no mechanic available or I'm too tight fisted to pay. Am I going to obey a

rule set by the mechanics' guild that says only the mechanic can fix a car or am I

going to fix my car and raise a finger in salute as I drive by the mechanics' guild

office?

To be fair to Bertrand Russell, he did create this paradox to demonstrate the limits

of logic to students who were beginning to believe at that time they could find

answers to all the great questions of humanity by mathematical reasoning.

The Barber paradox is only unanswerable to mathematicians whose addiction to

order requires that everything is put in a neat little box with a label on it. This is

because mathematics must deal in absolutes and in life, in nature there are very few

absolutes. We cannot even settle the question of whether death is absolute (Scientific

evidence for life after death).

Many people believe with great certainty that our spiritual being, the soul,

continues in some way after death. Others, myself included though I am not as

pedantic about it as a lot of people, believe death is the end of us as individuals. we

only live on as memories. We cannot however be absolutely certain that one or other

view is absolutely What if our understanding of the nature of being is wrong. An

example of the uncertainty is described in my article Quantum Metaphysics which

explores a theory that turns on its head all current scientific thinking about the nature

of life and being.

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