Outer Limits of Reason Read Online Free PDF

contradiction.
    There are many other forms of the liar paradox:
    â€¢ The only underlined sentence on this page is a total lie.
    â€¢ The boldface sentence on this page is a blatant falsehood.
    â€¢ The sentence after the boldface sentence on this page is not true.
    Are they true or false?
    The liar paradox has been around for over 2,500 years and philosophers have devised many different ways of avoiding such contradictions. Some philosophers try to avoid these linguistic paradoxes by saying that the liar sentences are neither true nor false. After all, not every sentence is true or false. Questions such as “Your place or mine?” and commands such as “Go directly to jail!” are neither true nor false. One usually thinks of declarative sentences like “Snow is white” as either true or false, but the liar sentences show that there are some declarative sentences that are also neither true nor false.
    There are those who say that the sentence “This sentence is false” is not even grammatically correct. After all, what does “This sentence” refer to? If it refers to something, we should be able to replace “This sentence” with whatever it refers to. Let’s give it a try:
    â€œThis sentence is false” is false.
    This is grammatically correct and it might be true or false. But it is not self-referential and not equivalent to the original liar sentence. This is similar to the sentence
    â€œThis sentence is false” has four words.
    which is true, while
    â€œThis sentence is false” has five words.
    is false. It would be nice to have a grammatically correct English sentence that is a self-referential paradox. W. V. O. Quine came up with a clever way around these problems. Consider the following Quine’s sentence :
    â€œYields falsehood when preceded by its quotation”
    yields falsehood when preceded by its quotation.
    First notice that this is a legitimate English sentence. The subject is the phrase in quote marks and the verb is yields . Now, let us ask ourselves if it is true. If it is true, then when you attach the subject to the rest of the sentence, as we did, we get falsehood. So the sentence is false. In contrast, what if the sentence is false? That means that when you attach the subject to the sentence, you do not get a falsehood; rather, you get a true sentence. So if you assume that Quine’s sentence is false, you derive that it is true. This is a grammatically correct English sentence that is self-contradictory.
    Another potential solution to paradoxical sentences is to restrict language so as to avoid such sentences. Some have said that language should be stratified into different levels. They have declared that sentences cannot talk about other sentences of their own level or higher. For example, at the lowest level there will be sentences like “Grass is green” and “My pen is blue.” The next level will be sentences about sentences on the lowest level. So we might have
    â€œGrass is green” is an obvious sentence.
    or
    â€œMy pen is blue” has four words in it.
    One goes on to higher-level phrases like
    â€œâ€˜My pen is blue’ has four words in it” is a dumb fact.
    By restricting the types of sentences, we will be avoiding sentences of the form
    The sentence in italics on this page is grammatically correct.
    This is a sentence dealing with itself and hence is a sentence on its own level. It is declared not kosher—that is, not a legitimate part of language. Every sentence is only permitted to talk about sentences that are “below” it. If a sentence does talk about a sentence that is on its own level, that sentence is proclaimed meaningless. This stratification will ensure that there are no self-references and hence no contradictions. With such restrictions in place, linguists are fairly certain that they have banned most paradoxical linguistic sentences. However, this