{"id":2394,"date":"2011-09-03T00:44:56","date_gmt":"2011-09-02T22:44:56","guid":{"rendered":"http:\/\/empreintesdigitales.wordpress.com\/?p=2394"},"modified":"2021-06-13T18:15:47","modified_gmt":"2021-06-13T16:15:47","slug":"on-denoting","status":"publish","type":"post","link":"https:\/\/disparates.org\/lun\/2011\/09\/on-denoting\/","title":{"rendered":"Sur la d\u00e9notation (de Bertrand Russell)"},"content":{"rendered":"
\"\"<\/a>

Bertrand Russell (1950)<\/p><\/div>\n

Comme j’entame \u00e0 la lecture du s\u00e9minaire ...ou pire<\/em>, j’y croise le terme de \u00ab\u00a0d\u00e9notation\u00a0\u00bb qu’il me semble que Miller a lui-m\u00eame employ\u00e9 cette ann\u00e9e.<\/p>\n

Une recherche rapide sur le site me ram\u00e8ne au cours du 16 mars<\/a>, o\u00f9 effectivement Miller commente le texte qui va suivre,  \u00ab\u00a0On denoting\u00a0\u00bb, \u00ab\u00a0Sur la d\u00e9notation\u00a0\u00bb, de Bertrand Russell :<\/p>\n

\u00ab\u00a0Y a quelqu\u2019un qui a fait quelque chose qui est comme un mot d\u2019esprit, qui n\u2019en n\u2019a pas moins inspir\u00e9 des r\u00e9flexions aux logiciens pendant tout le XX\u00e8 si\u00e8cle. \u00c7a tient en quelques pages, c\u2019est un article de quelqu’un dont Lacan a beaucoup  pratiqu\u00e9 l\u2019\u0153uvre, Bertrand Russell, c\u2019est un article qui s\u2019appelle \u00ab On denoting \u00bb (1905). \u00ab\u00a0Sur la d\u00e9notation\u00a0\u00bb. En termes fregiens, on dirait \u00ab\u00a0Sur la r\u00e9f\u00e9rence\u00a0\u00bb, nous dirions \u00ab\u00a0Sur l\u2019existence\u00a0\u00bb. Et dans cet article, il s\u2019occupe \u00e0 extraire, \u00e0 faire saillir dans tout \u00e9nonc\u00e9 l\u2019acte r\u00e9f\u00e9rentiel.\u00a0\u00bb<\/p><\/blockquote>\n

La \u00ab\u00a0d\u00e9notation\u00a0\u00bb \u00e0 laquelle Lacan fait r\u00e9f\u00e9rence dans …ou pire<\/em>, du moins \u00e0 l’endroit du texte o\u00f9 je suis arriv\u00e9e (p. 55), est celle de Frege dans ses Principes math\u00e9matiques<\/em>, celle-l\u00e0 m\u00eame que critique Russell dans \u00ab\u00a0On denoting\u00a0\u00bb. Lacan dit se r\u00e9f\u00e9rer \u00e0 la traduction de Claude Imbert qui traduit  Bedeutung<\/em>  par \u00ab\u00a0d\u00e9notation\u00a0\u00bb – l\u00e0 o\u00f9 Miller traduirait plut\u00f4t par  \u00ab\u00a0r\u00e9f\u00e9rence\u00a0\u00bb :<\/p>\n

\u00ab\u00a0Alors. Le r\u00e9el au sens de Lacan, pour en p\u00e9n\u00e9trer les arcanes, il faut se familiariser avec l\u2019usage du \u00ab il existe \u00bb en logique. Et pour \u00e7a,  le plus simple est de partir de la scission que Frege a op\u00e9r\u00e9e entre Sinn<\/em> et Bedeutung.<\/em><\/p>\n

Bedeutung<\/em> \u00e7a peut se  traduire comme la signification, c\u2019est en ce sens que Lacan dit \u00ab die Bedeutung des Phallus\u00bb. Faut dire que Freud emploie fr\u00e9quemment le mot, et dans ce sens-l\u00e0. Et sans doute Lacan l\u2019a-t-il employ\u00e9 parce qu\u2019il y voyait aussi une fa\u00e7on de faire allusion \u00e0 l\u2019usage de Frege. Mais chez Frege, Bedeutung <\/em>se traduit par \u00ab la r\u00e9f\u00e9rence \u00bb.  Ce qui d\u00e9note, ce qui pointe vers une existence. Sinn<\/em>, c\u2019est sens ou c\u2019est signification. Si on veut Sinn,<\/em> c\u2019est ce qui dit l\u2019essence, c\u2019est ce qui d\u00e9crit quelque chose, ce qui d\u00e9cerne des attributs, des propri\u00e9t\u00e9s \u00e0 quelque chose. Si je voulais encore parodier la phrase de Sartre \u00e0 la Frege, je dirais \u00ab La Bedeutung<\/em> pr\u00e9c\u00e8de le Sinn<\/em> \u00bb. Mais, \u00e7a n\u2019est pas ce que dit Frege. Il ne dit pas que l\u2019un pr\u00e9c\u00e8de l\u2019autre, mais que existence et essence, \u00e7a fait deux. L\u2019essence, la description, le nom peut bien \u00eatre essence d\u2019un \u00eatre, mais n\u2019assure d\u2019aucune existence. \u00ab Cercle carr\u00e9 \u00bb \u00e7a fait sens, ne serait-ce que pour dire \u00ab un cercle carr\u00e9 y en pas \u00bb. Une licorne, \u00e7a se d\u00e9crit, \u00e7a se repr\u00e9sente, on en r\u00eave, m\u00eame si dans la nature \u00e7a ne se rencontre pas. Vous pouvez parfaitement admettre \u00e7a dans votre ontologie, si \u00e7a vous chante.\u00a0\u00bb<\/p><\/blockquote>\n

Bon, il se trouve que dans l’extrait du s\u00e9minaire auquel je me r\u00e9f\u00e8re ici, Lacan \u00ab\u00a0explique\u00a0\u00bb pourquoi il utilise et traduit Bedeutung<\/em> par \u00ab\u00a0signification\u00a0\u00bb dans le titre de son expos\u00e9 \u00ab\u00a0La signification du phallus – Die Bedeutung des Phallus\u00a0\u00bb :<\/p>\n

J’ai pris soin de loger quelque part dans mes \u00c9crits<\/em> l’\u00e9nonciation que j’avais faite en 1958, il y a une paye, sous le titre La Signification du phallus<\/em>. J’ai \u00e9crit dessous Die Bedeutung des Phallus<\/em>. Ce n’est pas pour le plaisir de vous faire croire que je sais l’allemand, encore que ce soit en allemand, puisque c’\u00e9tait \u00e0 Munich, que j’ai cru devoir articuler ce dont j’ai donn\u00e9 l\u00e0 le texte retraduit. Il m’avait sembl\u00e9 opportun d’introduire sous le terme de Bedeutung<\/em> ce qu’en fran\u00e7ais, vu le degr\u00e9 de culture o\u00f9 nous \u00e9tions \u00e0 l’\u00e9poque parvenus, je ne pouvais d\u00e9cemment traduire que par signification<\/em>.<\/p>\n

Die Bedeutung des Phallus<\/em>, les Allemands eux-m\u00eames, \u00e9tant donn\u00e9 qu’ils \u00e9taient analystes – j’en marque la distance par une petite note au d\u00e9but du texte -, n’y ont entrav\u00e9 que pouic. […]<\/p>\n

Die Bedeutung<\/em>, pourtant, \u00e9tait bien ref\u00e9r\u00e9 \u00e0 l’usage que Frege fait de ce mot pour l’opposer au terme de Sinn<\/em>, lequel r\u00e9pond tr\u00e8s exactement \u00e0 ce que j’ai cru devoir vous rappeler au niveau de mon \u00e9nonc\u00e9 d’aujourd’hui, \u00e0 savoir le sens, le sens d’une proposition. On pourrait l’exprimer autrement – et ce n’est pas incompatible – ce qu’il en est de la n\u00e9cessit\u00e9 qui conduit \u00e0 cet art de la produire comme n\u00e9cessit\u00e9 de discours. On pourrait l’exprimer en disant – que faut-il pour qu’une parole d\u00e9note quelque chose<\/strong>? C’est le sens que Frege donne \u00e0 Bedeutung<\/em> – faites attention, les menus \u00e9changes commencent -, la d\u00e9notation.<\/p>\n

Si vous voulez bien ouvrir ce livre de Frege qui s’appelle Les Fondements de l\u2019arithm\u00e9tique<\/em> – il est traduit, ce qui le fait enti\u00e8rement accessible pour vous, \u00e0 la port\u00e9e de votre main, par une certaine Claude Imbert qui autrefois, si mon souvenir est bon, fr\u00e9quenta mon S\u00e9minaire -, il vous appara\u00eetra clair que, pour qu’il y ait \u00e0 coup s\u00fbr d\u00e9notation, il n’est pas mal de s’adresser d’abord, timidement, au champ de l\u2019arithm\u00e9tique, tel qu’il est d\u00e9fini par les nombres entiers.<\/p>\n

[…]<\/p>\n

Un effort logique peut au moins tenter de rendre compte des nombres entiers, et c’est pourquoi j’am\u00e8ne dans le champ de votre consid\u00e9ration le travail de Frege.<\/p><\/blockquote>\n

Je donne donc ici le texte de Bertrant Russel, On Denoting<\/em>, publi\u00e9 dans la revue Mind<\/em> en 1905 (traduit de l\u2019anglais par J-M Roy, in \u00c9crits de Logique philosophique<\/em>, Epim\u00e9th\u00e9e, PUF, Paris, 1989). J’ai trouv\u00e9 ce texte l\u00e0<\/a>, on en trouve une tr\u00e8s jolie copie l\u00e0 (pdf)<\/a>, et je compte le parsemer d’extraits traduits trouv\u00e9s dans ce texte d’un certain Gilles Plante, \u00ab\u00a0Questions de logique\u00a0\u00bb, tr\u00e8s \u00e9clairant, trouv\u00e9 ici<\/a>, ainsi que d’extraits du cours du 16 mars de Jacques-Alain Miller<\/a> pouvant l’illustrer.<\/p>\n

\n

 <\/h3>\n

On denoting<\/strong><\/h3>\n

By Bertrand Russell<\/p>\n

1905<\/h4>\n

By a \u00ab\u00a0denoting phrase<\/strong>\u00a0\u00bb 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 center 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<\/strong>. Thus a phrase is denoting solely in virtue of its form.<\/em> We may distinguish three cases: (1) A phrase may be denoting, and yet not denote anything<\/strong>; e.g.<\/em>, \u00ab\u00a0the present King of France<\/strong>\u00ab\u00a0. (2) A phrase may denote one definite object<\/strong>; e.g.<\/em>, \u00ab\u00a0the present King of England\u00a0\u00bb denotes a certain man. (3) A phrase may denote ambiguously<\/strong>; e.g. \u00ab\u00a0a man\u00a0\u00bb denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably 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.<\/p>\n

Par  \u00ab\u00a0locution d\u00e9notante<\/strong>\u00a0\u00bb  (\u00ab\u00a0denoting phrase\u00a0\u00bb), je veux dire (mean) une locution telle que l\u2019une des suivantes : a man, some man, any man, every man, all men, the present King of England, the present King of France, the center 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. Donc, la locution n’est d\u00e9notante qu’en vertu de sa forme<\/em>. Nous pouvons distinguer trois cas: (1) une locution peut \u00eatre d\u00e9notante, encore qu\u2019elle ne d\u00e9note rien<\/strong> ; v.g., \u00ab\u00a0l\u2019actuel Roi de France\u00a0\u00bb. (2) une locution peut d\u00e9noter un objet d\u00e9termin\u00e9<\/strong> ; v.g., \u00ab\u00a0l\u2019actuel Roi d\u2019Angleterre\u00a0\u00bb d\u00e9note un certain homme [en 1905, \u00c9douard VII]. (3) Une locution peut d\u00e9noter de mani\u00e8re ind\u00e9termin\u00e9e<\/strong> [ambiguously]; v.g. \u00ab\u00a0un homme\u00a0\u00bb ne d\u00e9note pas plusieurs hommes, mais un homme ind\u00e9termin\u00e9. L\u2019interpr\u00e9tation de telles locutions pr\u00e9sente une difficult\u00e9 consid\u00e9rable ; en effet, il est tr\u00e8s difficile de construire [to frame] une th\u00e9orie qui n\u2019est pas susceptible d\u2019une r\u00e9futation formelle. Toutes les difficult\u00e9s que je connais par exp\u00e9rience v\u00e9cue (All the difficulties with which I am acquainted), \u00e0 ce point de mes d\u00e9couvertes (so far as I can discover), sont r\u00e9solues par la th\u00e9orie que je suis sur le point d\u2019exposer (are met … by the theory which I am about to explain).<\/p>\n

The subject of denoting is of very great importance, not only in logic and mathematics, but also in the theory of knowledge. For example, we know that the center 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<\/em><\/strong> with this point, which is only known to us by description<\/strong>. The distinction between acquaintance<\/em> and knowledge about<\/em> is the distinction between the things we have presentations of<\/strong>, and the things we only reach by means of denoting phrases<\/strong>. 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 center of mass. In perception we have acquaintance with 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<\/strong>, seeing that these are not directly perceived; hence what we know about them is obtained through denoting<\/strong>. All thinking has to start from acquaintance; but it succeeds in thinking about<\/em> many things with which we have no acquaintance.<\/p>\n

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<\/strong> and Meinong<\/strong>, showing why neither of them satisfies me; then I shall give the grounds in favor of my theory; and finally I shall briefly indicate the philosophical consequences of my theory.<\/p>\n

\n

Eh bien par rapport aux propri\u00e9t\u00e9s, la question s\u00e9rieuse c\u2019est la question du \u00ab il existe \u00bb. Le sens est au niveau de la description, et disons en termes logiques de la fonction, le r\u00e9el est au niveau du \u00ab il existe \u00bb.<\/p>\n

C\u2019est l\u00e0 qu\u2019on introduit le x<\/em>, la variable.<\/p>\n

Le Sinn<\/em>, la description, se r\u00e9sume logiquement dans la lettre grand F de la fonction.  Et on d\u00e9crit, et on ajoute des attributs, etc. Et on attribue tout \u00e7a  \u00e0 \u00ab on ne sait quoi \u00bb dont on marque la place en \u00e9crivant x<\/em> entre parenth\u00e8ses : (x)<\/em>.  On dit que c\u2019est une variable<\/strong>, pas pour dire que \u00e7a  varie, pour dire qu\u2019on ne sait pas s\u2019il y a quelque chose de r\u00e9el<\/strong> qui peut venir \u00e0 remplacer ce trou.<\/p>\n

Et ce qui est la constante, <\/strong>c\u2019est le quelque chose qui peut remplir ce trou et qui dans tous les cas ne sera que Un signifiant, ce ne sera qu\u2019un exemplaire du signifiant Un.<\/p>\n

Mais, je ne renie pas le terme de variable, simplement, au fond pour la constante<\/strong> j\u2019utiliserais l\u2019adjectif  que j\u2019emprunte au logicien Kripke<\/strong>, dans sa th\u00e9orie des noms propres, je dirais que c\u2019est le rigide. A c\u00f4t\u00e9 de la variable, il y a le rigide qui lui est l\u2019index de l\u2019existence. <\/strong>Et, dans tous les cas, quel que soit le nom dont on le d\u00e9core, la nature de ce qui existe est d\u2019une nature si je puis dire signifiante.<\/p>\n

C\u2019est dans ce contexte que s\u2019inscrit le \u00ab Il n\u2019y pas le rapport sexuel \u00bb, cri\u00e9 par Lacan. Il n\u2019y a pas le rapport sexuel au niveau du r\u00e9el. Tout d\u2019abord parce qu\u2019au niveau du r\u00e9el, c\u2019est le Un qui r\u00e8gne, pas le deux. Le rapport sexuel ne fleurit qu\u2019au niveau du sens et Dieu sait si ses significations sont \u00e9quivoques et variables.<\/p>\n

Le \u00ab il existe \u00bb  dans la psychanalyse, Freud l\u2019a appel\u00e9 la fixation. <\/strong>L\u2019a rep\u00e9r\u00e9 comme la fixation.<\/p>\n

JAM, cours 7, \u00ab\u00a0Aujourd’hui on va s’amuser\u00a0\u00bb<\/a><\/p>\n<\/div>\n

My theory, briefly, is as follows. I take the notion of the variable<\/em><\/strong> as fundamental; I use \u00ab\u00a0C(x)\u00a0\u00bb<\/em> to mean a proposition in which x<\/em> is a constituent, where x,<\/em> the variable, is essentially and wholly undetermined<\/strong>. Then we can consider the two notions \u00ab\u00a0C(x)<\/em> is always<\/strong> true\u00a0\u00bb and \u00ab\u00a0C(x)<\/em> is sometimes<\/strong> true\u00a0\u00bb. Then everything<\/em><\/strong> and nothing<\/em><\/strong> and something<\/em><\/strong> (which are the most primitive of denoting phrases) are to be interpreted as follows:<\/p>\n

C<\/em>(everything) means \u00ab\u00a0C(x)<\/em> is always true<\/span>\u00ab\u00a0<\/strong>;
\n[C(x) est toujours vrai<\/em>
\nou  \u00ab\u00a0C(x) est vrai\u00a0\u00bb est toujours vrai
\n<\/em>= pour tout x C(x)<\/em>]<\/p>\n

C<\/em>(nothing) means \u00a0\u00bb ‘C(x)<\/em> is false’ is always true<\/span>\u00ab\u00a0<\/strong>;
\n[\u00ab\u00a0C(x) est faux\u00a0\u00bb est toujours vrai
\n= il n’existe pas de x tel que C(x)<\/em>]<\/p>\n

C<\/em>(something) means \u00ab\u00a0It is false that ‘C(x)<\/em> is false'\u00a0\u00bb is always true<\/span>.\u00a0\u00bb<\/strong>
\n[Il est faux que la fonction \u00ab\u00a0C(x) est fausse\u00a0\u00bb soit toujours vraie<\/em>]<\/p>\n

Here the notion \u00ab\u00a0C(x)<\/em> is always true\u00a0\u00bb is taken as ultimate and indefinable, and the others are defined by means of it. Everything,<\/em> nothing,<\/em> and something<\/em> are not assumed to have any meaning in isolation, but a meaning is assigned to every<\/em><\/strong> 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,<\/strong> 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.<\/p>\n

Suppose now we wish to interpret the proposition, \u00ab\u00a0I met a man\u00a0\u00bb. 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:<\/p>\n

\u00a0\u00bb ‘I met x,<\/em> and x<\/em> is human’ is not always false<\/strong>\u00ab\u00a0.<\/p>\n

[voir plus haut: <\/em><\/p>\n

C(<\/em>something) means \u00ab\u00a0It is false that ‘C(x) is false'\u00a0\u00bb is always true.\u00a0\u00bb<\/em> =Il est faux que la fonction \u00ab\u00a0C(x) est fausse\u00a0\u00bb soit toujours vraie <\/em><\/p>\n

–> a man = <\/em>something –> <\/em>sometimes (=not always)]<\/em><\/p><\/blockquote>\n

Generally, defining the class of men as the class of objects having the predicate human,<\/em> we say that:<\/p>\n

\u00ab\u00a0C<\/em>(a man) means \u00a0\u00bb ‘C(x)<\/em> and x<\/em> is human’ is not always false<\/strong>\u00ab\u00a0.<\/p><\/blockquote>\n

\n

La trouvaille de Russell, c\u2019est de diviser le dit. <\/strong>D\u2019un c\u00f4t\u00e9 il y a la description, ce qu\u2019il appelle la description d\u00e9finie \u00e0 Sinn<\/em> de Frege: \u00ab le roi de France est chauve \u00bb. \u00c7a laisse ouvert la question de savoir s\u2019il y a ou non un roi de France. Et \u00e7a dit que la question du \u00ab il y a \u00bb doit toujours \u00eatre pos\u00e9e, quelque soit la splendeur de la description. La question du \u00ab il existe. \u00bb D\u2019un c\u00f4t\u00e9, nous avons une liste de propri\u00e9t\u00e9s, et  il y a une d\u00e9nivellation par rapport \u00e0 la question qu\u2019il faut faire surgir : est-il vrai qu\u2019il existe quelque chose qui r\u00e9ponde \u00e0 cette description ou non ? Puisqu\u2019on parfaitement d\u00e9crire quelque chose qui n\u2019existe pas. Et donc on doit toujours faire surgir la question du  \u00ab il existe quelque chose ou quelqu\u2019un qui a ces propri\u00e9t\u00e9s \u00bb.<\/p>\n<\/div>\n

This leaves \u00ab\u00a0a<\/strong> man\u00a0\u00bb, by itself, wholly destitute of meaning, but gives a meaning to every proposition in whose verbal expression \u00ab\u00a0a man\u00a0\u00bb occurs.<\/p>\n

Consider next the proposition \u00ab\u00a0all<\/strong> men are mortal\u00a0\u00bb. This proposition is really hypothetical<\/strong> and states that if<\/em><\/strong> anything is a man, it is mortal. That is, it states that if x<\/em> is a man, x<\/em> is mortal, whatever x<\/em> may be. Hence, substituting `x<\/em> is human’ for `x<\/em> is a man’, we find:<\/p>\n

\u00ab\u00a0All men are mortal\u00a0\u00bb means \u00a0\u00bb ‘If x<\/em> is human, x<\/em> is mortal’ is always true<\/strong>.\u00a0\u00bb<\/p><\/blockquote>\n

This is what is expressed in symbolic logic by saying that ‘all men are mortal’ means ‘ ‘x<\/em> is human’ implies ‘x<\/em> is mortal’ for all values of x’<\/em><\/strong>. More generally, we say:<\/p>\n

`C<\/em>(all men)’ means ` \u00ab\u00a0If x<\/em> is human, then C(x)<\/em> is true\u00a0\u00bb is always true’<\/strong>.<\/p><\/blockquote>\n

Similarly<\/p>\n

`C<\/em>(no men)’ means ` \u00ab\u00a0If x<\/em> is human, then C(x)<\/em> is false\u00a0\u00bb is always true’.
\n`C<\/em>(some men)’ will mean the same as `C<\/em>(a man)’, and
\n`C<\/em>(a man)’ means `It is false that \u00ab\u00a0C(x)<\/em> and x<\/em> is human\u00a0\u00bb is always false’.
\n`C<\/em>(every man)’ will mean the same as `C<\/em>(all men)’.<\/p><\/blockquote>\n

It remains to interpret phrases containing the.<\/em><\/strong> These are by far the most interesting and difficult of denoting phrases. Take as an instance \u00ab\u00a0the father of Charles II was executed\u00a0\u00bb. This asserts that there was an x<\/em> who was the father of Charles II and was executed. Now the,<\/em> when it is strictly used, involves uniqueness<\/strong>; we do, it is true, speak of \u00ab\u00a0the<\/em> son of So-and-so\u00a0\u00bb even when So-and-so has several sons, but it would be more correct to say \u00ab\u00a0a<\/em> son of So-and-so\u00a0\u00bb. Thus for our purposes we take the<\/em> as involving uniqueness<\/strong>. Thus when we say \u00ab\u00a0x<\/em> was the<\/em> father of Charles II\u00a0\u00bb we not only assert that x<\/em> 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<\/strong>, is expressed by \u00ab\u00a0x<\/em> begat Charles II\u00a0\u00bb. To get an equivalent of \u00ab\u00a0x<\/em> was the father of Charles II\u00a0\u00bb, we must add \u00ab\u00a0If y<\/em> is other than x,<\/em> y<\/em> did not beget Charles II\u00a0\u00bb, or, what is equivalent, \u00ab\u00a0If y<\/em> begat Charles II, y<\/em> is identical with x<\/em>\u00ab\u00a0. Hence \u00ab\u00a0x<\/em> is the father of Charles II\u00a0\u00bb becomes: \u00ab\u00a0x<\/em> begat Charles II; and ‘If y<\/em> begat Charles II, y<\/em> is identical with x<\/em>‘ is always true of y<\/em>\u00ab\u00a0.<\/p>\n

Thus \u00ab\u00a0the father of Charles II was executed\u00a0\u00bb becomes: \u00ab\u00a0It is not always false of x<\/em> that x<\/em> begat Charles II and that x<\/em> was executed and that ‘if y<\/em> begat Charles II, y<\/em> is identical with x’<\/em> is always true of y\u00a0\u00bb<\/em>.<\/p><\/blockquote>\n

This may seem a somewhat incredible interpretation; but I am not at present giving reasons, I am merely stating<\/em> the theory.<\/p>\n

To interpret \u00ab\u00a0C<\/em>(the father of Charles II)\u00a0\u00bb, where C<\/em> stands for any statement about him, we have only to substitute C(x)<\/em> for \u00ab\u00a0x<\/em> was executed\u00a0\u00bb in the above. Observe that, according to the above interpretation, whatever statement C<\/em> may be, \u00ab\u00a0C<\/em>(the father of Charles II)\u00a0\u00bbimplies:<\/p>\n

`It is not always false of x<\/em> that \u00ab\u00a0if y<\/em> begat Charles II, y<\/em> is identical with x<\/em>\u00a0\u00bb is always true of y<\/em>‘,<\/p><\/blockquote>\n

which is what is expressed in common language by \u00ab\u00a0Charles II had one father and no more\u00a0\u00bb. Consequently if this condition fails, every<\/em> proposition of the form \u00ab\u00a0C<\/em>(the father of Charles II)\u00a0\u00bb is false. Thus e.g. every proposition of the form \u00ab\u00a0C<\/em>(the present King of France)\u00a0\u00bb 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.<\/p>\n

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.<\/p>\n

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<\/strong>. This theory regards any grammatically correct denoting phrase as standing for an <\/strong>object<\/strong>.<\/em> Thus \u00ab\u00a0the present King of France\u00a0\u00bb, \u00ab\u00a0the round square\u00a0\u00bb, etc., are supposed to be genuine objects. It is admitted that such objects do not subsist,<\/em> 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<\/strong>. It is contended, for example, that the existent 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.<\/p>\n

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<\/em> and the denotation<\/em>. Thus \u00ab\u00a0the center of mass of the solar system at the beginning of the twentieth century\u00a0\u00bb is highly complex in meaning,<\/em> but its denotation<\/em> is a certain point, which is simple. The solar system, the twentieth century, etc., are constituents of the meaning<\/em>; but the denotation<\/em> has no constituents at all . One advantage of this distinction is that it shows why it is often worth while to assert identity. If we say \u00ab\u00a0Scott is the author of Waverley,\u00a0\u00bb 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<\/em> a meaning and denote<\/em> a denotation, concerns the cases in which the denotation appears to be absent<\/strong>. If we say \u00ab\u00a0the King of England is bald\u00a0\u00bb, that is, it would seem, not a statement about the complex meaning<\/em> \u00ab\u00a0the King of England\u00a0\u00bb, but about the actual man denoted by the meaning. But now consider \u00ab\u00a0the king of France is bald<\/strong>\u00ab\u00a0. By parity of form, this also ought to be about the denotation of the phrase \u00ab\u00a0the King of France\u00a0\u00bb. But this phrase, though it has a meaning<\/em> provided \u00ab\u00a0the King of England\u00a0\u00bb has a meaning, has certainly no denotation<\/strong>, at least in any obvious sense. Hence one would suppose that \u00ab\u00a0the King of France is bald\u00a0\u00bb ought to be nonsense; but it is not nonsense, since it is plainly false<\/strong>. Or again consider such a proposition as the following: \u00ab\u00a0If u<\/em> is a class which has only one member, then that one member is a member of u\u00a0\u00bb<\/em>, or as we may state it, \u00ab\u00a0If u<\/em> is a unit class, the<\/em> u<\/em> is a u<\/em>\u00ab\u00a0. This proposition ought to be always<\/em> true, since the conclusion is true whenever the hypothesis is true. But \u00ab\u00a0the u\u00a0\u00bb<\/em> is a denoting phrase, and it is the denotation, not the meaning, that is said to be a u<\/em>. Now is u<\/em> is not<\/em> a unit class, \u00ab\u00a0the u<\/em>\u00a0\u00bb seems to denote nothing; hence our proposition would seem to become nonsense as soon as u<\/em> is not a unit class.<\/p>\n

Now it is plain that such propositions do not<\/em> become nonsense merely because their hypotheses are false. The King in The Tempest<\/cite> might say, \u00ab\u00a0If Ferdinand is not drowned, Ferdinand is my only son\u00a0\u00bb. Now \u00ab\u00a0my only son\u00a0\u00bb‘ is a denoting phrase, which, on the face of it, has a denotation when, and only when, I have exactly one son<\/strong>. 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<\/strong>. Thus \u00ab\u00a0the King of France\u00a0\u00bb, is to denote the null-class<\/strong>; \u00ab\u00a0the only son of Mr. So-and-so\u00a0\u00bb (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<\/strong>, 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<\/strong> both on the assumption that there really is a denotation and on the assumption that there really is none.<\/p>\n

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<\/strong>, 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.<\/p>\n

(1) If a<\/em> is identical with b,<\/em> 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<\/cite>; and in fact Scott was<\/em> the author of Waverley.<\/cite> Hence we may substitute Scott<\/em> for the author of `Waverley’,<\/em> 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.<\/p>\n

(2) By the law of the excluded middle, either `A<\/em> is B<\/em>‘ or `A<\/em> is not B<\/em>‘ 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.<\/p>\n

(3) Consider the proposition `A<\/em> differs from B<\/em>‘. If this is true, there is a difference between A<\/em> and B,<\/em> which fact may be expressed in the form `the difference between A<\/em> and B<\/em> subsists’. But if it is false that A<\/em> differs from B,<\/em> then there is no difference between A<\/em> and B,<\/em> which fact may be expressed in the form `the difference between A<\/em> and B<\/em> 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, 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<\/em> and B<\/em> do not differ, to suppose either that there is, or that there is not, such an object as `the difference between A<\/em> and B<\/em>‘ seems equally impossible.<\/p>\n

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.<\/p>\n

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

The center of mass of the solar system is a point, not a denoting complex;
\n`The center of mass of the solar system’ is a denoting complex, not a point.<\/p><\/blockquote>\n

Or again,<\/p>\n

The first line of Gray’s Elegy states a proposition.
\n`The first line of Gray’s Elegy’ does not state a proposition.<\/p><\/blockquote>\n

Thus taking any denoting phrase, say C,<\/em> we wish to consider the relation between C<\/em> and `C<\/em>‘, where the difference of the two is of the kind exemplified in the above two instances.<\/p>\n

We say, to begin with, that when C<\/em> occurs it is the denotation<\/em> that we are speaking about; but when `C<\/em>‘ occurs, it is the meaning.<\/em> 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<\/em> preserving the connexion of meaning and denotation and<\/em> 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.<\/p>\n

The one phrase C<\/em> was to have both meaning and denotation. But if we speak of `the meaning of C<\/em>‘, 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 \u00ab\u00a0The curfew tolls the knell of parting day\u00a0\u00bb,’ and is not the same as `The meaning of \u00ab\u00a0the first line of Gray’s Elegy\u00a0\u00bb.’ Thus in order to get the meaning we want, we must speak not of `the meaning of C<\/em>‘, but `the meaning of \u00ab\u00a0C<\/em>\u00ab\u00a0,’ which is the same as `C<\/em>‘ by itself. Similarly `the denotation of C<\/em>‘ 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<\/em>‘ be `the denoting complex occurring in the second of the above instances’. Then<\/p>\n

C<\/em> = `the first line of Gray’s Elegy’, and<\/p><\/blockquote>\n

the denotation of C<\/em> = The curfew tolls the knell of parting day. But what we meant <\/em>to have as the denotation was `the first line of Gray’s Elegy’. Thus we have failed to get what we wanted.<\/p>\n

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<\/em>‘, 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<\/em> both meaning and denotation. The right phrase, on the view in question, is that some meanings have denotations.<\/p>\n

But this only makes our difficulty in speaking of meanings more evident. For suppose that C<\/em> is our complex; then we are to say that C<\/em> is<\/em> the meaning of the complex. Nevertheless, whenever C<\/em> 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<\/em> itself, i.e. to make a proposition about the meaning, our subject must not be C,<\/em> but something which denotes C.<\/em> Thus `C<\/em>‘, 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<\/em> must not be a constituent of this complex (as it is of `the meaning of C<\/em>‘); for if C<\/em> 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.<\/p>\n

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

That the meaning is relevant when a denoting phrase occurs in a proposition is formally proved by the puzzle about the author of Waverley.<\/cite> The proposition `Scott was the author of Waverley<\/cite>‘ 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<\/cite>‘ 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.<\/p>\n

It remains to show how all the puzzles we have been considering are solved by the theory explained at the beginning of this article.<\/p>\n

According to the view which I advocate, a denoting phrase is essentially part<\/em> of a sentence, and does not, like most single words, have any significance on its own account. If I say \u00ab\u00a0Scott was a man\u00a0\u00bb, that is a statement of the form \u00ab\u00a0x<\/em> was a man\u00a0\u00bb, and it has \u00ab\u00a0Scott\u00a0\u00bb for its subject. But if I say \u00ab\u00a0the author of Waverley<\/cite> was a man\u00a0\u00bb, that is not a statement of the form \u00ab\u00a0x<\/em> was a man\u00a0\u00bb, and does not have \u00ab\u00a0the author of Waverley\u00a0\u00bb<\/cite> for its subject. Abbreviating the statement made at the beginning of this article, we may put, in place of \u00ab\u00a0the author of Waverley<\/cite> was a man\u00a0\u00bb, the following: \u00ab\u00a0One and only one entity wrote Waverley,<\/cite> and that one was a man<\/strong>\u00ab\u00a0. (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<\/cite> had property phi,<\/em> what we wish to say is equivalent to `One and only one entity wrote Waverley,<\/cite> and that one had the property phi<\/em>‘.<\/p>\n

The explanation of denotation<\/em> is now as follows. Every proposition in which `the author of Waverley<\/cite>‘ occurs being explained as above, the proposition `Scott was the author of Waverley<\/cite>‘ (i.e. `Scott was identical with the author of Waverley<\/cite>‘) becomes `One and only one entity wrote Waverley,<\/cite> and Scott was identical with that one’; or, reverting to the wholly explicit form: `It is not always false of x<\/em> that x<\/em> wrote Waverley,<\/cite> that it is always true of y<\/em> that if y<\/em> wrote Waverley<\/cite> y<\/em> is identical with x,<\/em> and that Scott is identical with x<\/em>.’ Thus if `C<\/em>‘ is a denoting phrase, it may happen that there is one entity x<\/em> (there cannot be more than one) for which the proposition `x<\/em> is identical with C<\/em>‘ is true, this proposition being interpreted as above. We may then say that the entity x<\/em> is the denotation of the phrase `C<\/em>‘. Thus Scott is the denotation of `the author of Waverley<\/cite>‘. The `C<\/em>‘ in inverted commas will be merely the phrase,<\/em> not anything that can be called the meaning.<\/em> The phrase per se<\/em> 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.<\/p>\n

The puzzle about George IV’s curiosity is now seen to have a very simple solution. The proposition \u00ab\u00a0Scott was the author of Waverley\u00a0\u00bb<\/cite>, which was written out in its unabbreviated form in the preceding paragraph, does not contain any constituent \u00ab\u00a0the author of Waverley\u00a0\u00bb<\/cite> for which we could substitute \u00ab\u00a0Scott\u00a0\u00bb. This does not interfere with the truth of inferences resulting from making what is verbally<\/em> the substitution of \u00ab\u00a0Scott\u00a0\u00bb for \u00ab\u00a0the author of Waverley\u00a0\u00bb<\/cite>, so long as `\u00a0\u00bbhe author of Waverley\u00a0\u00bb<\/cite> has what I call a primary<\/em> occurrence in the proposition considered. The difference of primary and secondary occurrences of denoting phrases is as follows:<\/p>\n

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,<\/cite> when we say `George IV wished to know whether Scott was the author of Waverley<\/cite><\/strong>‘ we normally mean `George IV wished to know whether one and only one man wrote Waverley<\/cite> and Scott was that man’; but we may<\/em> also mean: `One and only one man wrote Waverley,<\/cite> and George IV wished to know whether Scott was that man’. In the latter, `the author of Waverley<\/cite>‘ has a primary<\/em> occurrence; in the former, a secondary.<\/em> The latter might be expressed by `George IV wished to know, concerning the man who in fact wrote Waverley,<\/cite> 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<\/em> occurrence of a denoting phrase may be defined as one in which the phrase occurs in a proposition p<\/em> which is a mere constituent of the proposition we are considering, and the substitution for the denoting phrase is to be effected in p,<\/em> 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.<\/p>\n

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<\/em>‘ is a denoting phrase, say `the term having the property F<\/em>‘, then<\/p>\n

`C<\/em> has property phi<\/em>‘ means `one and only one term has the property F,<\/em> and that one has the property phi<\/em>‘.<\/p><\/blockquote>\n

If now the property F<\/em> belongs to no terms, or to several, it follows that `C<\/em> has property phi<\/em>‘ is false for all<\/em> values of phi.<\/em>Thus `the present King of France is not bald’ is false if it means<\/p>\n

`There is an entity which is now King of France and is not bald’,<\/p><\/blockquote>\n

but is true if it means<\/p>\n

`It is false that there is an entity which is now King of France and is bald’.<\/p><\/blockquote>\n

That is, `the King of France is not bald’ is false if the occurrence of `the King of France’ is primary,<\/em> and true if it is secondary.<\/em>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.<\/p>\n

We can now see also how to deny that there is such an object as the difference between A<\/em> and B<\/em> in the case when A<\/em> and B<\/em> do not differ. If A<\/em> and B<\/em> do differ, there is only and only one entity x<\/em> such that `x<\/em> is the difference between A<\/em> and B<\/em>‘ is a true proposition; if A<\/em> and B<\/em> do not differ, there is no such entity x.<\/em> Thus according to the meaning of denotation lately explained, `the difference between A<\/em> and B<\/em>‘ has a denotation when A<\/em> and B<\/em> differ, but not otherwise. This difference applies to true and false propositions generally. If `a R b<\/em>‘ stands for `a<\/em> has the relation R<\/em> to b<\/em>‘, then when a R b<\/em> is true, there is such an entity as the relation R<\/em> between a<\/em> and b<\/em>; when a R b<\/em> 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.<\/p>\n

The whole realm of non-entities<\/strong>, such as \u00ab\u00a0the round square\u00a0\u00bb, \u00ab\u00a0the even prime other than 2\u00a0\u00bb, \u00ab\u00a0Apollo\u00a0\u00bb, \u00ab\u00a0Hamlet\u00a0\u00bb, etc., can now be satisfactorily dealt with. All these are denoting phrases which do not denote anything.<\/strong> A proposition about Apollo means what we get by substituting what the classical dictionary tells us is meant by Apollo, say \u00ab\u00a0the sun-god\u00a0\u00bb. All propositions in which Apollo occurs are to be interpreted by the above rules for denoting phrases. If \u00ab\u00a0Apollo\u00a0\u00bb has a primary occurrence, the proposition containing the occurrence is false; if the occurrence is secondary, the proposition may be true. So again \u00ab\u00a0the round square is round\u00a0\u00bb means \u00ab\u00a0there is one and only one entity x<\/em> which is round and square, and that entity is round\u00a0\u00bb, which is a false proposition, not, as Meinong maintains, a true one. \u00ab\u00a0The most perfect Being has all perfections; existence is a perfection; therefore the most perfect Being exists\u00a0\u00bb becomes:<\/p>\n

\u00ab\u00a0There is one and only one entity x<\/em> which is most perfect; that one has all perfections; existence is a perfection; therefore that one exists.\u00a0\u00bb<\/p><\/blockquote>\n

As a proof, this fails for want of a proof of the premiss \u00ab\u00a0there is one and only one entity x<\/em> which is most perfect\u00a0\u00bb.<\/p>\n

Mr. MacColl<\/strong> (Mind,<\/cite> N.S., No. 54, and again No. 55, page 401) regards individuals as of two sorts, real and unreal<\/strong>; hence he defines the null-class<\/strong> as the class consisting of all unreal individuals<\/strong>. This assumes that such phrases as \u00ab\u00a0the present King of France<\/strong>\u00ab\u00a0, which do not denote a real individual, do, nevertheless, denote an individual, but an unreal one<\/strong>. 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<\/strong>; so that the null-class is the class containing no members<\/strong>, not the class containing as members all unreal individuals.<\/p>\n

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<\/em> means the number which, added to n,<\/em> gives m<\/em>‘. Thus m-n<\/em> is defined as meaning the same as a certain denoting phrase; but we agreed that denoting phrases have no meaning in isolation<\/strong>. Thus what the definition really ought to be is: `Any proposition containing m-n<\/em> is to mean the proposition which results from substituting for \u00ab\u00a0m-n<\/em>\u00a0\u00bb \u00ab\u00a0the number which, added to n,<\/em> gives m<\/em>\u00ab\u00a0.’ 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<\/em> and n<\/em> are such that there is one and only one number x<\/em> which, added to n,<\/em> gives m,<\/em> there is a number x<\/em> which can be substituted for m-n<\/em> in any proposition contain m-n<\/em> without altering the truth or falsehood of the proposition. But in other cases, all propositions in which `m-n<\/em>‘ has a primary occurrence are false.<\/p>\n

The usefulness of identity<\/em> is explained by the above theory. No one outside of a logic-book ever wishes to say `x<\/em> is x<\/em>‘, and yet assertions of identity are often made in such forms as `Scott was the author of Waverley<\/cite>‘ 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,<\/cite> or that thou are identical with another term, the man. The shortest statement of `Scott is the author of Waverley<\/cite>‘ seems to be `Scott wrote Waverley<\/cite>; and it is always true of y<\/em> that if y<\/em> wrote Waverley,<\/cite> y<\/em> is identical with Scott’. It is in this way that identity enters into `Scott is the author of Waverley<\/cite>‘; and it is owing to such uses that identity is worth affirming.<\/p>\n

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<\/em> with them, but we know them as what has such and such properties. Hence, although we can form propositional functions C(x)<\/em> 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<\/em> has such and such properties’, where A is<\/em> 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.<\/p>\n

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.<\/p>\n

\n

Mind,<\/cite> new series, 14<\/strong> (1905): 479–493; text from Logic and Knowledge,<\/cite> ed. Robert Marsh, 1956.<\/p>\n","protected":false},"excerpt":{"rendered":"

Comme j’entame \u00e0 la lecture du s\u00e9minaire …ou pire, j’y croise le terme de \u00ab\u00a0d\u00e9notation\u00a0\u00bb qu’il me semble que Miller a lui-m\u00eame employ\u00e9 cette ann\u00e9e. Une recherche rapide sur le site me ram\u00e8ne au cours du 16 mars, o\u00f9 effectivement … Continuer la lecture →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"aside","meta":{"spay_email":"","jetpack_publicize_message":"Sur la d\u00e9notation (de Bertrand Russell):","jetpack_is_tweetstorm":false},"categories":[238,6],"tags":[31,44,71,128,162,170,202],"jetpack_featured_media_url":"","jetpack_publicize_connections":[],"jetpack_shortlink":"https:\/\/wp.me\/p2zPSJ-CC","jetpack_sharing_enabled":true,"jetpack-related-posts":[{"id":937,"url":"https:\/\/disparates.org\/lun\/2011\/03\/jacques-alain-miller-notes-du-cours-du-16-mars-2011-partie-i-alors-faut-que-jvous-prenne-par-la-main\/","url_meta":{"origin":2394,"position":0},"title":"VII. L'existentialisme de Lacan est un logicisme \/\/","date":"16 mars 2011","format":false,"excerpt":"Bon. Aujourd'hui on va s'amuser. Il s'agit, pour moi de vous faire comprendre quelque chose, comprendre l\u00e0 o\u00f9 on prend plaisir. Moi, \u00e7a m'amuse. J'esp\u00e8re qu'il en sera de m\u00eame pour vous. \u00c7a ne va de soi, parce que cette ann\u00e9e plusieurs me font part du fait\u00a0 qu'ils ne sont\u2026","rel":"","context":"Dans "L'\u00eatre et l'Un"","img":{"alt_text":"","src":"https:\/\/i1.wp.com\/disparates.org\/lun\/wp-content\/uploads\/2011\/05\/mas_dazil01.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1220,"url":"https:\/\/disparates.org\/lun\/2011\/03\/8-cours-jam-23-mars-2011\/","url_meta":{"origin":2394,"position":1},"title":"VIII. \u2013 23 mars 2011","date":"25 mars 2011","format":false,"excerpt":"D\u00e9nivellation de l\u2019\u00eatre et de l\u2019existence J\u2019ai eu depuis la derni\u00e8re fois quelques t\u00e9moignages, trop nombreux pour que je puisse y r\u00e9pondre et je m'en excuse, t\u00e9moignant de ce que un pas a \u00e9t\u00e9 franchi la derni\u00e8re fois dans - pour ne pas dire \"la compr\u00e9hension\" - ce dont il\u2026","rel":"","context":"Dans "L'\u00eatre et l'Un"","img":{"alt_text":"","src":"https:\/\/i0.wp.com\/disparates.org\/lun\/wp-content\/uploads\/2011\/03\/tigre03.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":2238,"url":"https:\/\/disparates.org\/lun\/2011\/08\/lire-un-symptome\/","url_meta":{"origin":2394,"position":2},"title":"Lire un sympt\u00f4me","date":"1 ao\u00fbt 2011","format":"quote","excerpt":"Je soutiendrais volontiers que le bien dire dans la psychanalyse n'est rien sans le savoir lire, que le bien dire propre \u00e0 la psychanalyse se fonde sur le savoir lire. Si l'on s'en tient au bien dire, on n\u2019atteint que la moiti\u00e9 de ce dont il s'agit. Bien dire et\u2026","rel":"","context":"Dans "Compl\u00e9ments de lecture"","img":{"alt_text":"","src":"https:\/\/i1.wp.com\/disparates.org\/lun\/wp-content\/uploads\/2011\/08\/photo_jam2.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":874,"url":"https:\/\/disparates.org\/lun\/2011\/03\/encore-p-85-86\/","url_meta":{"origin":2394,"position":3},"title":"Lacan, Encore, \"Le savoir et la v\u00e9rit\u00e9\" (10 avril 1973), Extrait, p. 85, 86","date":"11 mars 2011","format":"aside","excerpt":"Cet extrait de Encore vient ici en compl\u00e9ment de mes notes du 6\u00b0 cours de Miller , \"quand Lacan baisse les bras s'agissant de l'objet a\" : \"Autre chose encore nous ligote quant \u00e0 ce qu'il en est de la v\u00e9rit\u00e9, c'est que la jouissance est une limite. Cela tient\u2026","rel":"","context":"Dans "Compl\u00e9ments de lecture"","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2317,"url":"https:\/\/disparates.org\/lun\/2011\/08\/les-propheties-de-lacan-par-jacques-alain-miller\/","url_meta":{"origin":2394,"position":4},"title":"Les proph\u00e9ties de Lacan, par Jacques-Alain Miller","date":"18 ao\u00fbt 2011","format":"aside","excerpt":"Article paru dans Le Point du 18 ao\u00fbt 2011. Propos recueillis par Christophe Labb\u00e9 et Olivia Recasens \u00c9clairant. Ce que Lacan aurait dit sur notre \u00e9poque, par son gendre et l\u00e9gataire intellectuel, le psychanalyste Jacques-Alain Miller.","rel":"","context":"Dans "Compl\u00e9ments de lecture"","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":844,"url":"https:\/\/disparates.org\/lun\/2011\/03\/la-science-et-la-verite-ecrits-p-870-871\/","url_meta":{"origin":2394,"position":5},"title":"Lacan, \"La science et la v\u00e9rit\u00e9\", Ecrits, p. 870-871","date":"11 mars 2011","format":"aside","excerpt":"Cet extrait des \u00c9crits vient en compl\u00e9ment de lecture de mes notes du cours 6 - \"Comment m\u00e9conna\u00eetre que l\u00e0 il \u00e9voque bien la 'Chose qui parle', mais cette fois c'est pour la r\u00e9cuser.\" \"Vous voyez le programme qui ici se dessine. Il n'est pas pr\u00e8s d'\u00eatre couvert. Je le\u2026","rel":"","context":"Dans "Compl\u00e9ments de lecture"","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/disparates.org\/lun\/wp-json\/wp\/v2\/posts\/2394"}],"collection":[{"href":"https:\/\/disparates.org\/lun\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/disparates.org\/lun\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/disparates.org\/lun\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/disparates.org\/lun\/wp-json\/wp\/v2\/comments?post=2394"}],"version-history":[{"count":1,"href":"https:\/\/disparates.org\/lun\/wp-json\/wp\/v2\/posts\/2394\/revisions"}],"predecessor-version":[{"id":3001,"href":"https:\/\/disparates.org\/lun\/wp-json\/wp\/v2\/posts\/2394\/revisions\/3001"}],"wp:attachment":[{"href":"https:\/\/disparates.org\/lun\/wp-json\/wp\/v2\/media?parent=2394"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/disparates.org\/lun\/wp-json\/wp\/v2\/categories?post=2394"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/disparates.org\/lun\/wp-json\/wp\/v2\/tags?post=2394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}