The Barber's Paradox and the ultimate mystery

The Barber's paradox has fascinated many logicians and philosophers.* So far, no one ever resolved the paradox, and any attempt would simply converge along a straightforward logical path leading to an undebatable contradiction. Nonetheless, the paradox conveys a profound philosophical message that continues to fascinate many brilliant minds who made numerous attempts to explore new arguments for avoiding a contradiction. In the following, I first added an extra time dimension, and naively proceeded with my thought experiment aiming to resolve the paradox. As I moved back in time, a contradiction emerged, as it must, but this time it was far more inspiring than just a logical contradiction. It is an unescapable impasse in the beginning of time, which I consider as the ultimate mystery of life!

The Paradox

Suppose there is a village with only one barber who is a man. In this village, the barber is a man who shaves all those, and only those, men who do not shave themselves.

So, who shaves the barber? This question results in a paradox, as the barber shaves himself if he does not shave himself, or he does not shave himself if he shaves himself!

Resolving the paradox: the mystery of the beginning

A quick intuition suggested a possible resolution of the paradox if an initial state is assigned to each man and a chronological order is introduced to the shaving events.** If each man was allowed to change his status as time elapsed, the impasse could be unlocked. The idea sounded exciting though I remained skeptical about resolving the paradox by merely adding an extra time dimension. So, I decided to walk through the logical steps seriously. Suppose each man is randomly assigned as either a self-shaver or a non-self-shaver. After an event is completed, the status of each man in the village is updated. For the sake of convenience of illustration, I assume each man gets shaved once per day, and in each day he is shaved according to his yesterday's status. The logic apparently goes as follows.

I consider each man's status, starting today. If a man other than the barber is a self-shaver today (initial status), he will shave himself tomorrow and remains as a self-shaver forever. Likewise, if a man other than the barber is a non-self-shaver today, he will be shaved by the barber tomorrow and in all subsequent days. For the barber, we consider two cases. First, the barber is a self-shaver today. According to the rule, he will continue to be a self-shaver. In the second case, the barber is a non-self-shaver today, and according to the rule, he will be shaved tomorrow by the barber who happened to be himself. After that, his status is updated to self-shaver, and continues to shave himself in all subsequent days.

Makes sense? Not really! What is the non-self-shaver status for the barber? Did he shave himself on the first day (the "today")? If he didn't, who did? In fact, the self-shaver status for the barber is equally ill defined. If he did shave himself on the first day, he couldn't be the barber, could he?

The mystery is always in the beginning! Is it necessary to invoke God to set the universe going? Or should we simply refrain from asking the question of how it all got started, and be bothered only by the perpetual cause-and-effect cycles? Whether you take a theistic approach (e.g., be a Christian) or a non-theistic approach (e.g., be a Buddhist) is not going to make much difference at the end. The ultimate mystery shall remain.

September 2014

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