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The Barber Paradox

. Thursday, August 22, 2013

barber The Barber paradox is attributed to the British philosopher Bertrand Russell. It highlights a fundamental problem in mathematics, exposing an inconsistency in the basic principles on which mathematics is founded. The barber paradox asks us to consider the following situation:

“In a village, the barber shaves everyone who does not shave himself, but no one else.”

The question that prompts the paradox is this: Who shaves the barber?

No matter how we try to answer this question, we get into trouble.

Scenario 1:

If we say that the barber shaves himself, then we get into trouble. The barber shaves only those who do not shave themselves, so if he shaves himself then he doesn’t shave himself, which is self-contradictory.

Scenario 2:

If we say that the barber does not shave himself, then problems also arise. The barber shaves everyone who does not shave himself, so if he doesn’t shave himself then he shaves himself, which is again absurd.

Clever One:

Even if we try to get clever, saying that the barber is a woman, we do not evade the paradox. 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).

Both cases, then, are impossible; the barber can neither shave himself nor not shave himself. And hence the question still remains ‘Who shaves the barber?’ is unanswerable.

Ship of Theseus

. Sunday, August 18, 2013

The ship of Theseus, also known as Theseus’ paradox, is a paradox that raises the question of whether an object which has had all its components replaced remains fundamentally the same object. Theseus paradox questions the very own existence of identity. Theseus is remembered in Greek mythology as the slayer of the Minotaur. For years, the Athenians had been sending sacrifices to be given to the Minotaur, a half-man, half-bull beast who inhabited the labyrinth of Knossos. One year, Theseus braved the labyrinth, and killed the Minotaur.

The paradox was first raised in Greek legend as reported by Plutarch,

"The ship wherein Theseus and the youth of Athens returned from Crete had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, in so much that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same."

—Plutarch, Theseus

The-Ship-of-Theseus

Let me try to put these into simple words as 2 scenarios

Scenarios 1:

The ship in which Theseus returned was long preserved. As parts of the ship needed repair, it was rebuilt plank by plank. Suppose that, eventually, every plank was replaced; would it still have been the same ship? A strong case can be made for saying that it would have been: When the first plank was replaced, the ship would still have been Theseus’ ship. When the second was replaced, the ship would still have been Theseus’ ship. Changing a single plank can never turn one ship into another. Even when every plank had been replaced, then, and no part of the original ship remained, it would still have been Theseus’ ship.

Scenario 2:

Suppose, though, that each of the planks removed from Theseus’ ship was restored, and that these planks were then recombined to once again form a ship. Would this have been Theseus’ ship? Again, a strong case can be made for saying that it would have been: this ship would have had precisely the same parts as Theseus’ ship, arranged in precisely the same way. If this happened, then, then it would seem that Theseus had returned from Knossos in two ships. First, there would have been Theseus’ ship that has had each of its parts replaced one by one. Second, there would have been Theseus’ ship that had been dismantled, restored, and then reassembled. Each of them would have been Theseus’ ship.

But the bigger question is - “Theseus, though, sailed in only one ship. Which one?”

So why suddenly coming to this logical paradox on Sunday Noon. Last Night I watched Ship of Theseus. Anand Gandhi’s work is a simulating work of cinema art.  A blind but superb photographer, an ailing monk fighting for animal rights and a stock broker who has got a kidney transplant done are three characters whose stories, when woven in a single thread, can be referred to as ‘Ship of Theseus’. A debut vehicle of Anand Gandhi, this film is strictly for a niche audience for a fact that it has been kept clear from any usual Bollywood paraphernalia that defines commercial cinema. To know any more than this you need to visit a screen and watch it.

 

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