Outer Limits of Reason Read Online Free PDF Page B

solution is somewhat artificial. Common human language has always dealt with some type of self- reference without problem:
    â€¢ Someone says, “Oh! I am groggy today and I do not know what I am talking about.” Is he aware of saying this sentence?
    â€¢ Carly Simon sings a song with the lyrics “You’re so vain, you probably think this song is about you.” But this song is about him!
    â€¢ “Every rule has an exception except one rule: this one.”
    â€¢ “Never say ‘never’!”
    â€¢ “The only rule is that there is no rule.”
    In all of these cases—and many more—human language is violating the restriction of only dealing with sentences that are “below” it. In each case, a sentence discusses itself. And yet, somehow, all these examples are a legitimate part of human language.
    Another possible solution to paradoxical sentences was mentioned in chapter 1 , namely, human language is a product of the human mind and, as such, subject to contradictions. Human language is not a perfect system that is free of discrepancies (in contrast to perfect systems like mathematics, science, logic, and the physical universe). Rather, we should simply accept the fact that human language is faulty and has contradictions. This seems reasonable to me.
    2.2  Self-Referential Paradoxes
    The cause of the problem with the liar paradox is that language can be used to describe language. In particular, one can have a sentence that discusses its own truthfulness. This ability of language to describe language is a form of self-reference. Paradoxes that arise from such self-reference are the subject of this section. While these paradoxes are not linguistic paradoxes per se, they are similar to the liar paradox and will help us understand the true nature of self-reference.
    The British philosopher Bertrand Russell described a delightful little paradox that has come to be known as the barber paradox. Imagine a small isolated village in the Austrian Alps that has only one barber. Some villagers shave themselves and some go to the barber. Everyone in the village abides by the following rule: all those who do not shave themselves must go to the only barber and all those who do shave themselves do not go to the barber. This seems like a pretty innocuous rule. After all, if they can save some money by shaving themselves, why go to the barber? And if they go to the barber, why shave themselves? Now, simply ask yourself:
    Who shaves the barber?
    He is a villager and so if he does not shave himself, must go to the barber. But he is the barber and so he shaves himself. If he does shave himself, then, since he is the barber, he goes to the barber and does not shave himself. 4
    We might envision the barber paradox with figure 2.1 . We split the set of villagers into two parts and look to see if the barber is on the right or left.
    Figure 2.1
    Which subset is the barber in?
    In contrast to the liar paradox, the barber paradox has a simple solution: the village described simply does not exist. It cannot exist because there is a contradiction inherent in its description. Our description entails a contradiction with the barber. Since the real world cannot have contradictions, the village does not really exist. There are many other villages in the Austrian Alps, but they have different setups. They might have two barbers that shave each other; they might have a female barber that does not shave; they might have long-haired hippie types who do not go to any barber regardless of need. These descriptions of other villages are totally legitimate; no contradictions result from them. But the village Russell described cannot exist.
    Another clever paradox deals with adjectives in English and is called the heterological paradox or Grelling’s paradox . Consider the word English . English is an English word. In contrast, French is not a French word (it is an English word). Let us look at some