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作者:陳保明
作者(外文):Paung-Ming Chen
論文名稱:說謊者悖論與兩種嘗試解決它的方案
論文名稱(外文):The Liar Paradox and Its Two Attempted Groups of Solutions
指導教授:王文方
指導教授(外文):Wen-Fang Wang
學位類別:碩士
系所名稱:心智哲學研究所
學號:30732006
出版年:110
畢業學年度:109
語文別:英文
論文頁數:32
中文關鍵詞:說謊者悖論固定點解釋強克林三值邏輯弱克林三值邏輯克里普奇
外文關鍵詞:liar paradoxfixed point interpretationstrong Kleene three-valued logicweak Kleene three-valued logicKripke
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作為哲學史上最重要的語意悖論之一,說謊者悖論引起了許多哲學家的關注並嘗試提出不同方案來解決它,像是(1)塔斯基將語言區分為「後設語言」及「對象語言」(前者為較後者「高階」的語言),認為「對象語言」中的語句無法表達自己的真謂詞,只有透過「後設語言」才能去說「對象語言」中的語句「為真」。(2)克里普奇的固定點解釋在強克林三值邏輯系統之下,沿用了塔斯基將語言分層的概念,對謂詞「為真」進行不同階層的解釋。語言的階層數是隨著我們對真謂詞所作的解釋次數而增加,而當解釋到一定次數後就會到達「固定點」的階段,在該階段中的語句就能夠說自己「為真」。(3)而另一個類似的固定點解釋則是由馬丁與古樸塔所提出的,其中一項差別在於克里普奇所使用的是強克林三值邏輯,而馬丁與古普塔所使用的是弱克林三值邏輯。
本論文主要的談論對象即強克林與弱克林固定點解釋,並比較兩者之間的差異。除了使用了不同的邏輯系統,弱克林固定點解釋除了能解釋謂詞「為真」之外,還能解釋謂詞「不真不假」,而後者是強克林固定點解釋無法做到的,因為這樣的特性,使得說謊者與老實人在包含了謂詞「不真不假」(即「說謊者為不真不假」以及「老實人為不真不假」)後產生了不同於強克林固定點解釋下的結果。雖然該項特性使得弱克林固定點解釋不只能讓一個語言說自己為真,還能說自己為不真不假,但同時也面臨了說謊者、老實人、「說謊者為不真不假」以及「老實人為不真不假」這四個語句所造成的困境。本論文將在結論中指出弱克林固定點解釋所面臨的困境,並藉此說明為何強克林固定點解釋會是一個更適當的選擇。
As one of the significant semantic paradoxes in the history of philosophy, the liar paradox has made many philosophers propose various solutions, such as (1) Tarski proposes to distinguish between the “meta-language” from the “object language” (the former is “higher order” in a sense than the latter one). In this sense, the sentence in the object language is not able to express its own semantics. Instead, only the sentence in the meta-language is able to state that the sentence in the object language is true (or false). (2) Kripke’s fixed-point interpretation which is based on the strong Kleene three-valued logic, also takes Tarski’s concept of hierarchy of meta-language to interpret the truth predicate. In his theory, the amount of the hierarchy of language increases with the amount of the interpretation of the truth predicate, and we will achieve certain stage of interpretation which is called “a fixed point”, at this stage, the sentence is able to express its own semantics. (3) Another fixed-point interpretation is proposed by Martin and Gupta, it is similar to Kripke’s method except that Martin and Gupta’s fixed-point interpretation is based on the weak Kleene three-valued logic.
In this paper, the main objectives are the strong Kleene and weak Kleene fixed point interpretations, and we are going to talk about the differences between them. In the weak Kleene fixed-point interpretation, not only can it interpret the truth predicate, it can also interpret the predicate “neither true nor false”. This makes sentences “the liar sentence is neither true nor false” and “the truth teller is neither true nor false” have a different semantic value from the one in the strong Kleene interpretation. Though the weak Kleene language is able to express its own truth predicate and express its own predicate “neither true nor false”, it has some difficulties which are caused by the four sentences that I have mentioned above. In the last chapter, I will point out the difficulties of the weak Kleene fixed-point interpretation to explain why the strong Kleene fixed-point interpretation is a more appropriate consideration.
Signature Page i
Thesis Approval Form ii
Chinese Abstract iii
Thesis Synopsis in Chinese v
English Abstract xv
Contents xvii
Chapter 1 Liar Paradox 1
1.1 Simple Liar 1
1.2 Strengthen Liar 2
1.3 Liar Cycle 2
1.4 Grelling’s Paradox 2
1.5 Naïve Truth Principle 5
Chapter 2 Diagonalization Lemma and Undefinability Theorem 7
2.1 Godel’s Diagonalization Lemma 8
2.2 Tarski’s Undefinability Theorem 9
Chapter 3 Kripke’s Fixed Point 12
Chapter 4 Proof of the Least Fixed Point 17
Chapter 5 Fixed Point Interpretation of Weak Kleene Scheme 21
5.1 Proof of the Maximal Fixed Point 25
5.2 Difference between the Fixed Point Interpretation of Strong Kleene and Weak Kleene 27
Chapter 6 Conclusion 30
References 32
1.Field, H. (2008). Saving Truth From Paradox. Oxford University Press.
2.Field, H. (1972). Tarski's Theory of Truth. The Journal of Philosophy, 69(13), 347-375.
3.Gupta, A., & Martin, R. (1984). A Fixed Point Theorem for the Weak Kleene Valuation Scheme. Journal of Philosophical Logic, 13(2), 131-135.
4.Gupta, A. (2001). Truth. In The Blackwell Guide to Philosophical Logic. L. Goble (ed.). Oxford: Blackwell, 90-114.
5.Kripke, S. (1975). Outline of a Theory of Truth. The Journal of Philosophy, 72(19), 690-716.
6.Martin, R.L., Woodruff, P.W. (1975). On representing ‘true-in-l’ in L. Philosophia 5 (3):213-217.
7.Priest, Graham (2008). An Introduction to Non-Classical Logic: From If to Is. Cambridge University Press.
8.Rescher, N. (2001). Paradoxes: their roots, range, and resolution. Open Court.
9.Sainsbury, R. M. (2009). Paradoxes. Cambridge University Press.
10.王文方,2008,「塔斯基的真理定義與物理論」,《邏輯學研究》(Studies in Logic),第1卷1期,廣州中山大學出版,第84頁至101頁。
11.王文方、李慧華 (2018)。〈語意悖論〉,《華文哲學百科》(2018 版本),王一奇(編)。
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