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论指称 - 罗素

已有 938 次阅读 2022-7-24 22:45 |个人分类:解读哥德尔不完全性定理|系统分类:科研笔记

一,译文


论指称 - 罗素


我所说的指称短语(denoting phrase是指以下任何一个短语:一个人,某个人,任何一个人,每一个人,所有的人,现在的英国国王,现在的法国国王,太阳系的质心在二十世纪的第一个瞬间,地球绕太阳的旋转,太阳绕地球的旋转。因此,一个短语完全是凭借其形式来指称的。我们可以区分三种情况:


1)短语可以指称,但却不指称任何东西;例如,当今的法国国王

2)短语可以指称一个确定的对象;例如,当今的英国国王指称某个人。

3)短语可以不明确地指称;例如,一个人,指称的不是许多人,而是一个不明确的人。


对这些短语的解释是一个相当困难的问题;事实上,很难构建任何一种不容易被形式反驳的理论。我所熟悉的所有困难,就我所发现的而言,都被我将要解释的理论所碰到。


短语的主体非常重要,不仅在逻辑和数学中,而且在知识论中也是如此。例如,我们知道太阳系的质心在某一确定的瞬间是某个确定的点,我们可以肯定一些关于它的命题;但我们对这个点并没有直接的认识,只是通过描述而被我们间接所知。认识和了解之间的区别是我们直接见到事物和我们通过指称短语达到的事物之间的区别。经常发生的情况是,我们知道某个短语毫不含糊地指称,尽管我们对它所表示的东西并不熟悉;这发生在上述质心的例子中。在感知中,我们感知的对象,在思想中,我们熟悉更抽象的逻辑性质的对象;但我们不一定熟悉由我们熟悉的词的含义组成的短语所指称的对象。举一个非常重要的例子,似乎没有理由相信我们曾经熟悉过别人的思想,因为这些思想不是直接被感知的;因此我们对它们的了解是通过指称获得的。所有的思考都必须从熟悉开始;但它在思考许多我们不熟悉的事物时却获得了成功。


我的论证过程将是这样的,我将首先说明我打算倡导的理论;然后我将讨论弗雷格和迈农的理论,说明为什么它们都不能使我满意;然后我将给出支持我的理论的理由;最后我将简要说明我的理论的哲学结论。


我的理论,简单地说,是这样的。我把变量作为基本概念;我用C(x)来指一个命题,其中x是一个成分,而x这个变量在本质上是完全不确定的。然后我们可以考虑两个概念:“C(x)总是真的“C(x)有时是真的。那么每个东西(everything)和没有东西(nothing)以及某些东西(something)(这些都是最原始的指称短语)将被解释为如下:

C(每个东西)意味着 “C(x)总是真的

C(没有东西)意味着“’C(x)是假的永远是真的

C(某些东西)意味着 ”’C(x)永远是真的是假的’”


在这里,“C(x)总是真的这一概念被视为终极的和不可定义的,而其他概念则通过它来定义。 所有、没有和某些都不被假定为有任何独立的意义,但它们出现的每一个命题都被赋予一种意义。这就是我想倡导的指称理论的原则:指称短语本身不具有任何意义,但它们出现在其言语表达中的每个命题都有一个意义。我认为,有关指称的困难都是对言语表达包含指称短语的命题的错误分析造成的。正确的分析,如果我没有弄错的话,可以进一步阐述如下。


假设我们现在想解释这个命题,我遇到一个人。如果命题为真,我遇到了某个确定的人;但这不是我所断定的。根据我所主张的理论,我所断定的是:

      “’我遇到了X,而X是人并不总是假的

     一般来说,把人的类别定义为具有人这个谓词的对象的类别,我们说:

      C(一个人)'意味着'"C(x)x是人 "并不总是假的'

      这使得本身完全没有意义,但却给每个命题赋予了意义,在这些命题中,''的言语表达出现。


接下来考虑一下,所有的人都会死,这个命题实际上是假设性,它指出,如果任何东西是一个人,它就是必死的。也就是说,它指出,如果x是人,x就会死。因此,用’x是人(x is human代替’x是人(x is a man,我们将看到:


            '所有的人都是必死的'意味着'如果x是人,x是必死的'总是真的。

      这就是在符号逻辑中所表达的,说'所有的人都会死'意味着'"x是人 "意味着 "x会死 "对于x的所有值都是如此'。更一般地说,我们说。

     C(所有的人)意味着如果x是人,那么Cx)是真的'总是真的'


相似地



'C(no men)'意味着'"如果x是人,那么C(x)是假的 « 总是真的'

‘C(一些人)'的意思与'C(一个人)'相同,而

'C(a man 6))'意味着'C(x)x是人是假的'永远是假的。

‘C(每个人)'的意思与'C(所有的人)'相同。


剩下的就是解释含有the的短语。这些短语是迄今为止最有趣和最困难的指称。以查理二世的父亲被处决为例。这句话断言,有一个X是查理二世的父亲,并且被处决了。现在,当它被严格使用时,涉及到唯一性;我们确实在说某某的儿子,即使某某有几个儿子,但说'某某的儿子'会更正确。因此,为了我们的目的,我们把the作为涉及唯一性的。因此,当我们说'x是查理二世的父亲'时,我们不仅断言x与查理二世有某种关系,而且还断言没有别的人有这种关系。在没有唯一性假设的情况下,在没有任何表示性短语的情况下,有关的关系由'x生了查理二世'来表达。为了得到'x是查理二世的父亲'的等价物,我们必须加上'如果y不是xy没有生下查理二世',或者,相当于'如果y生了查理二世,yx是相同的'。因此,'x是查理二世的父亲'变成:'x生了查理二世;而'如果y生了查理二世,yx相同'y来说永远是真的'


因此,查理二世的父亲被处死'变成:'x生查理二世和x被处死对x来说并不总是假的,而且'如果y生查理二世,y就与x相同'y来说总是真的'


这似乎是一个有点不可思议的解释;但我现在不是在说明理由,我只是在陈述理论。

要解释'C(查理二世的父亲)',其中C代表关于他的任何陈述,我们只需用Cx)代替上面的'x被处决'。请注意,根据上述解释,无论陈述C是什么,'C(查理二世的父亲)'都意味着。

      “如果y生了查理二世,y就与x相同y来说并不总是假的。


这就是普通语言中所表达的查理二世只有一个父亲,没有其他父亲'。因此,如果这个条件不成立,每一个形式为'C(查理二世的父亲)'的命题都是假的。因此,例如,每一个形式为'C(现任法国国王)'的命题都是假的。这对目前的理论来说是一个很大的优势。我将在后面说明,它并不像最初设想的那样与矛盾法则相悖。


以上给出了将所有出现指称短语的命题还原为不出现此类短语的形式。为什么必须进行这样的还原,下面的讨论将努力说明。


上述理论的证据来自于如果我们把指称短语看作是它们出现在言语表达中的命题的真正成分,那么这些困难似乎是不可避免的。在承认这种成分的可能理论中,最简单的是梅农的理论7)。这个理论认为任何语法上正确的指称短语都是代表一个对象。因此, “当今的法国国王 “圆形的广场,等等,都被认为是真正的对象。人们承认,这些对象并不存在,但它们仍被认为是对象。这本身就是一个困难的观点;但主要的反对意见是,这种物体,公认的,很容易违反矛盾律。例如,有人争辩说,现在的法国国王存在,也不存在;圆形广场是圆的,也不是圆的,等等。但这是不可容忍的;如果能找到任何理论来避免这种结果,那肯定是首选。


弗雷格的理论避免了上述对矛盾法则的违反。他在一个指称短语中区分了两个要素,我们可以称之为意义和指称。因此,二十世纪初太阳系的质心在意义上是非常复杂的,但它的指称是某个点,这很简单。太阳系、二十世纪等等,都是意义的构成要素;但指称却没有任何构成要素。这种区分的一个好处是,它显示了为什么主张同一性往往是值得的。如果我们说斯科特是《韦弗利》的作者,我们就在意义不同的情况下宣称了指称的相同。然而,我将不重复支持这一理论的理由,因为我已经在其他地方敦促其主张(同上),现在我关心的是对这些主张的争议。


当我们采用指称短语表达一个意义并表示一个指称的观点时,我们面临的第一个困难是关于指称似乎不存在的情况。如果我们说英国国王是个秃子',这似乎不是关于'英国国王'这个复杂意义的陈述,而是关于这个意义所表示的实际的人。但现在考虑'法国国王是个秃子'。根据形式上的对等,这也应该是关于'法国国王'这个短语的含义。但这个短语,尽管它有一个意义,但只要'英国国王'有一个意义,就肯定没有指称,至少在任何明显的意义上。因此,人们会认为'法国国王是秃头'应该是无稽之谈;但它不是无稽之谈,因为它显然是错误的。或者再考虑下面这样一个命题。如果u是一个只有一个成员的类,那么这个成员就是u的成员',或者我们可以这样说,'如果u是一个单位类,那么u就是u'。这个命题应该永远是真的,因为只要假设是真的,结论就是真的。但是'u'是一个指称短语,而且它是指称,而不是意义,被说成是u。现在,如果u不是一个单位类,'u'似乎没有指称;因此,一旦u不是一个单位类,我们的命题似乎就成了废话。


现在很明显,这种命题不会仅仅因为其假设是错误的而成为无稽之谈。暴风雨中的国王可能会说:如果费迪南德没有被淹死,费迪南德就是我唯一的儿子。现在我唯一的儿子是一个指称短语,从表面上看,当且仅当我正好有一个儿子时,它才有指称。但是,如果费迪南德事实上被淹死了,上述陈述仍将是真实的。因此,我们必须在乍一看没有指称的情况下提供一个指称,或者我们必须放弃指称是包含指称短语的命题所关注的观点。后者是我所主张的路线。前者可以采取梅农的做法,即承认不存在的对象,并否认它们服从矛盾法则;然而,如果可能的话,应避免这样做。弗雷格采用了另一种采取同样做法的方式(就我们目前的选择而言),他通过定义为那些本来不存在的情况提供了一些纯粹的常规指称。因此,"法国国王",是表示无效等级;"某某先生的唯一儿子"(他有一个10人的大家庭),是表示他所有儿子的等级;等等。但是这种程序,尽管它可能不会导致实际的逻辑错误,但显然是人为的,并没有对问题进行准确的分析。因此,如果我们允许指称短语在一般情况下具有意义和指称的两面性,那么在假设真的有指称和假设真的没有指称的情况下,似乎没有指称的情况都会造成困难。


一个逻辑理论可以通过其处理难题的能力来检验,在思考逻辑问题时,用尽可能多的难题来储备头脑是一个有益的计划,因为这些难题的作用与物理科学中的实验的作用基本相同。因此,我将陈述一个关于指称的理论应该能够解决的三个难题;我将在后面证明我的理论解决了这些难题。


      (1) 如果ab是相同的,那么,凡是对a正确的,对b也是正确的,在任何命题中,任何一个都可以代替另一个而不改变该命题的真假。现在,乔治四世想知道斯科特是否是《韦弗利》的作者;而事实上,斯科特是《韦弗利》的作者。因此,我们可以用斯科特代替《韦弗利》的作者,从而证明乔治四世希望知道斯科特是否就是斯科特。然而,对身份法的兴趣很难被归因于欧洲的第一位绅士。


(2) 根据排中律,要么’AB’,要么'A不是B',都必须是真的。因此,要么'现任法国国王是秃头',要么'现任法国国王不是秃头'一定是真的。然而,如果我们先列举秃头的事物,然后再列举不秃头的事物,我们就不应该在任何一个名单中找到现任法国国王。喜欢综合的黑格尔主义者可能会得出结论:他戴着假发。


(3) 考虑命题'AB不同'。如果这是真的,那么AB之间就有差异,这一事实可以用'AB之间的差异存在'的形式表达。但如果说AB不同是假的,那么AB之间就没有差异,这一事实可以用'AB之间的差异不存在'的形式来表达。但是,一个非实体怎么可能成为一个命题的主体呢?'我思故我在'并不比'我是命题的主体,故我在'更明显;只要'我在'被认为是断言存在或存在)而不是存在。因此,似乎否认任何事物的存在总是自相矛盾的;但我们已经看到,在与梅农的联系中,承认存在有时也会导致矛盾。因此,如果AB没有差异,假设有或没有 "AB之间的差异 « 这样一个对象,似乎也是不可能的。


意义与指称的关系涉及某些相当奇怪的困难,这些困难本身似乎足以证明导致这种困难的理论一定是错误的。


当我们想谈论一个指称短语的意义,而不是它的指称,这样做的自然模式是通过倒置的逗号。因此,我们说:

太阳系的质心是一个点,而不是一个指称复合体;

太阳系的质心 "是一个表示复数,而不是一个点。

    

或者再来一次。


格雷的挽歌的第一行陈述了一个命题。


因此,以任何一个指称短语为例,比如说C,我们希望考虑C’C'之间的关系,其中两者的区别是上述两个例子中所体现的那种。


我们说,首先,当C出现时,我们谈论的是指称;但当’C’出现时,它是意义。现在,意义和指称的关系不仅仅是通过短语的语言学关系:必须有一种逻辑关系,我们通过说意义指称来表达这种关系。但我们面临的困难是,我们无法既保持意义和指称的联系,又防止它们成为同一事物;而且,除非通过指称短语,否则无法获得意义。这种情况发生在以下方面。


一个短语C同时具有意义和指称。但如果我们说 "C的意义",那就给了我们指称的意义(如果有的话)。'《格雷的挽歌》第一行的意义''宵禁敲响离别日的丧钟'的意义相同,而与'《格雷的挽歌》第一行的意义'不相同。因此,为了得到我们想要的意义,我们必须说的不是'C的意义',而是'C的意义',它与'C'本身是一样的。同样,"C的指称 « 也不是指我们想要的指称,而是指某种东西,如果它是指称的话,就是指称我们想要的指称所指称的东西。例如,让'C'成为'上述实例中第二个出现的指称复合体'。那么


C=‘格雷的挽歌的第一行',并且

C的指称 = 宵禁敲响了离别之日的钟声。但我们想得到的是 « 格雷的挽歌的第一句 »。因此,我们没有得到我们想要的东西。


谈论一个指称复合体的意义的困难可以这样说,当我们把复合体放在一个命题里的时候,这个命题就是关于指称的;如果我们做一个命题,其中的主语是 « C的意义",那么主语就是指称的意义(如果有的话),而这并不是有意的。这使我们说,当我们区分意义和指称时,我们必须处理的是意义:意义有指称,是一个复合体,而除了意义之外,没有其他东西可以被称为复合体,并被说成既有意义又有指称。在有关的观点上,正确的说法是,有些意义有指称。


但这只会使我们在谈论意义时的困难更加明显。因为假设C是我们的复合体;那么我们就要说,C是复合体的意义。然而,每当C出现时不加倒数逗号,我们所说的就不是意义的真实,而只是指称的真实,就像我们说的那样。太阳系的质心是一个点。因此,要谈论C本身,即提出关于意义的命题,我们的主体必须不是C,而是表示C的东西。因此,当我们想谈论意义时,我们所使用的’C’必须不是意义,而是表示意义的东西。而且,C一定不是这个复合体的成分(就像它是'C的意义'的成分一样);因为如果C出现在复合体中,那么出现的将是它的指称,而不是它的意义,而且从指称到意义没有后路可走,因为每个对象都可以被无限多的不同指称短语所指称。


这样看来,’C’C是不同的实体,这样'C'就表示C;但这不能成为一种解释,因为'C'C的关系仍然是完全神秘的;而且我们在哪里可以找到表示C的指称复合体'C'?此外,当C出现在一个命题中时,它不仅仅是指称(正如我们将在下一段中看到的);然而,在上述观点中,C只是指称,意义完全被归于'C'。这是一个无法摆脱的纠结,似乎证明意义和指称之间的整个区别被错误地设想了。


当命题中出现一个指称短语时,其含义是相关的,这一点已被有关《韦弗利》作者的难题正式证明。命题’ScottWaverley的作者有一个'ScottScott'不具备的属性,即乔治四世想知道它是否是真的。因此,这两个命题并不完全相同;因此,如果我们坚持这种区分所属于的观点,那么'《韦弗利》的作者'的意义和指称也必须是相关的。然而,正如我们刚刚看到的,只要我们坚持这个观点,我们就不得不认为只有指称是相关的。因此,有关的观点必须被放弃。


现在需要说明的是,我们所考虑的所有难题是如何通过本文开头解释的理论来解决的。


根据我所主张的观点,一个指称短语本质上是一个句子的一部分,并不像大多数单字一样,有其自身的任何意义。如果我说'斯科特是个男人',这就是一个形式为'X是个男人'的陈述,它的主语是'斯科特'。但如果我说'《韦弗利》的作者是个男人',那就不是'X是个男人'这种形式的陈述,也没有'《韦弗利》的作者'作为其主题。缩减本文开头的陈述,我们可以用以下内容来代替'韦弗利的作者是一个人'。有且仅有一个实体写了《韦弗利》,而那个人是个男人。(这与前面所说的严格意义上的意思不同;但它更容易理解。) 一般来说,假设我们想说韦弗利的作者有属性f,我们想说的相当于只有一个实体写了韦弗利,而那个人有属性f’


现在对指称的解释如下。每一个出现韦弗利的作者的命题都被解释为上述内容,'斯科特是韦弗利的作者'(即'斯科特与韦弗利的作者相同')这一命题就变成了'一个而且只有一个实体写了韦弗利,斯科特与那个实体相同';或者,恢复到完全明确的形式。'x来说,x写了《韦弗利》并不总是假的,对y来说,如果y写了《韦弗利》,yx是相同的,斯科特与x是相同的,这总是真的。因此,如果'C'是一个指称短语,可能会发生有一个实体x(不可能有多个)的命题'xC相同'是真的,这个命题的解释如上。那么我们可以说,实体x'C'这个短语的指称。因此,Scott'Waverley的作者'的指称。倒逗号中的'C'将仅仅是短语,而不是任何可以被称为意义的东西。这个短语本身没有任何意义,因为在它出现的任何命题中,完整表达的命题都不包含这个已经被拆散的短语。


关于乔治四世的好奇心的谜题,现在看来有一个非常简单的解决方案。上一段中以非简略形式写出的 "斯科特是《韦弗利》的作者 "这一命题,并不包含我们可以用 "斯科特 "代替的 "韦弗利的作者 « 这一成分。只要韦弗利的作者'在所考虑的命题中具有我所说的主要出现,这并不妨碍将'斯科特'替换为'韦弗利的作者'所产生的推论的真实性。表示性短语的主要出现和次要出现的区别如下。


当我们说:'乔治四世希望知道某某',或者当我们说'某某令人惊讶''某某是真的',等等,'某某'必须是一个命题。假设'某某'包含一个表示词组。我们可以从从属命题'某某'中剔除这个指称短语,也可以从整个命题中剔除这个指称短语,而'某某'只是其中的一个成分而已。根据我们的做法,会产生不同的命题。我听说过一个有感而发的游艇主人,一个客人第一次看到游艇时说,'我以为你的游艇比它大';主人回答,'不,我的游艇不比它大'。这位客人的意思是,'我以为你的游艇的尺寸比你的游艇的尺寸大';归结到他身上的意思是,'我以为你的游艇的尺寸比你的游艇的尺寸大'。回到乔治四世和韦弗利,当我们说'乔治四世希望知道斯科特是否是韦弗利的作者'时,我们通常是指'乔治四世希望知道是否有且只有一个人写了韦弗利,斯科特就是那个人';但我们也可能是指。'只有一个人写了《韦弗利》,而乔治四世希望知道斯科特是否是那个人'。在后者中,'《韦弗利》的作者'是主要出现的;在前者中,是次要出现的。后者可以用'乔治四世希望知道,关于事实上写了《韦弗利》的人,他是否就是斯科特'来表达。例如,如果乔治四世在远处看到斯科特,并问道'那是斯科特吗',那么这就是事实。指代短语的二次出现可以定义为:该短语出现在一个命题p中,而该命题只是我们所考虑的命题的一个组成部分,对指代短语的替换是在p中实现的,而不是在整个相关的命题中。在语言中,主要发生和次要发生之间的模糊性是很难避免的;但如果我们对它保持警惕,它就不会有什么危害。在符号逻辑中,它当然很容易避免。


主要发生和次要发生的区别也使我们能够处理现在的法国国王是秃头还是不秃头的问题,以及处理表示什么的表示短语的逻辑地位的问题。如果'C'是一个表示词组,比如'具有F属性的术语',那么


'C有属性F'意味着'有且只有一个词有属性F,而且这个词有属性F'12)


如果现在属性F不属于任何术语,或者属于多个术语,那么对于所有的f值来说,’C具有属性f'是假的。


'有一个对象现在是法国国王,而且不是秃头'


但如果它的意思是

    有一个对象现在是法国国王,而且是秃头,这是假的'


也就是说,如果'法国国王'的出现是主要的,那么'法国国王不是秃头'就是假的,如果是次要的,就是真的。因此,所有'法国国王'主要出现的命题都是假的:对这种命题的否定是真的,但在它们中'法国国王'是次要出现的。因此,我们逃避了 "法国国王有假发 "的结论。


我们现在还可以看到,在AB不存在差异的情况下,如何否认存在AB之间的差异这样一个对象。如果AB确实不同,就只有一个实体x,使'xAB之间的差异'是一个真命题;如果AB没有差异,就没有这样的实体x。因此,根据刚才解释的指称的含义,'AB之间的差异'AB不同时有一个指称,但在其他情况下没有。这种差异一般适用于真命题和假命题。如果'a R b'代表'ab有关系R',那么当a R b为真时,就有ab之间的关系R这样一个实体;当a R b为假时,就没有这样一个实体。因此,从任何命题中,我们都可以做出一个指称短语,如果该命题为真,则指称一个实体,如果该命题为假,则不指称一个实体。例如,地球绕着太阳转是真的(至少我们会这么认为),而太阳绕着地球转是假的;因此地球绕着太阳转'表示一个实体,而'太阳绕着地球转'不表示一个实体13)。


整个非实体的领域,如 "圆形广场""2以外的偶数素数""阿波罗""哈姆雷特 "等等,现在可以令人满意地处理了。所有这些都是表示的短语,并不表示任何东西。一个关于阿波罗的命题意味着我们通过替换古典字典告诉我们的阿波罗的意思,比如说'太阳神',得到了什么。所有出现阿波罗的命题都要按照上述表示词组的规则来解释。如果'阿波罗'有一次出现,包含该出现的命题就是假的;如果该出现是次要的,该命题可能是真的。所以,'圆方是圆的'又意味着'有一个而且只有一个实体x是圆的,而且是方的,这个实体是圆的',这是一个假命题,而不是像迈农所坚持的那样,是一个真命题。'最完美的存在者具有所有的完美性;存在是一种完美性;因此最完美的存在者存在'成为。


'有一个而且只有一个对象x是最完美的;那个实体有所有的完美;存在是一种完美;因此那个对象存在。


作为一个证明,由于缺乏对有一个也只有一个对象x是最完美的'这一前提的证明,这就失败了14)。


麦克科尔先生(MindN.S.,第54号,以及第55号,第401页)认为个人有两种,即真实的和不真实的;因此他把空类定义为由所有不真实的个人组成的类。这就假定,像 "现任法国国王 "这样的短语并不表示一个真实的个人,但它确实表示一个个人,但却是一个不真实的个人。这基本上是梅农的理论,我们已经看到有理由拒绝它,因为它与矛盾法则相冲突。有了我们的指称理论,我们就可以认为不存在不真实的个体;因此,空类是不包含成员的类,而不是包含所有不真实的个体的类。


重要的是,要注意我们的理论对通过表示短语进行的定义的解释的影响。大多数数学定义都是这种类型的;例如,"m-n指的是与n相加后得到m的数字"。因此,m-n被定义为与某个表示词组的含义相同;但我们同意表示词组没有单独的含义。因此,定义应该是:'任何包含m-n的命题都是指用 "m-n "代替 "n相加得出m的数字 "所产生的命题。由此产生的命题将根据已经给出的解释言语表达包含指称短语的命题的规则进行解释。在mn是这样的情况下,有一个而且只有一个数字x,与n相加,得到m,有一个数字x可以在任何包含m-n的命题中代替m-n而不改变命题的真假。但在其他情况下,所有 "m-n "主要出现的命题都是假的。


上述理论解释了身份的有用性。在逻辑书之外,没有人想说'xx',但身份的断言却经常以'斯科特是《韦弗利》的作者''你是那个人'这样的形式提出来。如果没有同一性的概念,就不能说明这些命题的意义,尽管它们并不是简单地说明斯科特与另一个术语--《韦弗利》的作者相同,或者你与另一个术语--那个人相同。斯科特是《韦弗利》的作者 "的最简短的陈述似乎是 "斯科特写了《韦弗利》15);而对于y来说,如果y写了《韦弗利》,y就与斯科特相同,这总是真的。正是以这种方式,身份进入了'ScottWaverley的作者';正是由于这种使用,身份才值得肯定。


上述指称理论的一个有趣的结果是:当有一个我们并不直接认识的东西,而只是通过指称短语来定义时,那么通过指称短语介绍这个东西的命题并不真正包含这个东西作为一个成分,而是包含指称短语的几个词所表达的成分。因此,在我们能够理解的每一个命题中(即不仅在那些我们能够判断其真假的命题中,而且在所有我们能够思考的命题中),所有的成分都是我们能够直接了解的实体。现在,像物质(在物理学中物质出现的意义上)和其他人的思想这样的东西,我们只是通过表示短语来知道,也就是说,我们并不熟悉它们,但我们知道它们是具有这样那样属性的东西。因此,尽管我们可以形成命题函数C(x),这些命题函数对这样那样的物质粒子或某某的心灵来说必须是成立的,但我们并不熟悉肯定这些我们知道必须是真的东西的命题,因为我们无法领会相关的实际实体。我们所知道的是'某某有一个思想,它有这样那样的属性',但我们不知道'A有这样那样的属性',其中A是有关的思想。在这种情况下,我们知道一个事物的属性,但并不了解该事物本身,因此也不知道该事物本身为构成要素的任何单一命题。


关于我所主张的观点的许多其他后果,我将不说了。我只想请读者在尝试构建自己关于指称主题的理论之前,不要下定决心反对这个观点因为他可能会因为这个观点显然过于复杂而下定决心。我相信,这种尝试将使他相信,无论真正的理论是什么,它都不可能像人们事先预期的那样简单。


二,原文

 

On denoting


By a " denoting phrase " I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the centre of mass of the Solar System at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish three cases: 


  1. A phrase may be denoting, and yet not denote anything; e.g., the present King of France 

  2. A phrase may denote one definite object; e.g., "the present King of England " denotes a certain man. 

  3. A phrase may denote ambiguously; e.g., " a man " denotes not many men, but an ambiguous man. 


The interpretation of such phrases is a matter of considerable difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain


The subject of denoting is of very great importance, not only in logic and mathematics, but also in theory of knowledge. For example, we know that the centre of mass of the Solar System at a definite instant is some definite point, and we can affirm a number of propositions about it; but we have no immediate acquaintance with this point, which is only known to us by description. The distinction between acquaintance and knowledge about is the distinction between the things we have presentations of, and the things we only reach by means of denoting phrases. It often happens that we know that a certain phrase denotes unambiguously, although we have no acquaintance with what it denotes; this occurs in the above case of the centre of mass. In perception we have acquaintance with the objects of perception, and in thought we have acquaintance with objects of a more abstract logical character; but we do not necessarily have acquaintance with the objects denoted by phrases composed of words with whose meanings we are acquainted. To take a very important instance: There seems no reason to believe that we are ever acquainted with other people's minds, seeing that these are not directly perceived; hence what we know about them is obtained through denoting. All thinking has to start from acquaintance; but it succeeds in thinking about many things with which we have no acquaintance.


The course of my argument will be as follows. I shall begin by stating the theory I intend to advocate; I shall then discuss the theories of Frege and Meinong, showing why neither of them satisfies me; then I shall give the grounds in favour of my theory; and finally I shall briefly indicate the philosophical consequences of my theory. 


My theory, briefly, is as follows. I take the notion of the variable as fundamental; I use " C (x) " to mean a proposition in which x is a constituent, where x, the variable, is essentially and wholly undetermined. Then we can consider the two notions "C (x) is always true" and " C (x) is some- times true ". Then everything and nothing and something (which are the most primitive of denoting phrases) are to be interpreted as follows: 

C (everything) means " C (x) is always true"; 

C (nothing) means "'C (x) is false' is always true"; 

C (something) means "It is false that ' C (x) is false' is always true « 


Here the notion 'C(x) is always true' is taken as ultimate and indefinable, and the others are defined by means of it. Everythingnothing, and something are not assumed to have any meaning in isolation, but a meaning is assigned to every proposition in which they occur. This is the principle of the theory of denoting I wish to advocate: that denoting phrases never have any meaning in themselves, but that every proposition in whose verbal expression they occur has a meaning. The difficulties concerning denoting are, I believe, all the result of a wrong analysis of propositions whose verbal expressions contain denoting phrases. The proper analysis, if I am not mistaken, may be further set forth as follows.


Suppose now we wish to interpret the proposition, 'I met a man'. If this is true, I met some definite man; but that is not what I affirm. What I affirm is, according to the theory I advocate:

      ' "I met x, and x is human" is not always false’.

     Generally, defining the class of men as the class of objects having the predicate human, we say that:

      'C(a man)' means '"C(x) and x is human" is not always false’.

      This leaves 'a man', by itself, wholly destitute of meaning, but gives a meaning to every proposition in whose verbal expression 'a man' occurs.


Consider next the proposition 'all men are mortal'. This proposition is really hypothetical 5) and states that if anything is a man, it is mortal. That is, it states that if x is a man, x is mortal, whatever x may be. Hence, substituting 'x is human' for 'x is a man', we find:


      'All men are mortal' means ' "If x is human, x is mortal" is always true.’

      This is what is expressed in symbolic logic by saying that 'all men are mortal' means '"x is human" implies "x is mortal" for all values of x'. More generally, we say:

     'C(all men)' means '"If x is human, then C(x) is true" is always true’.

     

Similarly


 'C(no men)' means '"If x is human, then C(x) is false" is always true’.

 

      'C(some men)' will mean the same as 'C(a man)', and


     'C(a man 6))' means 'It is false that "C(x) and x is human" is always false’.


      'C(every man)' will mean the same as 'C(all men)'.


It remains to interpret phrases containing the. These are by far the most interesting and difficult of denoting phrases. Take as an instance 'the father of Charles II was executed'. This asserts that there was an x who was the father of Charles II and was executed. Now the, when it is strictly used, involves uniqueness; we do, it is true, speak of 'the son of So-and-so' even when So-and-so has several sons, but it would be more correct to say 'a son of So-and-so'. Thus for our purposes we take the as involving uniqueness. Thus when we say 'x was the father of Charles II' we not only assert that x had a certain relation to Charles II, but also that nothing else had this relation. The relation in question, without the assumption of uniqueness, and without any denoting phrases, is expressed by 'x begat Charles II'. To get an equivalent of 'x was the father of Charles II', we must add 'If y is other than x, y did not beget Charles II', or, what is equivalent, 'If y begat Charles II, y is identical with x'. Hence 'x is the father of Charles II' becomes: 'x begat Charles II; and "If y begat Charles II, y is identical with x" is always true of y'.


Thus 'the father of Charles II was executed' becomes: 'It is not always false of x that x begat Charles II and that x was executed and that "if y begat Charles II, y is identical with x" is always true of y’.


      This may seem a somewhat incredible interpretation; but I am not at present giving reasons, I am merely stating the theory.


      To interpret 'C(the father of Charles II)', where C stands for any statement about him, we have only to substitute C(x) for 'x was executed' in the above. Observe that, according to the above interpretation, whatever statement C may be, 'C(the father of Charles II)' implies:


      'It is not always false of x that "if y begat Charles II, y is identical with x" is always true of y’,

      

which is what is expressed in common language by 'Charles II had one father and no more'. Consequently if this condition fails, every proposition of the form 'C(the father of Charles II)' is false. Thus e.g. every proposition of the form 'C(the present King of France)' is false. This is a great advantage to the present theory. I shall show later that it is not contrary to the law of contradiction, as might be at first supposed.


      The above gives a reduction of all propositions in which denoting phrases occur to forms in which no such phrases occur. Why it is imperative to effect such a reduction, the subsequent discussion will endeavor to show.

      

The evidence for the above theory is derived from the difficulties which seem unavoidable if we regard denoting phrases as standing for genuine constituents of the propositions in whose verbal expressions they occur. Of the possible theories which admit such constituents the simplest is that of Meinong 7). This theory regards any grammatically correct denoting phrase as standing for an object. Thus 'the present King of France', 'the round square', etc., are supposed to be genuine objects. It is admitted that such objects do not subsist, but nevertheless they are supposed to be objects. This is in itself a difficult view; but the chief objection is that such objects, admittedly, are apt to infringe the law of contradiction. It is contended, for example, that the present King of France exists, and also does not exist; that the round square is round, and also not round, etc. But this is intolerable; and if any theory can be found to avoid this result, it is surely to be preferred.


The above breach of the law of contradiction is avoided by Frege's theory. He distinguishes, in a denoting phrase, two elements, which we may call the meaning and the denotation 8). Thus 'the center of mass of the solar system at the beginning of the twentieth century' is highly complex in meaning, but its denotation is a certain point, which is simple. The solar system, the twentieth century, etc., are constituents of the meaning; but the denotation has no constituents at all 9). One advantage of this distinction is that it shows why it is often worth while to assert identity. If we say 'Scott is the author of Waverley,' we assert an identity of denotation with a difference of meaning. I shall, however, not repeat the grounds in favor of this theory, as I have urged its claims elsewhere (loc. cit.), and am now concerned to dispute those claims.


One of the first difficulties that confront us, when we adopt the view that denoting phrases express a meaning and denote a denotation 10), concerns the cases in which the denotation appears to be absent. If we say 'the King of England is bald', that is, it would seem, not a statement about the complex meaning 'the King of England', but about the actual man denoted by the meaning. But now consider 'the king of France is bald'. By parity of form, this also ought to be about the denotation of the phrase 'the King of France'. But this phrase, though it has a meaning provided 'the King of England' has a meaning, has certainly no denotation, at least in any obvious sense. Hence one would suppose that 'the King of France is bald' ought to be nonsense; but it is not nonsense, since it is plainly false. Or again consider such a proposition as the following: 'If u is a class which has only one member, then that one member is a member of u', or as we may state it, 'If u is a unit class, the u is a u'. This proposition ought to be always true, since the conclusion is true whenever the hypothesis is true. But 'the u' is a denoting phrase, and it is the denotation, not the meaning, that is said to be a u. Now is u is not a unit class, 'the u' seems to denote nothing; hence our proposition would seem to become nonsense as soon as u is not a unit class.


Now it is plain that such propositions do not become nonsense merely because their hypotheses are false. The King in The Tempest might say, 'If Ferdinand is not drowned, Ferdinand is my only son'.' Now 'my only son' is a denoting phrase, which, on the face of it, has a denotation when, and only when, I have exactly one son. But the above statement would nevertheless have remained true if Ferdinand had been in fact drowned. Thus we must either provide a denotation in cases in which it is at first sight absent, or we must abandon the view that denotation is what is concerned in propositions which contain denoting phrases. The latter is the course that I advocate. The former course may be taken, as Meinong, by admitting objects which do not subsist, and denying that they obey the law of contradiction; this, however, is to be avoided if possible. Another way of taking the same course (so far as our present alternative is concerned) is adopted by Frege, who provides by definition some purely conventional denotation for the cases in which otherwise there would be none. Thus 'the King of France', is to denote the null-class; 'the only son of Mr. So-and-so' (who has a fine family of ten), is to denote the class of all his sons; and so on. But this procedure, though it may not lead to actual logical error, is plainly artificial, and does not give an exact analysis of the matter. Thus if we allow that denoting phrases, in general, have the two sides of meaning and denotation, the cases where there seems to be no denotation cause difficulties both on the assumption that there really is a denotation and on the assumption that there really is none.


A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science. I shall therefore state three puzzles which a theory as to denoting ought to be able to solve; and I shall show later that my theory solves them.


     (1) If a is identical with b, whatever is true of the one is true of the other, and either may be substituted for the other in any proposition without altering the truth or falsehood of that proposition. Now George IV wished to know whether Scott was the author of Waverley; and in fact Scott was the author of Waverley. Hence we may substitute Scott for the author of 'Waverley', and thereby prove that George IV wished to know whether Scott was Scott. Yet an interest in the law of identity can hardly be attributed to the first gentleman of Europe.

    

 (2) By the law of the excluded middle, either 'A is B' or 'A is not B' must be true. Hence either 'the present King of France is bald' or 'the present King of France is not bald' must be true. Yet if we enumerated the things that are bald, and then the things that are not bald, we should not find the present King of France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig.


  (3) Consider the proposition 'A differs from B'. If this is true, there is a difference between A and B, which fact may be expressed in the form 'the difference between A and B subsists'. But if it is false that A differs from B, then there is no difference between A and B, which fact may be expressed in the form 'the difference between A and B does not subsist'. But how can a non-entity be the subject of a proposition? 'I think, therefore I am' is no more evident than 'I am the subject of a proposition, therefore I am'; provided 'I am' is taken to assert subsistence or being 11), not existence. Hence, it would appear, it must always be self-contradictory to deny the being of anything; but we have seen, in connexion with Meinong, that to admit being also sometimes leads to contradictions. Thus if A and B do not differ, to suppose either that there is, or that there is not, such an object as 'the difference between A and B' seems equally impossible.


The relation of the meaning to the denotation involves certain rather curious difficulties, which seem in themselves sufficient to prove that the theory which leads to such difficulties must be wrong.


      When we wish to speak about the meaning of a denoting phrase, as opposed to its denotation, the natural mode of doing so is by inverted commas. Thus we say:


      The center of mass of the solar system is a point, not a denoting complex;

      'The center of mass of the solar system' is a denoting complex, not a point.

     Or again,


The first line of Gray's Elegy states a proposition.


      'The first line of Gray's Elegy' does not state a proposition.


     Thus taking any denoting phrase, say C, we wish to consider the relation between C and 'C', where the difference of the two is of the kind exemplified in the above two instances.


      We say, to begin with, that when C occurs it is the denotation that we are speaking about; but when 'C' occurs, it is the meaning. Now the relation of meaning and denotation is not merely linguistic through the phrase: there must be a logical relation involved, which we express by saying that the meaning denotes the denotation. But the difficulty which confronts us is that we cannot succeed in both preserving the connexion of meaning and denotation and preventing them from being one and the same; also that the meaning cannot be got at except by means of denoting phrases. This happens as follows.


The one phrase C was to have both meaning and denotation. But if we speak of 'the meaning of C', that gives us the meaning (if any) of the denotation. 'The meaning of the first line of Gray's Elegy' is the same as 'The meaning of "The curfew tolls the knell of parting day",' and is not the same as 'The meaning of "the first line of Gray's Elegy".' Thus in order to get the meaning we want, we must speak not of 'the meaning of C', but 'the meaning of "C",' which is the same as 'C' by itself. Similarly 'the denotation of C' does not mean the denotation we want, but means something which, if it denotes at all, denotes what is denoted by the denotation we want. For example, let 'C' be 'the denoting complex occurring in the second of the above instances'. Then


      C = 'the first line of Gray's Elegy', and


      the denotation of C = The curfew tolls the knell of parting day. But what we meant to have as the denotation was 'the first line of Gray's Elegy'. Thus we have failed to get what we wanted.

     

The difficulty in speaking of the meaning of a denoting complex may be stated thus: The moment we put the complex in a proposition, the proposition is about the denotation; and if we make a proposition in which the subject is 'the meaning of C', then the subject is the meaning (if any) of the denotation, which was not intended. This leads us to say that, when we distinguish meaning and denotation, we must be dealing with the meaning: the meaning has denotation and is a complex, and there is not something other than the meaning, which can be called the complex, and be said to have both meaning and denotation. The right phrase, on the view in question, is that some meanings have denotations.


But this only makes our difficulty in speaking of meanings more evident. For suppose that C is our complex; then we are to say that C is the meaning of the complex. Nevertheless, whenever C occurs without inverted commas, what is said is not true of the meaning, but only of the denotation, as when we say: The center of mass of the solar system is a point. Thus to speak of C itself, i.e. to make a proposition about the meaning, our subject must not be C, but something which denotes C. Thus 'C', which is what we use when we want to speak of the meaning, must not be the meaning, but must be something which denotes the meaning. And C must not be a constituent of this complex (as it is of 'the meaning of C'); for if C occurs in the complex, it will be its denotation, not its meaning, that will occur, and there is no backward road from denotations to meaning, because every object can be denoted by an infinite number of different denoting phrases.


Thus it would seem that 'C' and C are different entities, such that 'C' denotes C; but this cannot be an explanation, because the relation of 'C' to C remains wholly mysterious; and where are we to find the denoting complex 'C' which is to denote C? Moreover, when C occurs in a proposition, it is not only the denotation that occurs (as we shall see in the next paragraph); yet, on the view in question, C is only the denotation, the meaning being wholly relegated to 'C'. This is an inextricable tangle, and seems to prove that the whole distinction between meaning and denotation has been wrongly conceived.


That the meaning is relevant when a denoting phrase occurs in a proposition is formally proved by the puzzle about the author of Waverley. The proposition 'Scott was the author of Waverley' has a property not possessed by 'Scott was Scott', namely the property that George IV wished to know whether it was true. Thus the two are not identical propositions; hence the meaning of 'the author of Waverley' must be relevant as well as the denotation, if we adhere to the point of view to which this distinction belongs. Yet, as we have just seen, so long as we adhere to this point of view, we are compelled to hold that only the denotation is relevant. Thus the point of view in question must be abandoned.


It remains to show how all the puzzles we have been considering are solved by the theory explained at the beginning of this article.


      According to the view which I advocate, a denoting phrase is essentially part of a sentence, and does not, like most single words, have any significance on its own account. If I say 'Scott was a man', that is a statement of the form 'x was a man', and it has 'Scott' for its subject. But if I say 'the author of Waverley was a man', that is not a statement of the form 'x was a man', and does not have 'the author of Waverley' for its subject. Abbreviating the statement made at the beginning of this article, we may put, in place of 'the author of Waverley was a man', the following: 'One and only one entity wrote Waverley, and that one was a man'. (this is not so strictly what is meant as what was said earlier; but it is easier to follow.) And speaking generally, suppose we wish to say that the author of Waverley had property f, what we wish to say is equivalent to 'One and only one entity wrote Waverley, and that one had the property f’.


The explanation of denotation is now as follows. Every proposition in which 'the author of Waverley' occurs being explained as above, the proposition 'Scott was the author of Waverley' (i.e. 'Scott was identical with the author of Waverley') becomes 'One and only one entity wrote Waverley, and Scott was identical with that one'; or, reverting to the wholly explicit form: 'It is not always false of x that x wrote Waverley, that it is always true of y that if y wrote Waverley y is identical with x, and that Scott is identical with x.' Thus if 'C' is a denoting phrase, it may happen that there is one entity x (there cannot be more than one) for which the proposition 'x is identical with C' is true, this proposition being interpreted as above. We may then say that the entity x is the denotation of the phrase 'C'. Thus Scott is the denotation of 'the author of Waverley'. The 'C' in inverted commas will be merely the phrase, not anything that can be called the meaning. The phrase per se has no meaning, because in any proposition in which it occurs the proposition, fully expressed, does not contain the phrase, which has been broken up.


The puzzle about George IV's curiosity is now seen to have a very simple solution. The proposition 'Scott was the author of Waverley', which was written out in its unabbreviated form in the preceding paragraph, does not contain any constituent 'the author of Waverley' for which we could substitute 'Scott'. This does not interfere with the truth of inferences resulting from making what is verbally the substitution of 'Scott' for 'the author of Waverley', so long as 'the author of Waverley' has what I call a primary occurrence in the proposition considered. The difference of primary and secondary occurrences of denoting phrases is as follows:


When we say: 'George IV wished to know whether so-and-so', or when we say 'So-and-so is surprising' or 'So-and-so is true', etc., the 'so-and-so' must be a proposition. Suppose now that 'so-and-so' contains a denoting phrase. We may either eliminate this denoting phrase from the subordinate proposition 'so-and-so', or from the whole proposition in which 'so-and-so' is a mere constituent. Different propositions result according to which we do. I have heard of a touchy owner of a yacht to whom a guest, on first seeing it, remarked, 'I thought your yacht was larger than it is'; and the owner replied, 'No, my yacht is not larger than it is'. What the guest meant was, 'The size that I thought your yacht was is greater than the size your yacht is'; the meaning attributed to him is, 'I thought the size of your yacht was greater than the size of your yacht'. To return to George IV and Waverley, when we say 'George IV wished to know whether Scott was the author of Waverley' we normally mean 'George IV wished to know whether one and only one man wrote Waverley and Scott was that man'; but we may also mean: 'One and only one man wrote Waverley, and George IV wished to know whether Scott was that man'. In the latter, 'the author of Waverley' has a primary occurrence; in the former, a secondary. The latter might be expressed by 'George IV wished to know, concerning the man who in fact wrote Waverley, whether he was Scott'. This would be true, for example, if George IV had seen scott at a distance, and had asked 'Is that Scott?'. A secondary occurrence of a denoting phrase may be defined as one in which the phrase occurs in a proposition p which is a mere constituent of the proposition we are considering, and the substitution for the denoting phrase is to be effected in p, and not in the whole proposition concerned. The ambiguity as between primary and secondary occurrences is hard to avoid in language; but it does no harm if we are on our guard against it. In symbolic logic it is of course easily avoided.


 The distinction of primary and secondary occurrences also enables us to deal with the question whether the present King of France is bald or not bald, and general with the logical status of denoting phrases that denote nothing. If 'C' is a denoting phrase, say 'the term having the property F', then


      'C has property f' means 'one and only one term has the property F, and that one has the property f'. 12)


      If now the property F belongs to no terms, or to several, it follows that 'C has property f' is false for all values of f. Thus 'the present King of France is not bald' is false if it means


      'There is an entity which is now King of France and is not bald’,



      but is true if it means

      'It is false that there is an entity which is now King of France and is bald'.

   

That is, 'the King of France is not bald' is false if the occurrence of 'the King of France' is primary, and true if it is secondary. Thus all propositions in which 'the King of France' has a primary occurrence are false: the denials of such propositions are true, but in them 'the King of France' has a secondary occurrence. Thus we escape the conclusion that the King of France has a wig.


      We can now see also how to deny that there is such an object as the difference between A and B in the case when A and B do not differ. If A and B do differ, there is only and only one entity x such that 'x is the difference between A and B' is a true proposition; if A and B do not differ, there is no such entity x. Thus according to the meaning of denotation lately explained, 'the difference between A and B' has a denotation when A and B differ, but not otherwise. This difference applies to true and false propositions generally. If 'a R b' stands for 'a has the relation R to b', then when a R b is true, there is such an entity as the relation R between a and b; when a R b is false, there is no such entity. Thus out of any proposition we can make a denoting phrase, which denotes an entity if the proposition is true, but does not denote an entity if the proposition is false. E.g., it is true (at least we will suppose so) that the earth revolves round the sun, and false that the sun revolves round the earth; hence 'the revolution of the earth round the sun' denotes an entity, while 'the revolution of the sun round the earth' does not denote an entity 13).



     

The whole realm of non-entities, such as 'the round square', 'the even prime other than 2', 'Apollo', 'Hamlet', etc., can now be satisfactorily dealt with. All these are denoting phrases which do not denote anything. A proposition about Apollo means what we get by substituting what the classical dictionary tells us is meant by Apollo, say 'the sun-god'. All propositions in which Apollo occurs are to be interpreted by the above rules for denoting phrases. If 'Apollo' has a primary occurrence, the proposition containing the occurrence is false; if the occurrence is secondary, the proposition may be true. So again 'the round square is round' means 'there is one and only one entity x which is round and square, and that entity is round', which is a false proposition, not, as Meinong maintains, a true one. 'The most perfect Being has all perfections; existence is a perfection; therefore the most perfect Being exists' becomes:



      'There is one and only one entity x which is most perfect; that one has all perfections; existence is a perfection; therefore that one exists.’


      As a proof, this fails for want of a proof of the premiss 'there is one and only one entity x which is most perfect' 14)

     

Mr. MacColl (Mind, N.S., No. 54, and again No. 55, page 401) regards individuals as of two sorts, real and unreal; hence he defines the null-class as the class consisting of all unreal individuals. This assumes that such phrases as 'the present King of France', which do not denote a real individual, do, nevertheless, denote an individual, but an unreal one. This is essentially Meinong's theory, which we have seen reason to reject because it conflicts with the law of contradiction. With our theory of denoting, we are able to hold that there are no unreal individuals; so that the null-class is the class containing no members, not the class containing as members all unreal individuals.


      It is important to observe the effect of our theory on the interpretation of definitions which proceed by means of denoting phrases. Most mathematical definitions are of this sort; for example 'm-n means the number which, added to n, gives m'. Thus m-n is defined as meaning the same as a certain denoting phrase; but we agreed that denoting phrases have no meaning in isolation. Thus what the definition really ought to be is: 'Any proposition containing m-n is to mean the proposition which results from substituting for "m-n" "the number which, added to n, gives m".' The resulting proposition is interpreted according to the rules already given for interpreting propositions whose verbal expression contains a denoting phrase. In the case where m and n are such that there is one and only one number x which, added to n, gives m, there is a number x which can be substituted for m-n in any proposition contain m-n without altering the truth or falsehood of the proposition. But in other cases, all propositions in which 'm-n' has a primary occurrence are false.


The usefulness of identity is explained by the above theory. No one outside of a logic-book ever wishes to say 'x is x', and yet assertions of identity are often made in such forms as 'Scott was the author of Waverley' or 'thou are the man'. The meaning of such propositions cannot be stated without the notion of identity, although they are not simply statements that Scott is identical with another term, the author of Waverley, or that thou are identical with another term, the man. The shortest statement of 'Scott is the author of Waverley' seems to be 'Scott wrote Waverley 15); and it is always true of y that if y wrote Waverley, y is identical with Scott'. It is in this way that identity enters into 'Scott is the author of Waverley'; and it is owing to such uses that identity is worth affirming.


      One interesting result of the above theory of denoting is this: when there is an anything with which we do not have immediate acquaintance, but only definition by denoting phrases, then the propositions in which this thing is introduced by means of a denoting phrase do not really contain this thing as a constituent, but contain instead the constituents expressed by the several words of the denoting phrase. Thus in every proposition that we can apprehend (i.e. not only in those whose truth or falsehood we can judge of, but in all that we can think about), all the constituents are really entities with which we have immediate acquaintance. Now such things as matter (in the sense in which matter occurs in physics) and the minds of other people are known to us only by denoting phrases, i.e. we are not acquainted with them, but we know them as what has such and such properties. Hence, although we can form propositional functions C(x) which must hold of such and such a material particle, or of So-and-so's mind, yet we are not acquainted with the propositions which affirm these things that we know must be true, because we cannot apprehend the actual entities concerned. What we know is 'So-and-so has a mind which has such and such properties' but we do not know 'A has such and such properties', where A is the mind in question. In such a case, we know the properties of a thing without having acquaintance with the thing itself, and without, consequently, knowing any single proposition of which the thing itself is a constituent.


      Of the many other consequences of the view I have been advocating, I will say nothing. I will only beg the reader not to make up his mind against the view - as he might be tempted to do, on account of its apparently excessive complication - until he has attempted to construct a theory of his own on the subject of denotation. This attempt, I believe, will convince him that, whatever the true theory may be, it cannot have such a simplicity as one might have expected beforehand.

 



参考文献:

1】对罗素摹状词理论的另一种解释,https://zhuanlan.zhihu.com/p/32310123

2】【笔记】论指称,https://zhuanlan.zhihu.com/p/384802250


 




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