Epimenides' Paradox Revisited埃庇米尼得斯悖論的再

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Friday 07 Oct, 2005星期五2005年10月7日

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Mohd Elfie Nieshaem Juferi莫哈末Elfie Nieshaem Juferi

In response to our argument that Paul's fumbling of the Epimenides paradox is proof that the ad-hoc “apostle” was not inspired after all, one Christian has raised為響應我們的論點,保羅的摸索的埃庇米尼得斯悖論證明,特設“使徒”畢竟不是啟發,提出了一個基督教 an objection反對 . The attempted rebuttal acknowledges the paradoxical nature of Epimenides' statement, but then makes the bizarre claim that Paul's statement is true nonetheless due to other elements attributed to the Cretan “prophet” by the “apostle”.試圖進行辯駁承認矛盾的性質,埃庇米尼得斯的聲明,但奇怪的要求,然後使保羅的說法是真實不過由於其他因素歸因於克里特島“先知”的“使徒”。

While it is true that external factors can sometimes help us solve a paradox, the elements brought to witness by the Christian author of this defense of Paul fail to help us in any way, and worse, demonstrate that the critic raising this objection does not understand logic.誠然,外來因素可有時幫助我們解決一個矛盾,對證人的因素帶來的基督教作家保羅這個防禦不能以任何方式幫助我們,更糟的是,證明了評論家提出這個異議不明白邏輯。 The critic writes as follows:批評家寫道如下:

We notice that Paul, who was probably very aware of the PURE logical meaningless sentence “Cretans are always liars” told by a Cretan, uses a more complex form of the sentence, “Cretans are always liars, evil brutes, lazy gluttons.” We can now use the additional FACTS to prove or disprove the testimony. 我們看到保羅,誰可能是很清楚的純邏輯意義的句子:“克里特人總是說謊”告訴一個克里特,採用了更複雜形式的句子,“克里特人總是撒謊,乃是惡獸,又饞又懶。”我們現在可以使用更多的事實證明或者反駁的證據。

The critic tries to further elucidate this point by giving the analogy of a person in a court of law testifying: “I always lie, I am an evil bully and I am a lazy worker.” The critic's point is that while the statement “I always lie” is paradoxical, the sentence overall is true (or its truth can be determined by checking the other qualities noted).批評家試圖進一步闡明這點,給予比喻一個人在法院依法作證:“我總是撒謊,我是一個邪惡的欺負,而我是一個懶惰的工人。”評論員的一點是,雖然該聲明說:“我總是說謊“是自相矛盾的,整體的句子為真(或它的真理可以通過檢查來確定的其他素質說明)。 While some readers may not have caught it yet, the shocking reality is that in this discussion on whether or not Paul understood logic, the defender has himself exhibited deep logical deficiencies.雖然有些讀者可能無法趕上它,但令人震驚的事實是,在這次討論中對是否保羅理解的邏輯,展示自己的後衛已經深深的邏輯缺陷。 The problem here is that the critic does not realize that his statements involve logical conjuncts which he has not properly interpreted.這裡的問題是,影評人沒有意識到,他的講話涉及的邏輯並列,他沒有好好解釋。

In logic, for a conjunctive proposition to be true all its conjuncts must be true.在邏輯中,為合取命題是真實的一切必須是真實的並列。 So, what is a conjunctive proposition and what is a conjunct?那麼,什麼是一個合取命題,什麼是一個契合? Well, if I say “my name is Mohd and I am a Muslim”, that is a conjunctive proposition.好吧,如果我說“我的名字是穆罕默德,我是一個穆斯林”,這是一個合取命題。 The proposition has two conjuncts, the first being “my name is Mohd”, the second being “I am a Muslim.” If my name is Mohd, but I am not a Muslim, the sentence is false, and if my name is not Mohd, but I am a Muslim, the sentence is again false.這個命題有兩個並列,第一次是“我的名字是穆罕默德”,第二是“我是一個穆斯林。”如果我的名字是穆罕默德,但我不是一個穆斯林,這句話是假的,如果我的名字是不莫哈末,但我是一個穆斯林,這句話是假的。 The sentence “my name is Mohd and I am a Muslim” can be true if, and only if both conjuncts are true; ie if my name is Mohd and I am a Muslim.這句話“我的名字是穆罕默德和我是穆斯林”,可真,當且僅當兩個並列為真,即如果我的名字是穆罕默德,我是一個穆斯林。

So, if a man says “everything I say is a lie, I am lazy, and I am a bully”, the statement cannot be true on the grounds that in order for it to be true, all three of its conjuncts must be true, but the first conjunct is clearly untrue.所以,如果一個人說:“所有我要說的是一個謊言,我很懶惰,我是一個恃強凌弱”的語句不能是真實的,理由是為了它是真實的,所有三個並列必須是真實的,但第一個契合顯然是不真實的。 So, in response to the Christian who defended Paul, if we assume the sentence “all Cretans are liars” (or “Cretans are always liars”) is meaningless, or even false, combining it with other statements in a conjunction does not create a true sentence.因此,在應對誰捍衛基督教的保羅,如果我們假設這句話“所有克里特人都是說謊者”(或“克里特人總是說謊的人”)是沒有意義的,甚至是虛假的,並將其與其他報表中的一道不創建真正的句子。 This is because the original statement in question is still not true, thus it being a conjunct in a larger sentence results in the sentence also being untrue.這是因為原來的聲明,問題仍然是不正確的,因此它是一個合取結果在一個更大的句子的句子也被不真實的。

Interestingly, this exact sort of sentence was touched on by Dr. Laurence Goldstein of the University of Hong Kong, in an article on Epimenides, written for a scholarly journal more than fifteen years ago.有趣的是,這確實有點感動的一句勞倫斯戈爾茨坦博士的香港大學,在一篇文章中對埃庇米尼得斯,是學術期刊的書面超過 15年前。 An example of a simple pseudomenon would be the proposition 'x', where proposition 'x' is “x is false”.一個簡單的例子pseudomenon將是命題的'X',其中命題的'X'為“x是錯誤的”。 Goldstein, however, brings in an extra proposition, creating a conjunction.戈爾茨坦,但是,帶來了額外的建議,建立一個同時使用。 Goldstein gives the example of sentence 'E', and sentence 'E' is “E is not true and q” where 'q' is some other proposition.戈爾茨坦給出的例子一句'E'和一句'e'是“E是不正確的和Q”其中'Q的是一些其他的建議。 From there, he writes the following:從那裡,他寫道如下:

Here 'q' is both conjoined with a statement about E, and also part of E (so, although 'q' is arbitrary, it is not independent of E).這裡'q'已經與這兩個連體一份聲明中關於 E,也部分電子(所以,雖然'Q的是任意的,它不是獨立的權證)。 If 'q' is not true, then, in virtue of E containing 'q' as a conjunct, E is not true, and this is consistent with what the first conjunct (the statement about E) says.如果'Q的是不正確的,那麼,憑藉電子含有'Q的一個契合,E是不正確的,這是符合了第一批契合(聲明關於 E)說。 However, if 'q' is true then we have the absurd (and thus to be rejected) implication that E is both true and not true.但是,如果'Q的是真的話,我們有荒謬(因此被拒絕)暗示E是既真實,不正確的。 1

Thus we see that conjoining a paradoxical statement with other statements (regardless of their truth value) does not result in the creation of a true statement.因此,我們看到,交接一個似是而非的陳述與其他陳述(不論其真值)不會導致建立一個真正的聲明。

It should be further noted that this methodology still applies even if it is argued that the statement is not paradoxical, but merely false.應該進一步指出,這一方法仍然適用,即使有人認為這種說法並不矛盾,只是假的。 In bivalent logic, statements are either true or false.在二價邏輯,陳述或真或假的。 In trivalent and multi-valued logics, statements can be true, false or have some other truth-value.在三價和多值邏輯,語句可以是真實的,虛假的或有其他真值。 Nonetheless, in all realms of logic the rule of conjunction is still the same: in order for a conjunctive proposition to be true, all its conjuncts must be true.然而,在所有領域的邏輯規則的結合仍然是相同的:為了讓一合取命題是真實的,其所有並列必須是真實的。 If a conjunctive statement has some conjuncts that are true, and one that is meaningless or false, the statement is not true; rather it is meaningless or false.如果有一些並列連接詞聲明是真實的,而且是毫無意義的或虛假的陳述是不正確的,而是它是毫無意義的或虛假的。 Note that the statement “my name is Mohd Elfie and I like to gergleplex with Jabberwockies” cannot be considered logically true since one of the conjuncts is meaningless.請注意,聲明“我的名字是莫哈末Elfie,我想gergleplex與Jabberwockies”不能被視為邏輯上無疑的,因為一人並列,是沒有意義的。

Thus either way, the following seven-point syllogism still applies:因此無論哪種方式,下面的7點三段論仍然適用:

  • Paul claims a Cretan uttered a certain proposition.保羅聲稱克里特說出某一個命題。
  • The proposition is not true.這個命題是不正確的。
  • Paul claims the proposition is true.保羅聲稱主張是正確的。
  • Paul's claim is an error.保羅的說法是錯誤的。
  • Paul's writings are errant rather than inerrant.保羅的著作是犯錯誤,而不是無誤。
  • Errant scripture is not inspired scripture (a common assumption among Christians and Muslims).聚散兩依依不啟發聖經經文(假設一個共同的基督徒和穆斯林之間)。
  • Therefore, Paul was not inspired (or at least not when he wrote the epistle to Titus).因此,保羅沒有靈感(或者至少不是在他寫的書信,以提圖斯)。

And only God knows best!而且,只有上帝知道最好的!

  1. Laurence Goldstein, “Epimenides and Curry,” Analysis , Vol.勞倫斯戈德斯坦,“埃庇米尼得斯和咖哩, 分析 ”,卷。 46, 1986, p. 46,1986,頁 121 [ 121 [ back背面 ] ]
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  1. Greg says: 格雷格 說:

    Your syllogism is presumptuous.您的三段論是狂妄。 Paul's teachings assert that all men (including Cretans) are sinners – thus liars, brutes, gluttons.保羅的教導斷言,所有的人(包括克里特)都是罪人 - 因此騙子,畜生,貪食。 Just because Epimenides' statement is nonsensical when uttered by a Cretan does not necessarily mean it is absolutely false – the manner in which Paul refers to it.正因為埃庇米尼得斯的聲明是荒謬的克里特時,說出了一個並不一定意味著它是絕對錯誤的 - 保羅的方式,是指它。

  2. Greg says: 格雷格 說:

    … heh heh, that it is absolutely true. ...嘿嘿嘿,這是千真萬確的。

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