The Liar Paradox: Whether the Two Theories, by Burge and Gaifman Respectively, Sovle the Paradox

• Main Authors: Chun-An Chou, 周峻安
• Other Authors: Wen-Fang Wang
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/73922680920188162569

碩士 === 國立陽明大學 === 心智哲學研究所 === 99 === The liar sentence can lead to a paradox. The liar is a sentence which states itself false or states itself untrue. More specifically, a sentence which states itself false is called “the simple liar”; and a sentence which states itself untrue is called “the strengthened liar.” The liar sentence seems acceptable, or at least well-formed and meaningful. On the other hand, the liar and some likely acceptable inferences jointly lead to a contradiction. That is why it is called the liar paradox. The liar paradox has been discussed for a long time. In 1933, Taski proposed a definition of truth in a formal language and pointed out that the natural language contains the liar paradox. Therefore, when Tarski proposed the definition of truth, he precluded the natural language. However, some philosophers think that we can deal with the liar paradox and a theory of truth for the natural language is possible. A well-known theory is the fixed point theory proposed by Kripke in 1975. But the fixed point theory is not satisfactory for philosophers. In this paper, the subjects are Burge’s and Gaifman’s theories of truth. According to Burge, the truth value of the liar sentence is context-dependent. Burge thinks that since the liar can lead to a contradiction, it is pathological. But the liar sentence can have a truth value in a broader context. Therefore, we can talk about the truth value of the liar sentence. When we say “the liar is not true”, what we say is true. According to Gaifman, the truth value of a sentence does not only depend on its type, but also depends on the relations among sentence tokens. The liar sentence is a self-referential sentence and thus is GAP. When we say “the liar is not true”, what we say is not self-referential. And since the liar is not true, what we say is true. I have four suspects to Burge’s and Gaifman’s theories. First, Burge’s theory does not provide enough rules to determine which sentence a given sentence is in. Second, Burge and Gaifman do not provide enough reasons to explain why the liar is pathological or GAP. However, it seems that we intuitively think that if the liar is pathological or GAP, it is true. It seems that Burge and Gaifman do not explain why the above reasoning is not valid. Third, the theories by Burge and Gaifman have a difficulty with the super liar paradox. Burge and Gaifman think that the liar is pathological or GAP in a context but can be true in another context. I provide two versions of the super liar. One is a sentence which states itself untrue in all contexts; another is a sentence which states itself untrue in the present context. It seems that the two theories do not deal with the two versions of the super liar well. Fourth, we discuss infinite sequences constituted by sentences. Sentences of some infinite sequences have truth values; sentences of some are uncertain; and sentences of some lead to contradictions. It seems that the two theories cannot distinguish the three kinds of infinite sequences. In sum, it seems that there are some problems in Burge’s and Gaifman’s theories. I am not very sure whether we should accept these two theories of truth.