![]() ![]() The subject is the phrase in quotation marks and the verb is yields. “Yields falsehood when preceded by its quotation” yields falsehood when preceded by its quotation.įirst notice that this is a legitimate English sentence. Quine came up with a clever way around these problems. It would be nice to have a grammatically correct English sentence that is a self-referential paradox. But it is not self-referential and not equivalent to the original liar sentence. This is grammatically correct and it might be true or false. 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. ![]() There are those who say that the sentence “This sentence is false” is not even grammatically correct. 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. Questions such as “Your place or mine?” and commands such as “Go directly to jail!” are neither true nor false. After all, not every sentence is true or false. Some philosophers try to avoid these linguistic paradoxes by saying that the liar sentences are neither true nor false. The liar paradox has been around for over 2,500 years and philosophers have devised many different ways of avoiding such contradictions. The sentence after the boldface sentence on this page is not true. The boldface sentence on this page is a blatant falsehood. There are many other forms of the liar paradox: Neither assumption leads you to a contradiction. Similarly, if you start with the premise that L4 is true, you get that L5 is false, and hence L4 is true. It is important to note that just because sentences refer to themselves and their falsehoods does not mean there is a contradiction. In contrast, if L2 is false, then 元 is true and 元 asserts that L2 is true. If L2 is true, then 元 is false, which would mean that “L2 is true” is false and hence L2 is false. Other variations of the liar paradox have sentences that are not directly self- referential. For example, we can denote a sentence L1 and then say that L1 asserts its own falsehood:Īgain, if L1 is true, then it is false. The liar paradox is found in many different forms. Furthermore, if they are false, then they are true. If these sentences are true, then they are false. The liar paradox is a simple sentence like “I am lying,” or, “This sentence is false.” There are many linguistic paradoxes similar to Epimenides’ statement. In contrast, if it is false, then Epimenides is not a liar and the line is true. If this statement is true, then since Epimenides is a Cretan, he is including himself as a liar and this line of the poem is false. He wrote: “The Cretans, always liars, evil beasts, idle bellies!” This seems paradoxical. ![]() This dates back more than two and a half millennia to when Epimenides (600 B.C.), a philosopher and poet who lived in Crete, complained about his neighbors in a poem called Cretica. The classic example of a linguistic paradox is the famous Epimenides paradox. Some examples are “original copies,” “open secret,” “clearly confused,” “militant pacifist,” “larger half,” “alone together,” and my favorite, “act naturally.” Even though these phrases do not really make sense, we human beings have no problem using them in common everyday speech. These are phrases, usually consisting of two words, that contradict each other. A baby version of a linguistic paradox is an oxymoron (from the Greek oxys “sharp” and moros “stupid”-together they mean “pointedly foolish” or “pointedly dull”). Then, in the last section, we meet several paradoxes involving descriptions of numbers.Ī linguistic paradox is a phrase or sentence that contradicts itself. The following section contains a collection of self-referential paradoxes. These are relatively easy puzzles that will get us started. In the first section, we encounter the famous liar paradox and its many variants. However, don’t confuse the map with the territory! There is one major difference between the world we live in and language: Whereas the real world is free of contradictions, the man-made linguistic descriptions of that world can have contradictions. Language is a tool used to describe the world in which we live. Rather than jumping headfirst into the limitations of reason, let us start by just getting our toes wet and examining the limitations of language. ![]() Posted on: Nautilus (The MIT Press on Nautilus)| March 2017 ![]()
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