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第2行： − + − {{简述〉<font color="#ff8000">一个指向自己的概念或公式 </font>}} − {{Selfref|For the self-reference template on Wikipedia, see [[Template:Selfref]].}} − {{自指|有关Wikipedia上的自引用模板，请参见[[模板：自指]].}} − {{Use dmy dates|date=July 2012}} − {{使用dmy日期|日期=2012年7月}} + − <!-- Note to anyone who is thinking of making this article self referential: Please do not do this, see the note at top of the recursion article for why --> − + − < ! ——注意：任何人都请不要试图让本文自述，详细原因请参阅递归文章顶部的注释 -- > − [[Image:ouroboros.png|thumb|The ancient symbol [[Ouroboros]], a dragon that continually consumes itself, denotes self-reference.<ref>{{cite web |last1=Soto-Andrade |first1=Jorge |last2=Jaramillo |first2=Sebastian |last3=Gutierrez |first3=Claudio |last4=Letelier |first4=Juan-Carlos |title=Ouroboros avatars: A mathematical exploration of Self-reference and Metabolic Closure |url=https://mitpress.mit.edu/sites/default/files/titles/alife/0262297140chap115.pdf |publisher=MIT Press |accessdate=16 May 2015}}</ref>]] − The ancient symbol [[Ouroboros, a dragon that continually consumes itself, denotes self-reference.]]+ − − 古代的符号[[衔尾蛇，一条吞噬自己尾巴的蛇，表示自指]] − − − − '''Self-reference''' occurs in [[natural language|natural]] or [[formal language]]s when a [[Sentence (linguistics)|sentence]], idea or [[Well-formed formula|formula]] refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some [[Semantics encoding|encoding]]. In [[philosophy]], it also refers to the ability of a subject to speak of or refer to itself, that is, to have the kind of thought expressed by the first person nominative singular pronoun [[I (pronoun)|"I"]] in English. − − Self-reference occurs in natural or formal languages when a sentence, idea or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding. In philosophy, it also refers to the ability of a subject to speak of or refer to itself, that is, to have the kind of thought expressed by the first person nominative singular pronoun "I" in English. − − 在自然语言或<font color='ff8800'>形式语言formal language</font>中，当一个句子、想法或公式指向自己时，就会出现<font color='ff8800'>自指现象Self-reference</font>。（自指的英文Self-reference中，reference有“参照”的意思。）参照可以直接通过一些中间句或公式来表达，也可以通过一些编码来表达。在哲学中，它也指一个主语谈论或指称自己的能力，也就是说，具有第一人称主格单数代词“我”在英语中所表达的那种思想。 − − − − Self-reference is studied and has applications in [[mathematics]], [[philosophy]], [[computer programming]], and [[linguistics]]. Self-referential statements are sometimes [[paradox]]ical, and can also be considered [[Recursion|recursive]]. − − Self-reference is studied and has applications in mathematics, philosophy, computer programming, and linguistics. Self-referential statements are sometimes paradoxical, and can also be considered recursive. − − <font color='ff8800'>自指Self-reference</font>研究和应用在数学，哲学，计算机编程和语言学中。自指陈述有时是矛盾的，也可以被认为是递归的。 − − − − − − In classical [[philosophy]], [[paradoxes]] were created by self-referential concepts such as the [[omnipotence paradox]] of asking if it was possible for a being to exist so powerful that it could create a stone that it could not lift. The [[Epimenides paradox]], 'All Cretans are liars' when uttered by an ancient Greek Cretan was one of the first recorded versions. Contemporary philosophy sometimes employs the same technique to demonstrate that a supposed concept is meaningless or ill-defined.<ref>[https://plato.stanford.edu/entries/liar-paradox/ ''Liar Paradox'']</ref> + − + − In [[mathematics]] and [[computability theory]], self-reference (also known as [[Impredicativity]]) is the key concept in proving limitations of many systems. [[Gödel's incompleteness theorems|Gödel's theorem]] uses it to show that no formal [[Consistency|consistent]] system of mathematics can ever contain all possible mathematical truths, because it cannot prove some truths about its own structure. [[The halting problem]] equivalent, in computation theory, shows that there is always some task that a computer cannot perform, namely reasoning about itself. These proofs relate to a long tradition of mathematical paradoxes such as [[Russell's paradox]] and [[Berry's paradox]], and ultimately to classical philosophical paradoxes. − 在数学和可计算性理论中，<font color='ff8800'>自指</font>(也被称为<font color='ff8800'>不确定性</font>)是证明许多系统局限性的关键概念。<font color='ff8800'>哥德尔定理Gödel's theorem</font>用它来表明，没有一个形式上一致的数学系统可以包含所有可能的数学真理，因为它不能证明某些关于它自身结构的真理。<font color="#ff8000"> 在计算理论中，哥德尔定理的等价表述是停机问题，这一问题表明计算机不能完成关于自身的推理。</font>这些证明关系到数学悖论的悠久传统，如<font color='ff8800'>罗素悖论</font>和<font color='ff8800'>贝瑞悖论</font>，并最终关系到经典哲学悖论。+
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{{short description|A sentence, idea or formula that refers to itself}}
[[Image:ouroboros.png|thumb|古代的符号[[衔尾蛇，一条吞噬自己尾巴的蛇，表示自指]].<ref>{{cite web |last1=Soto-Andrade |first1=Jorge |last2=Jaramillo |first2=Sebastian |last3=Gutierrez |first3=Claudio |last4=Letelier |first4=Juan-Carlos |title=Ouroboros avatars: A mathematical exploration of Self-reference and Metabolic Closure |url=https://mitpress.mit.edu/sites/default/files/titles/alife/0262297140chap115.pdf |publisher=MIT Press |accessdate=16 May 2015}}</ref>]]
在自然语言或<font color='ff8800'>形式语言formal language</font>中，当一个句子、想法或公式指向自己时，就会出现<font color='ff8800'>自指现象 Self-reference</font>。（自指的英文Self-reference中，reference有“参照”的意思。）参照可以直接通过一些中间句或公式来表达，也可以通过一些编码来表达。在哲学中，它也指一个主体谈论或指称自己的能力，也就是说，具有第一人称主格单数代词“我”在英语中所表达的那种思想。
<!-- Note to anyone who is thinking of making this article self referential: Please do not do this, see the note at top of the recursion article for why -->
<font color='ff8800'>自指Self-reference</font>经常在数学，哲学，计算机编程和语言学中被研究和应用。自指陈述有时是自相矛盾的，也可以被认为是递归的。
==自指在逻辑、数学和计算中的体现 ==
==In logic, mathematics and computing 逻辑、数学和计算==
In classical [[philosophy]], [[paradoxes]] were created by self-referential concepts such as the [[omnipotence paradox]] of asking if it was possible for a being to exist so powerful that it could create a stone that it could not lift. The [[Epimenides paradox]], 'All Cretans are liars' when uttered by an ancient Greek Cretan was one of the first recorded versions. Contemporary philosophy sometimes employs the same technique to demonstrate that a supposed concept is meaningless or ill-defined.
In classical philosophy, paradoxes were created by self-referential concepts such as the omnipotence paradox of asking if it was possible for a being to exist so powerful that it could create a stone that it could not lift. The Epimenides paradox, 'All Cretans are liars' when uttered by an ancient Greek Cretan was one of the first recorded versions. Contemporary philosophy sometimes employs the same technique to demonstrate that a supposed concept is meaningless or ill-defined.
In classical philosophy, paradoxes were created by self-referential concepts such as the omnipotence paradox of asking if it was possible for a being to exist so powerful that it could create a stone that it could not lift. The Epimenides paradox, 'All Cretans are liars' when uttered by an ancient Greek Cretan was one of the first recorded versions. Contemporary philosophy sometimes employs the same technique to demonstrate that a supposed concept is meaningless or ill-defined.
在古典哲学中，<font color="#ff8000"> 悖论Paradoxes</font>是由<font color='ff8800'>自指</font>概念创造出来的，比如<font color="#ff8000">全能悖论：是否有一个足够强大的存在，可以创造出一个祂自己也举不起的石块？ </font><font color="#ff8000">还有埃庇米尼得斯悖论。这一悖论有许多不同的表述形式，古希腊克里特岛人说的“所有克里特岛人都是骗子”是有记载的最早版本之一。 </font>当代哲学有时使用同样的技巧来证明一个假定的概念是没有意义的或者定义不明确的。
在古典哲学中，<font color="#ff8000"> 悖论Paradoxes</font>是由<font color='ff8800'>自指</font>概念创造出来的，比如<font color="#ff8000">全能悖论：是否有一个足够强大的存在，可以创造出一个祂自己也举不起的石块？ </font><font color="#ff8000">还有埃庇米尼得斯悖论。这一悖论有许多不同的表述形式，古希腊克里特岛人说的“所有克里特岛人都是骗子”是有记载的最早版本之一。 </font>当代哲学有时使用同样的技巧来证明一个假定的概念是没有意义的或者定义不明确的。<ref>[https://plato.stanford.edu/entries/liar-paradox/ ''Liar Paradox'']</ref>
In mathematics and computability theory, self-reference (also known as Impredicativity) is the key concept in proving limitations of many systems. Gödel's theorem uses it to show that no formal consistent system of mathematics can ever contain all possible mathematical truths, because it cannot prove some truths about its own structure. The halting problem equivalent, in computation theory, shows that there is always some task that a computer cannot perform, namely reasoning about itself. These proofs relate to a long tradition of mathematical paradoxes such as Russell's paradox and Berry's paradox, and ultimately to classical philosophical paradoxes.
In mathematics and computability theory, self-reference (also known as Impredicativity) is the key concept in proving limitations of many systems. Gödel's theorem uses it to show that no formal consistent system of mathematics can ever contain all possible mathematical truths, because it cannot prove some truths about its own structure. The halting problem equivalent, in computation theory, shows that there is always some task that a computer cannot perform, namely reasoning about itself. These proofs relate to a long tradition of mathematical paradoxes such as Russell's paradox and Berry's paradox, and ultimately to classical philosophical paradoxes.
在数学和[[可计算性理论]]中，<font color='ff8800'>自指</font>(也被称为<font color='ff8800'>不确定性</font>)是证明许多系统局限性的关键概念。<font color='ff8800'>哥德尔定理Gödel's theorem</font>用它来表明，没有一个形式上一致的数学系统可以包含所有可能的数学真理，因为它不能证明某些关于它自身结构的真理。<font color="#ff8000"> 在计算理论中，哥德尔定理的等价表述是停机问题，这一问题表明计算机不能完成关于自身的推理。</font>这些证明关系到数学悖论的悠久传统，如<font color='ff8800'>罗素悖论</font>和<font color='ff8800'>贝瑞悖论</font>，并最终关系到经典哲学悖论。