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While reading some open books in the shelves of National Bookstore, I came across this article regarding one of Bertrand Russell’s paradoxes. It is called “the barber’s paradox”. It goes like this: Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men who do not shave themselves.
Under this scenario, we can ask the following question: Does the barber shave himself?
Asking this, however, we discover that the situation presented is in fact impossible:
If the barber does not shave himself, he must abide by the rule and shave himself.
If he does shave himself, according to the rule he will not shave himself.
No one really understands what a paradox is. I heard one person in LU saying that paradoxes are nothing but semantic mistakes. I guess he hasn’t been reading a lot of philosophy books lately. Some dictionary define a paradox simply as statements that contradicts itself, but I think a paradox is more better understood as an argument that derives or appears to derive an absurd conclusion by rigorous deduction from obviously true premises.

Zeno of Elea (circa 495-430 BCE) is best known for his paradoxes that is said to be the first recorded examples of argument of ‘reductio ad absurdum’ (literally, reduction to absurdity) in which an opponent’s view is shown to be false because it leads to contradiction. The paradox of Achilles is perhaps the best known of Zeno’s puzzles. Swift Achilles is to run a race against a tortoise, and the tortoise is given a head start. Zeno argues that, no matter how fast Achilles runs, he can never overtake the tortoise. First Achilles must reach the point atwhich the tortoise started, call it P1. By the time he does so, however, the tortoise will have traveled some short distance further, to a point we can call P2. So Achilles’snext task is to run from P1 to P2. By the time he achieves this, the tortoise will have traveled a bit further, to P3. SoAchilles’s next task is to run to P3. But by then the tortoise will have reached P4, and so on.

Thus, according to Zeno, Achilles can never pass the tortoise and win the race, because, no matter how fast he runs, each time he reaches a point where the tortoise was, the tortoise will have moved a bit farther on.

Stating the conclusion more carefully, Zeno’s argument does not (and was most likely not intended to) show that Achilles cannot overtake the tortoise; rather, it demonstrates that there is a conceptual puzzle regarding how he does so.

Another famous  Zeno’s paradox is the runner, who, before she can reach her destination, first has to reach the point halfway there, and who, before reaching the halfway point, has to reach the quarter point, before which she must reach the point one-eighth of the way to the destination, and so on. The conclusion is that no runner ever reaches her goal, or even gets started.

Aristotle tackled Zeno’s paradox and said that it was not possible to partition Achilles’s path into infinitely many parts. Any segment of Achilles’s course can be divided in two, so that there is no finite bound on how many pieces the path contains, but the process of partitioning the path never concludes in a path with infinitely many parts. The number of segments that make up the path is said to be potentially infinite. The moral Aristotle drew from Zeno is that there is, in nature or in mathematics, no actual infinite.

This in turn was later use by the Arabs in their Kalam Argument for the Existence of God, which in turn was made famous by the Christian apologist William Craig Lane.

According to this Christian apologist, there are two types of infinite process: actual or potential. An actual infinite series is one that is completed. A potential infinite series is one that continues to go on without end. (I think Norman Giesler also promote this definition) Since it is absurd to imagine something infinite that can be completed, then actual infinites cannot exist. Potential infinite in the other hand, can only exist through ideas (abstract). Numbers are good example of a partial infinite.

Thanks to these wonderful Christian apologists, their god is now ensnared on their own ridicules explanations. God is said to be infinite. So is he partial or an actual infinite being? If you say actual, then he cannot exist, but if you say he’s a partial infinite, then he’s an abstract idea. In addition, if actual infinite does not exist, then how the Christian can god becomes “omnipotent” and “omniscient”. According to the divine attributes of omniscience, god has all the ideas of infinite knowledge because “he is the greatest being conceivable” (compare to worldly knowledge that is said to be finite). If actual infinite is impossible – then an omniscient being cannot exist. 

This brings us back to Russell’s Barber paradox. The puzzle about the barber has an easy solution. – Such a barber does not exist. Now does the Christian god also suffer the same conclusion as Russell’s barber?

John the Atheist