FASCICULES 1 ET 2
RENAISSANCE
REVUE TRIMESTRIELLE PUBLIEE PAR
L'ECOLE LIBRE DES HAUTES ETUDES
EXTRAIT
ALEXANDRE KOYRE
REFLEXIONS SUR LE MENSONGE
ee EN
NEW YORK, 1943
A. KOYRE, LE MENSONGE
RENAISSANCE
REVUE TRIMESTRIELLE
PUBLIEE EN LANGUE FRANQGAISE PAR
L’ECOLE LIBRE DES HAUTES ETUDES
REFLEXIONS SUR LE MENSONGE.
On n’a jamais
Directeur : Henrnr GREGOIRE
menti autant que de nos jours. Ni menti d’une ma-
niére aussi éhonté
/ a
On nous dira peut-€tre qu'il n’en est rien,
aussi vieux que le monde
; que le mensonge politique est né avec la cité elle-méme, ainsi
> . 5 - .
Comité de Rédaction: que, surabondamment, nous lenseigne Vhistoire;
INARD, GUSTAVE COHEN, ee i
JEAN BENOIT-LEVY, GILBERT CH R
GEO Vv LE VI-STRAUSS ACQUES
niveaux et établi des records quil sera bien difficile de dépasser.
AN WAHL.
AUL SCHRECKER, JE
OUIS RAPKINE, P
HENRI PEYRE, L
Tout cela est vrai, sans doute. Ou presque. I] est certain que
-cl entraine la possibilité du
mensonge et que — n’en déplaise A Porphyre — le mentir, beaucoup
RENAISSANCE
plus que le rire, est Je propre de l’homm
homme se définit par la parole, que celle
e. Il est certain également que
ée quatre fascicules de cent soixante ee le mensonge politique est de tous temps, que les régles et la technique
° V1 . . ae Ss F * 99 . “
publiera chaque ni ee annuel est de rei dollars de ce que jadis on appelait démagogie” et de nos jours, “propagande”
- TIX * 5 5 Nt eT. SP , ae . , . *I1- ,
environ. Le P t de quatre dollars cinquante cents a l'étra at Ont ete systematisées et codifiées il y a des milliers d’années;! et que
: e : ie ents.
ag ae" iy scicule : un dollar vingt-cinq Cc
Prix au fa
ent, aujourd’hui encore, du haut des
murs de Karnak et des rochers d’Ankara.
destinée @ la Revue doit étre adressée a
ce destinée
La correspondan
Il est incontestable que ’homme a toujours
k. |
’Ecole des Hautes Etudes, 21 West 12th Street, New Yor |
Eco
’ et de créer, par sa parole,
un monde dont il est seu] responsable et auteur. Ment
défense:
Copyright 1943 by aa
ECOLE LIBRE DES HAUTES ETUDES
s earch) ey, trouve déja dans
(New School for Social Res d’Aristote, une analyse
technique, de ja propa
1 aussi pour sa
le mensonge est une arme. L’arme préférée de l’inférieur et
96 RENAISSANCE
du faible? qui, en trompant l’adversaire s’affirme et se venge de lui®
Mais nous n’allons pas procéder ici a l’analyse phénoménologique
du mensonge, a |’étude de la place qu'il occupe dans la structure de
Vétre humain: ceci remplirait un volume. C’est au mensonge moderne,
et méme plus étroitement, au mensonge politique moderne surtout,
que nous voudrions consacrer quelques réflexions. Car. malgré les
critiques que l’on nous fera, et celles que nous nous faisons 4 nous-
mémes, nous restons convaincus que, dans ce domaine quo nihil
antiquius, ’époque actuelle, ou plus exactement, les régimes totali-
taires, ont puissamment innové.
L’innovation n’est pas totale, sans doute, et les régimes totalitaires
n’ont fait que pousser jusqu’au bout certaines tendances, certaines atti-
tudes, certaines techniques qui existaient bien avant eux. Mais rien
n’est entigrement nouveau dans le monde, tout a des sources, des ra-
cines, des germes; et tout phénoméne, toute notion, toute tendance,
poussés jusqu’au bout, salt@rent et se transforment en quelque chose
de sensiblement différent.
Nous maintenons donc qu’on n’a jamais menti autant que de nos
jours et qu’on n’a jamais menti aussi massivement et aussi totalement
gu’on le fait aujourd'hui.
* + *
On n’a jamais menti autant .. . en effet, jour par jour, heure par
heure, minute par minute, des flots de mensonges se déversent sur le
A. KOYRE, LE MENSONGE 97
volume. Cela se compre 25
sagen prend, du reste. Le mensonge moderne — c'est 1a
sa qualité distinctive ~— est fabriqué en masse et s’adresse 4 la masse
Or toute production de masse, toute production — toute production in-
tellectuelle surtout — destinée 4 la masse, est obligée d’abaisser ses
standards. Aussi, si rien n’est plus raffiné que la technique de la propa-
gande moderne, rien n’est pl :
7 est plus grossier que le contenu de ses assertions,
qui révélent un mépris absolu et total de la vérité. Et méme de la
simple vraisemblance. Mépris qui n’est égalé que par celui — qu'il
implique — des facultés mentales de ceux a qui elle s’adresse
Pe 4 ¥
On pourrait méme se demander — et I’on s'est demandé effective-
ment — si l'on avait encore le droit de parler ici de “mensonge”. En
effet, la notion de “mensonge” présuppose celle de la véracité, dont
elle est Yopposé et la négation, de méme que la notion du Fam pré-
suppose celle du vrai. Or, les philosophies officielles des régimes totali-
taires proclament unanimement que la conception de la vérité objec-
site une pour tous, n’a aucun sens; et que le critére de la “Vérité”
nest pas sa valeur universelle, mais sa conformité a l’esprit de la race
de la nation ou de la classe, son utilité raciale, nationale ou wide
siete as et poussant jusqu’au bout les théories biologistes, pragma-
a activistes, de la vérité, et consommant ainsi ce que I’on a trés
bien nommé “la trahison des clercs”, les philosophies officielles des ré-
gimes totalitaires nient la valeur propre de la pensée qui pour eux
: ? ?
monde. La parole, l’écrit, le journal, la radio . . . tout le progrés tech-
nique est mis au service du mensonge. L’homme moderne — 1a encore,
cest A homme totalitaire que nous pensons — baigne dans le men-
songe, respire le mensonge, est soumis au mensonge & tous les instants
de sa vie.*
Quant 4 la qualité — nous voulons parler de la qualité intellectu-
elle — du mensonge moderne, elle a évolué en sems inverse de son
2 En trompant son adversaire —ou son maitre —le plus faible s’avére “plus
fort” que celui-ci.
’ Tromper, c’est aussi humilier, ce qui explique le mensonge souvent gratuit
des femmes et des esclaves.
‘ Le régime totalitaire est essentiellement lié au mensonge. Aussi n’a-t-on
jamais autant menti en France que depuis le jour ol, inaugurant
vers un Ir
mensonge’’.
la marche
égime totalitaire, le Maréc al Pétain a proclamé: “Je hais le
,
nig 3 sei rapradeomagt phe et sep rt
, cest-a-dire, ce qui est, mais de
nous aider a le modifier, 4 le transformer en nous guidant vers ce qui
n'est pas. Or, pour cela, ainsi quon I’a reconnu depuis bien long-
temps, le mythe est souvent préférable a la science, et la thétorique
See
ui ° 4 , . .
qui sadresse aux passions, 4 la démonstration qui sadresse a J’intelli-
gence.
: Aussi dans leurs publications (méme dans celles qui se disent scien-
tiiques), dans leurs discours et, bien entendu, dans leur propagande
s Oe. e °
les représentants des régimes totalitaires s’embarrassent-ils trés peu de
la vérité objective. Plus forts que Dieu tout puissant lui-méme, ils
?
ee a
98 RENAISSANCE
transforment 4 leur guise le présent, et méme le passé.5 On pourrait
en conclure — et on I’a fait parfois — que les régimes totalitaires sont
au dela de la vérité et du mensonge.
Nous croyons, pour notre part, qu’il n’en est rien. La distinction entre
la vérité et le mensonge, limaginaire et le réel, reste bien valable a
l'intérieur méme des conceptions et des régimes totalitaires. C’est leur
place et leur réle seulement qui sont, en quelque sorte, intervertis: les
régime totalitaires sont fondés sur la primauté du mensonge.
% * *
La place du mensonge dans la vie humaine est bien curieuse. Les
codes de morale religieuse, du moins en ce qui concerne les grandes
religions universalistes, surtout celles qui sont issues du monothéisme
biblique, condamnent le mensonge d’une maniére rigoureuse et absolue.
Cela se comprend du reste: leur Dieu étant celui de la lumiére et de
létre, il en résulte nécessairement qu'il est aussi celui de la vérité.
Mentir, c’est-a-dire, dire ce qui n’est pas, déformer la vérité et voiler
létre, est donc un péché; et méme un péché trés grave, péché d’orgueil
et péché contre I’esprit, péché qui nous sépare de Dieu et nous oppose
a Dieu. La parole d’un juste, de méme que la parole divine, ne peut
et ne doit étre que celle de la vérité.
Les morales philosophiques, quelques cas de rigorisme extréme,
tels ceux de Kant et de Fichte, mis a part, sont, généralement parlant,
beaucoup plus indulgentes. Plus humaines. Intransigeantes en qui con-
cerne la forme positive et active du mensonge, suggestio falsi, elles le
sont beaucoup moins en qui concerne sa forme négative et passive:
suppressio veri. Elles savent que, selon le proverbe, “toute vérité n’est
pas bonne a dire”. Du moins pas toujours. Et pas 4 tout le monde.
Beaucoup plus que les morales 4 base purement religieuse, les
morales philosophiques tiennent compte du fait que le mensonge s’ex-
prime en paroles, et que toute parole® s'adresse 4 quelqu’un.”? On ne
° Il est intéressant d’étudier, de ce point de vue, l’enseignement historique des
régimes totalitaires, et ses variations. Les nouveaux manuels d’histoire des
écoles frangaises offriraient une ample moisson 4 la réflexion.
* Le terme “parole” est pris ici dans le sens le plus large d’expression et de
suggestion. I] est évident que l’on peut mentir sans ouvrir la bouche.
* Les morales religieuses font de la vérité une “eran envers Dieu et non
envers les hommes. Elles interdisent de mentir “devant Dieu” et non “aux
hommes”.
A. KOYRE, LE MENSONGE 99
ment pas “en }’air’. On ment — comme on dit, ou ne dit pas, la vérité —
a quelqu’un. Or, si la vérité est bien “la nourriture de lame”, elle est
sourtout celle des 4mes fortes.® Elle peut étre dangereuse aux autres.
Du moins a l’état pur. Elle peut méme les blesser. I] faut la leur doser,
la diluer, Vhabiller. En outre, il faut bien tenir compte des consé-
quences, de |’usage qu’en feront ceux a qui on la dira.
Il n’y a donc pas, généralement parlant, d’obligation morale de dire
la vérité a tout le monde. Et tout le monde n’a pas le droit de lexiger
de nous.®
Les régles de la morale sociale, de la morale réelle qui s'exprime
dans les moeurs et qui gouverne, en fait, nos actions, sont bien plus
laches encore que celle de la morale philosophique. Ces régles, générale-
ment parlant, condamnent le mensonge. Tout le monde sait qu'il est
“laid”?° de mentir. Mais cette condamnation est loin d’étre absolue.
Liinterdiction est loin d’étre totale. Il y a des cas ov le mensonge est
toléré, permis, et méme recommandé.
La encore I’analyse précise nous aménerait bien trop loin. Grosso
modo on peut constater que le mensonge est toléré tant qu'il ne nuit
pas au bon fonctionnement des relations sociales, tant quill ne “fait
de mal a personne”; il est permis tant qu’il ne déchire pas le lien social
qui unit le groupe, c'est 4 dire, tant qu'il s‘exerce non pas a l’intérieur
du groupe, du “nous”, mais en dehors de lui: on ne trompe pas les
“siens’; quant aux autres!2 . . . ma foi, ne sont-ils pas justement “les
autres”?
Le mensonge est une arme. II est donc licite de l’employer dans
la lutte. Il serait méme stupide de ne pas le faire. A condition toutefois
de ne l’employer que contre l’adversaire et de ne pas la tourner contre
les amis et alliés.
On peut donc, généralement parlant, mentir a l’adversaire, tromper
pe * P pe
* Cette considération est parfois présente méme dans les morales religieuses.
Du lait aux enfants, du vin aux adultes, dit Saint Paul.
* On doit la vérité 4 ceux qu’on estime, a ses pairs et a ses supérieurs. Inverse-
ment, le refus de la vérité implique manque d’estime, manque de respect.
* “Un gentleman ne ment pas”. La véracité est une vertu aristocratique, liée
a la notion de “l’honneur”. — Pour I’esclave, elle n’est pas une vertu, mais
un devoir, une obligation.
™ L’hypocrisie des formes conventionnelles du comportement social — urba-
nité, politesse, etc., n’est pas “mensonge”.
* Les “siens” ont droit a la vérité; mais non les “autres”.
100 RENAISSANCE
l’ennemi. I] y a peu de sociétés qui, tels les Maoris, soient chevaleres-
ques au point de s‘interdire les ruses de guerre. I] y en a encore moins
qui, tels les Quakers, et les Wahabites, soient religieuses au point
de s'interdire tout mensonge envers l'autre, l’étranger, |’adversaire.
Presque partout l’on admet que la déception est permise dans la guerre.
Le mensonge n’est pas, généralement parlant, recommandé dans les
relations pacifiques. Pourtant (l’étranger étant un ennemi potentiel ),
la véracité n’a jamais été considérée comme la qualité maitresse des
diplomates.
Le mensonge est, plus ou moins, admis dans le commerce: la
encore les moeurs nous imposent des limites qui ont tendance a devenir
de plus en plus étroites.1* Toutefois les moeurs commerciales les plus
rigides tolérent sans broncher le mensonge avoué de la réclame.
Le mensonge reste donc toléré et admis. Mais justement . . . il
n’est que toléré et admis. Dans certains cas. I] reste exception, comme
la guerre, lors de laquelle, seule, il devient juste et bon d’en user.
Mais si la guerre, d’état exceptionnel, épisodique, passager, devenait
un état perpétuel et normal? II est clair que le mensonge, de cas ex:
ceptionnel, deviendrait lui aussi, cas normal, et qu'un groupe social
qui se verrait et se sentirait entouré d’ennemis, n’hésiterait jamais a
employer contre eux le mensonge. Vérité pour les siens, mensonge pour
les autres, deviendrait une régle de conduite, entrerait dans les moeurs
du groupe en question.
Allons plus loin. Consommons la rupture entre “nous” et les
“autres”. Transformons lhostilité de fait en une inimitié en quelque
sorte essentielle, fondée dans la nature méme des choses.** Rendons
nos ennemis menacants et puissants. II est clair que tout groupe, placé
ainsi au milieu d’un monde d’adversaires irréductibles et irréconciliables,
verrait un abime s’ouvrir entre eux et lui-méme; un abime qu’aucun
lien, aucune obligation sociale ne pourrait plus franchir.’® Il parait
3 Commercant et menteur étaient jadis des notions synonymes. “Qui ne
trompe, ne vend” dit un vieux proverbe slave. Aujourd’hui on admet que,
pour le commercant, honesty is the best policy.
4 Le meilleur moyen de pousser ]’opposition jusqu’au bout, c’est de la rendre
biologique. Ce n’est pas un hasard que le fascisme soit devenu racisme.
% Ta guerre état normal . . . L’hostilité du monde extérieur . . . Ce sont ]a
les ena constants de la conscience de soi que les totalitaires inculquent &
leurs peuples.
A. KOYRE, LE MENSONGE 101
té ’, } . ] . .
ge
acte simplement
sociale: il deviendrait
vertu. En revanche, la véracité mal
mentir, bien loin d’étre considérée comme un
trait chevaleresque, deviendrait une tare, un signe de faiblesse et d’in-
capacité.
toléré, ni méme une simple régle de conduite
obligatoire, il se transformerait en
placée, lincapacité de
* * *
Or ces degrés, dont nous avons d’ailleurs suivi l’échelle ascendante
expriment, nous semble-t-il, l’action de trois facteurs: |
] , x7 . , e.e ;
) Le degré d’éloignement et d Opposition entre les groupes en
question. II y a loin de l’hostilité naturelle pour |’étranger, ennemi po
te . . 4 . , f
ntiel et méme ennemi réel, A la haine sacrée qui inspire les combattants
d’une guerre religieuse;7 et loin de celle-ci 3 la férocité biologique qui
anime ceux d’une guerre d’extermination raciale.
*° Citons au hasard, lentrainem
i ent au menson
i Indien; la mentalité du marrane, ou du ecise
C’est la mentalité de Ja guerre reli
102 RENAISSANCE
3) Le degré de fréquence des contacts saciid — a i ciewam
et leurs membres. En effet, si ces groupes, sl hostiles cent it _
trent jamais en contact, ou seulement as wi champ de oo es
membres d’un groupe ne fréquentent jamais ceux des —_ . au-
ront — en dehors de la ruse guerriére — bien rarement hicintou de
mentir 4 ceux-ci. Le mensonge présuppose le contact; il implique et
ig commerce.
sa derniére remarque nous oblige 4 pousser l’analyse . peu
avant. Supprimons Il’existence autonome de notre erg by on seam 4
tout entier, dans le monde hostile d'un oie teu ia i li —
geons-le, tout entier, au sein d’une société ennemie, avec laquelle, ce
endant, il reste journellement en contact: il est clair que, dans et
? ;
: roupement en question, la faculté de mentir sera d’autant
pour le g
b * EY ue
plus nécessaire, et la vertu du mensonge d’autant plus appréciée, q
fi bP] a3 ” e
i i nous” et les “autres”, qu
la pression extérieure, que la tension entre we
Vinimitié des “autres” pour “nous”, que la menace que ces
ds *,/
. i entera dintensiteé.
font peser sur “nous”, grandira et augm ea a
ituation limite; fai
Poussons, une fois de plus, jusqu’a la aus . :
ou
ilité } 2 et totale. Il est clair que le gr
Vhostilité jusqu’a la rendre absolue fgg gis 0
e sulvre les ava
social dont nous sommes en train 3 : ota
obligé de disparaitre. Disparaitre en fait, ou bien, en appliq
. A
aux
jusqu’au bout la technique et l’arme du mensonge, disparaitre
| 2 enace
: 2 saires, et se dérober 4 leur m
yeux des autres, échapper a ses adver :
en se réfugiant dans la nuit du secret. a
1 I onge ur notre gr 2
L’inversion désormais est totale: le mens 7 a dl
b
ad vertu. Il sera deven
devenu groupe secret,*” sera plus qu'une
: ental et premier.
d’existence, son mode d’étre habituel, oe Pp
* +
. . ek. . S 4
Du fait méme du secret, certains traits caracteristiques, propre
: érés
tout groupe social en tant que tel, se trouveront accentues et exag
ige une
au dela de la mesure. Ainsi, par exemple, tout groupement érig i
. a A e
barrigre plus ou moins perméable et franchissable entre lui-méme
re la socio-
© Létude du oupement secret a été onsnacihargs Cm ee =
logie. Sans doute connaissons-nous relativement bien les
i ue tout, de
l’Afrique Equatoriale; en revanche, nous se sdsrner Pome” eT 5 Hi ei
celles qui ont existé, et qui existent, en Europe. " 2 pa ae oe
naissons l’histoire, nous ignorons la structure typologi
ments, dont Simmel fut 4 peu prés le seul a reconnaitre l'importance.
4. KOYRE, LE MENSONGE 103
les autres; tout groupement réserve pour ses membres un traitement
privilégié, établit entre eux un certain degré d’union, de solidarité,
d’“amitié”; tout groupement attribue une importante particuliére au
maintien des limites de séparation entre lui et les “autres”, et donc a
la préservation des éléments symboliques gui en forment, en quelque
sorte, le contenu; tout groupement, tout groupement vivant du moins,
considere I’appartenance au groupe comme un privilége et un honneur,?°
et voit dans la fidélité ay groupe un devoir pour ses membres; tout
groupement, enfin, dés qu'il se consolide et atteint une certaine dimen-
sion, comporte une certaine organisation, une certaine hiérarchie.
Tous ces traits sexaspérent dans le groupement secret: la barriére,
tout en restant, dans certaines conditions, franchissable, devient imper-
méable;?1 l’agrégation au groupe devient initiation irrévocable;2? la soli-
darité sa transforme en un attachement passionné et exclusif; les sym-
boles acquiérent une valeur sacrée; la fidélité au groupe devient le
devoir supréme, parfois méme unique, de ses membres; quant 4 la hié-
rarchie, devenant secréte elle acquiert, elle aussi, une valeur absolue
et sacrée; la distance entre ses degrés augmente, l’autorité devient illi-
mitée, et l’obéissance perinde ac cadaver, la régle et la norme des rap-
ports entre le membre du groupe et ses chefs.
Mais il y a plus. Tout groupement secret, que ce soit un groupe-
ment de doctrine ou un groupement d’action, une secte ou une conspi-
ration — et, d’ailleurs, la limite entre les deux types de groupements
est assez difficile 4 tracer, le groupement d'action étant, ou devenant
presque toujours, un groupement de doctrine — est un groupement
a secret, ou méme 4 secrets. Nous voulons dire que, lors méme que, pur
groupement d'action, tel une bande de gangsters ou une conspiration
de couloirs, il ne posséde point de doctrine ésotérique et secréte dont
il soit obligé de sauvegarder les mystéres en les voilant aux yeux de
” Il y a, sans doute, des groupes — les groupes de parias — qui considérent
eux-mémes l’appartenance au groupement comme un malheur ou un déshon-
neur. Ces groupes-la finissent généralement par disparaitre. Mais tant
existent, ils considérent toute évasion comme une trahison.
“ Le type classique de groupement secret est le groupe auquel on accéde par
une initiation qui, généralement, comporte des degrés; des groupes secrets
héréditaires existent également, mais ils sont trés rares et de plus, ces groupes
comportent eux aussi, des initiations. Au fond, dans ces groupements-la,
c'est l’initiation qui est héréditaire ou héréditairement réservée.
= Les groupes d’initiation ne sont pas nécessairement des groupements secrets.
qu’ils
104 RENAISSANCE
non-initiés. son existence méme est indissolublement liée au maintien
>
é - 3 savoir du secret de sa propre
d’un secret et méme d’un double secret; a savo prop
existence ainsi que des buts de son action.
Il en résulte que le devoir supreme du membre d'un .
secret, l’acte dans lequel sexprime son attachement et sa pi
celui-ci, l’acte par lequel s'afhrme et se contre son _— P
groupe, consiste, paradoxalement, dans la Seeewaretion e at wl
Dissimuler ce qu'il est et, pour pouvoir le faire, awatles ce qui
pas: voila donc le mode d'existence que, nécessairement, tout groupe
ment secret impose a ses membres.
+ + +
5 5 = . . ue
isSi J -e qu'on n’est pas . . . Cela impliq
Dissimuler ce qu on est, simuler ce q p
?
jamais — ce qu se et ce quon
de toute évidence: ne pas dire — jamais — ce quon pense ? .
dire — toujours — le contraire. Pour tout membre dun
croit; et aussi: |
7 n’est, en fait, qu'un moyen de cacher sa pensée.
?
9 é ole
roupe secret, la par :
te
Ainsi donc tout ce qu'on dit est faux. Toute parole, du moins tou
’
/ ’
<
‘oc 24
étre, vraies. es.
Ssoteri ; amais
La vérité est donc toujours ésotérique et cachée. Elle n’est j
i a celui qui
accessible au commun, au vulgaire, au profane. Ni méme gq
t initié.
n’est pas complétemen |
: eine
Tout membre du groupement secret, digne de son réle, en a pl :
a-t-il jamais ce qu'il entendra dire en public
. Aussi ne croir :
par un membre de son propre groupemen
A
‘amais comme vrai quelque chose qui sera publiquement proclamé pes
amai | :
| ce n’est pas a lui que s’adresse son chef, mais aux autres ,
25
quiil a le devoir d’aveugler, de berner, de a,
le refus de croire 4 ce quiil
aes chef. Car
a ces “autres”
>
Ainsi, par un nouveau paradoxe, cest dans
si nde religieuse ou
—— roupement de propaga
°3 T] en va tout autrement pour un ¢g deygerer: in acceptent ou recherchent
pour qui le martyre constitue un
politique ouvert, groupement dont |
le martyre en témoignage de leur foi,
5 .
agande et d'action. ee
= Atal: Sout tielaoue soigneusement entre la déclaration publiq
* Aussi - neuseme
communication, plus ou raga ares
cobain bet ions ésotériques, c’est démontrer par
. ux rt
%* Croire aux ee i ie — - a Gea oi detalii:
\ A as = ?
la méme |’insufhsance
te et complete, de la vérité ésoteérique
A. KOYRE, LE MENSONGE 105
dit et proclame que s'exprime la confiance du membre du groupement
secret en son chef.
Pd . a , 4
On pourrait nous objecter sans doute que notre analyse, si juste
quelle soit, s’écarte du sujet. Les gouvernement totalitaires ne sont,
hélas, rien moins que des sociétés secrétes, entourées d’ennemis mena-
gants et puissants, et obligés, de ce fait, de chercher la protection du
mensonge, de se cacher, de se dissimuler.2¢ Et méme les “partis
uniques” qui forment I’armature des régimes totalitaires, ne peuvent,
nous dira-t-on, avoir rien de commun avec des groupements de conspira-
teurs: ils opérent, en effet, en plein jour. Aussi, bien loin de vouloir
se fermer, et d’élever une barriére entre eux-mémes et les autres, leur
but, avoué et patent, est-il justement d’absorber tous ces “autres”,
d’englober et d’embrasser la nation Cou la race) tout entiére.
D’ailleurs, on pourrait contester également le lien que nous pré-
tendons établir entre totalitarisme et mensonge. On pourrait faire valoir
que, bien loin de cacher et de dissimuler les buts proches et lointains
de leurs actions, les gouvernements totalitaires les ont toujours pro-
clamés urbi et orbi (ce dont aucun gouvernement démocratique n’a
jamais eu le courage), et qu'il est ridicule d’accuser de mensonge quel-
qu'un qui, comme Hitler, a annoncé publiquement (et méme imprimé
"oir sur blanc dans Mein Kampf) le programme qu'il a ensuite réalisé
noint par point.
Tout cela est juste sans doute, mais en partie seulement. Et c’est
pour cela que les objections que nous venons de formuler ne nous
semblent aucunement décisives.
Il est vrai que Hitler (ainsi que les autres chefs des pays totalitaires)
a annoncé publiquement tout son programme d'action. Mais c’était
justement parce qu'il savait qu'il ne serait pas cru par les “autres”, que
ses déclarations ne seraient pas prises au sérieux par les non-initiés;
Cest justement en leur disant la vérité quil était sir de tromper et
* On sait cependant a quel point les régimes totalitaires cultivent chez leurs
adhérents et leurs peuples la psychologie du juste persécuté, du peuple élu
entouré d’un soir Pesidicinte qui lésent ses droits et le menacent dans
son existence. Inversion caractéristique de la situation réelle, qui nourrit le
sursaut d’infériorité des totalitaires.
siete tii
<a
106 RENAISSANCE
d’endormir ses adversaire.2’ C'est la une vieille technique machiave-
lique du mensonge au deuxiéme degré, technique perverse entre toutes,
et dans laquelle la vérité elle-méme devient un pur et simple instrument
de déception.”* Il semble clair que cette “érité” 1a n’a rien de commun
avec la vérité.
artis totalitaires ne
I] est vrai, également, que ni les Etats, ni les p
étes au sens précis de ce terme et quiils agissent
d renfort de publicité. C'est que juste-
novation dont nous avons
sont des sociétés secr
publiquement. Et méme a gran
ment — et cest en cela que consiste lin
ut — ce sont des conspirations en plein jour.
parlé plus ha
* + +
Une conspiration en plein jou
groupement d’action, propre 4 l’époque démocratique, a
civilisation de masses — n’est pas entourée de menace et n’a donc pas
besoin de se dissimuler; bien au contraire, étant obligée d’agir sur les
gagner les masses, d’englober et d’organiser les masses, elle
» la lumiére, et méme de concentrer cette lumiére
ses chefs. Les membres du groupement,
r: bien au contraire, ils peuvent
"ils peuvent la ren-
par des
masses, de
a besoin de paraitre
sur elle-méme et surtout sur
de méme, n’ont pas besoin de se cache
aficher leur appartenance au groupement, au “parti,
dre visible et reconnaissable aux autres — et méme aux leurs
signes extérieurs, des emblémes, des insignes, par le port de brassards ou
niformes, par des gestes rituels accomplis en public. Mais
autant que les membres d’une société secrete — et ceci malgré le fait, que
nous venons de mentionner, que la conspiration en plein jour tend
nécessairement 4 devenir une organisation de masses — ils garderont la
l’adoption de signes extérieurs
distance entre eux-mémes et les autres;
ne fera quaccentuer opposition et rendre
e de ceux du dehors; la fidélité au
es membres; la hiérarchie
méme du
d’appartenance au “parti’
plus nette la barriére qui les sépar
ment restera la vertu principale de s
groupe
arti” prendra l’aspect, et aura la structure, d'une organi-
intérieure du “p
été, on le sait bien, large-
Son utilisation, concurre-
nsonge au deuxieme degré a
ultat de confondre
la diplomatie bismarkienne.
i a pour rés
ment avec celle
l’adversaire — est caractéristique de
* Déception
sont dignes de I’
des adversaires; en revanche les
b
étre y trouveront l’annonce et le
- wae 8 ey ener
\cashitnantpunnhcnessneteanslincnenaditaetiecieatin mean aon .
eee Soe
ASS stesesntenstesnersns
——————
A. KOYRE, LE MENS
ONGE
107
sation militair ,
plu ] $1 CSR RSgIS OR Server fides infidelibus n’en
S SCcrupuleuse , sera que
ite ie ment observée. Car la conspiration en plein jour, si *
n é
- ane Société secréte, est tout de méme une société g , e
a victoire, c’est-a-di sh igs
ire la réussite d .
; e la conspirati
pas les traits que piration, ne détruira
ing ) que nous venons de mentionner; elle se bornera 4 affaibli
ins, Mails en revanche, a intensifier ] eee
ment, a renforcer le senti d <r les autres et, tout particuliére-
iment de supériori
dirigeant : peniorit€ de la nouvel
€, sa conviction d’ velle classe
appartenir a une élite, 3
, : e élite .
entiérement séparée de la masse.?9 , a une aristocratie
Les régi vor .
mes
Pies g : rare n€ sont rien d’autre que de telles conspi
, Issues de ; nspira-
Piigne ; a haine, de la peur, de l’envie, nourries par un 3 Sj
nce, de nati ; esIr
eee Shs domination, de rapine; conspirations qui ont réussi
xX — et cest 1a un point i seine
N point important
. : — ce sont d os
qui ont partiellem pe ie ; €s conspirations
: ‘coat €nt reussi: qui ont réussi a s'imposer dans Sui
rir le ee a
2 pouvoir, 4 s'emparer de I'Etat. Mais qui n’ont pays,
S encore—a réali ; pas réussi —
EE, : liser les buts quils se sont proposés,®° et qui, d
4 " >
5 » continuent a conspirer. qul, de ce
N pourrait se .
Bea demander si la notion de la conspiration en plei
as u wee. ; : n plein
myste P ne contradiction in adjecto. Une conspiration i 4
ére et secret ion implique
satipe atpyee pourrait-elle se faire en plein jour? Pilg
oute. ou ~ » . °
cosa Sells ) te conspiration implique le secret; secret qui
isément les buts d ; , 1 con-
: € son action; b ,
uts quelle doit dissi
justement , ? quelle doit dissimu
. pour pouvoir les atteindre et qui ne sont co 2
X gui “en sont” , a nnus que de
scoop . Mais la conspiration en plein jour ne fait ie
Cc ai i m
heaid ette régle, car, ainsi que nous venons de le dire. t¢ a
Ss une ié out e
ae société secréte, elle est tout de mé :
secret. meme une société @
Comme
nt toutefois bed
qui opére sur la pl cas société de ce genre, c’est-a-dire une société
a place publique, qui
ui che .
dont la propagande s’adresse » gq rche a organiser les masses, et
a aux masses, pourrait-elle garder
question est tout a fait léciti un secret?
difficile qu’elle ] 8 ait Mais la réponse n’est pas aus i
€ parai st
parait tout d’abord. Elle est méme assez simple
, car
* On :
pourrait l’appeler “I’ari 2
aristocratie d aya
pas entre e En u mensonge”
oa ux. effet, une éli ge si ces termes ne jurai
élite ? élite du m : S ne juraient
wy selene a ee et non ‘aapene ae necessairement, une
ul sait li atie.
5 t lire, le but de domination mondiale est cla;
airement
formulé dans Mein Kampf.
108 RENAISSANCE
il n’y a qu'un seul moyen de garder un secret: c'est de ne pas shateidenaene
ou de ne le révéler qu’a ceux dont on est stir: 4 une élite d’initiés.
Or, dans la conspiration en plein jour, cette élite qui, seule, est
versée dans les buts réels du complot est, tout naturellement, poenbe
par les chefs, les membres dirigeants du “parti”. Et comune celui-ci
exerce une action publique et que ses chefs agissent « public sg sont
obligés d’exposer publiquement leur doctrine, - faire nes ia
publics et des déclarations publiques, il s‘ensuit que le painters u
secret implique l’application constante de la regle : toute —— pu-
blique est cryptogramme et mensonge; une eas doctrinale “7 Ri
qu'une promesse politique, la théorie** ou la foi officielle autant qu’une
obligation contractée par traité.
Non servatur fides infidelibus reste la régle supréme. Les initiés le
savent. Les initiés et ceux qui sont dignes de |’étre. Ils comprendront,
déchiffreront et perceront le voile qui masque la vérité.
srents au
Les autres, les adversaires, la masse, la masse oe part :
groupement y compris, accepteront comme vraies les assertions publiques
et, par 14 méme, se révéleront indignes de recevoir la vérité secréte et
?
de faire partie de |’élite.
Les initiés, les membres de I’élite, — et cela par une espéce de savoir
intuitif et direct?? — connaissent la pensée intime et profonde du oa
connaissent les fins secrétes et réelles du mouvement. Aussi ne sont-ils
nullement troublés par les contradictions et les Pers - Ses
assertions publiques: ils savent qu’elles ont pour but de wanes x
masse, les adversaires, les “autres”, et ils admirent - chef ave —
et pratique si bien le mensonge. Quant aux rs ° ceux qui raion
ils montrent par ce fait méme quils sont insensibles 4 la contradiction,
imperméables au doute et incapables de penser.
* * +
L’attitude spirituelle que nous venons de décrire, attitude qui est
celle de tous les régimes totalitaires et surtout, bien entendu, du régime
woe ee
“= Les théories, c’est encore de la propagande. Propagée, il est vrai, par des
non-initiés qui y croient. Cyr oa
*2 Une espéce de contact mystique s’établit pour l’initié —ou pour celui qui
croit l’étre — entre lui-méme et le chef.
A. KOYRE, LE MENSONGE 109
totalitaire par excellence, Cest-a-dire du régime hitlérien,33 implique, de
toute évidence, une conception de homme, une anthropologie. Mais
pour etre opposée a l’anthropologie démocratique, ou libérale, }’anthro-
pologie totalitaire ne consiste aucunement dans un renversement de
valeurs qui, en abaissant la pensée, l'intelligence, la raison, mettrait au
sommet de |’étre humain les forces obscures,
“telluriques”, de l’instinct
et du sang.
Sans doute, l’anthropologie totalitaire insiste-t-elle sur limportance,
le réle et Ja primauté de I’action. Mais elle ne méprise aucunement la
raison.** Ou du moins, ce qu'elle améprise, ou plus exactement, abhorre,
ce ne sont que ses formes les plus hautes, lintelligence intuitive, la
pensée théorique, le nous comme l'appelaient les Grecs. Quant a la
raison discursive, la raison ratiocinante et calculatrice, elle n’en mécon-
nait nullement la valeur.®5 Bien au contraire. Elle la met si haut
quelle la dénie au commun des mortels.
Dans Vanthropologie totalitaire "homme ne se défnit pas par la
pensée, la raison, le jugement, justement parce que, selon elle, |’im-
mense majorité des hommes en est dénuée. Dyailleurs, peut-on encore
y parler de l’homme? Aucunement. Car Yanthropologie _totalitaire
n’admet pas l’existence d’une essence humaine une et commune 4
tous.°° Entre un homme et “un autre homme” la différence n’est pas,
pour elle, une différence de degré, mais une différence de nature. La
vieille définition grecque, qui détermine homme comme zoon logicon,
repose sur une équivoque:
logos-raison, et logos-p
il n’y a pas de liaison nécessaire entre
arole, pas plus qu’il n’y a de commune mesure
entre l’homme, animal raisonnable et homme, animal parlant. Car
~ te fascisme italien bien que tempore prior n'est qu’une péle imitation, si
ce nest une caricature, du totalitarisme hitlérien.
* Elle méprise "homme, et plus particuliérement, ]’homme totalitaire. Cf.
hommes, France Libre, N° 16, 1942.
* Comment le pourrait-elle? Le totalitarisme qui, officiellement (c’est-d-dire,
nigre la raison et l’organisation rationnelle,
au profit de la vision et de la liaison organiques, ne réalise en fait que la
plus rigide des mécaniques,
e” et le reste de Vhumanité, l’homo sapiens et
homo credulus, il y a pou
r l’anthropologie totalitaire autant de différence
quill y en a pour l’anthropologi
tiques ou dans l’anthropologi
’esclave.
€ gnostique entre les hyliques et les pneuma-
€ aristotélicienne, entre |’homme libre et
110 RENAISSANCE
: ani rédule
l’animal parlant est avant tout un animal crédule, et l’animal c
. . 37
est précisément celui qui ne pense pas.
La pensée, estime-t-elle, c’est-a-dire la raison, oe du vrai
et du faux, décision et jugement, est une chose trés rare et trés peu
répandue dans le monde. Une affaire de |’élite - ea ay
Quant 4 celle-ci elle est guidée, ou mieux, mue, par l’instinct, la pas .
i r. Ni vou-
par les sentiments et les ressentiments. Elle ne sait pas pense
. * 38
loir. Elle ne sait qu obéir et que croire.
Elle croit tout ce qu’on lui dit. Pourvu aves le dise sa gpcn
d’insistance. Pourvu aussi que l’on flatte ses Poe a a.
frayeurs. I] est donc inutile de chercher a rester en — Bh a
la vraisemblance: au contraire, plus on ment fein ed
ment et crédment, mieux sera-t-on cru et suivi. Inutile éga em °
chercher 4 éviter la contradiction: la asia ne la remarquera ” ~
inutile de chercher 4 coordonner ce que l’on agg il :
l’on dit aux autres: personne ne py = : ures a Ci
roira ce qu’on lui dit @ lui;*® inutile
at Pe pas Ps mémoire;*? inutile ae cae sage la ged
elle est radicalement incapable de la pescevoir; ome Po hag
cacher qu’on la trompe: elle ne comprendra jamais quil sagi é;
la soumet.*!
qu'il s’agit du traitement auquel on
C’est cette anthropologie-la qui est a la base a5 la propagande i
membres de la conspiration en plein pa: : c'est le a
qu'elle remporte qui explique le mépris _. Sosegaapnaia - eg .
totalitaires — nous voulons dire des membres de I’élite qui sai po
—_—-— -_—-
* T’animal pensant recherche I’intellection; l’animal crédule, la certitude.
t
% Credere, obedire, combattere —tel est le devoir du peuple. La pensée es
réservée au chef. x
; hae incipe: “ye suis Oi-
La technique du mensonge multiple — : pg pas oemad avantage
sean, voyez mes ailes, je suis sours, équival ot Ceicae de la fausse initia-
’ ulvaien
a fausse confidence, ; i ET
de gery’ aux trompés la (fausse) satisfaction de sonic 3 ayn oe
Gon, : ig ire dans le “secret”, et d’éprouver un — eae
oe j appear chine e en voyant “les autres” succomber au m
et donc,
hitlérien.
Sori dans Mein
i Hi til d’exposer sa théorie du mensonge
: Kono. Tabs Ss rl Conca ont compris que c’était d’eux que l'on
parlait.
A. KOYRE, LE MENSONGE
la masse, *?
adhérents; , Cest-a-dire pour tous ceux qui les croient
et les suivent; pour tous ceux aussi qui,
Nous n’allons pas contester le bien-fo
nous parait, a nous, passablement
sans les suivre, les croient.
ndé de cette attitude. Elle
justifiée. D’ailleurs, les représentants
et les chefs des régimes totalitaires sont bien
valeur intellectuelle et morale de
Nous
» pour les pays démocra-
tiques qui, en demeurant obstinément incrédules,
, N/a pu, en fin de compte,
sant “élite sociale”. Ainsi
au fond, n’en est pas un — ce sont
justement les masses populaires des pays démocratiques, de ces pays
prétendtiment dégénérés et abatardis qui, selon les principes mémes
de l’anthropologie totalitaire, se sont avérés appartenir 4 la catégorie
supérieure de l’humanité et étre composés d’hommes pensants, et ce
sont, en revanche, les pseudo-aristocraties totalitaires q
Sa catégorie inférieure, celle de ]
tromper qu'une certaine partie de la soi-di
par un dernier paradoxe — qui,
ul représentent
‘homme crédule et qui ne pense pas.
ALEXANDRE Koyré
€ croire aux doctrines, aux
nsi » aux promesses des Fiihrer, des Duce et autres chefs des
régimes totalitaires. I] est clair
que pris dans ce sens, le terme “masse”,
sociale, mais une catégorie intellectuelle et
se recrutent bien souvent parmi ceux des
ésigne non plus une catégorie
que les membres de la “masse”
‘és
élites sociales’.
SOMMAIRE
FASCICULE I
LetrreE pu Présment F. D. caecsogiy ast cet EO ROCCE Wo IBSI A ak a 3
Jacques Marrramw Henri Focillon: In Memoriam. ............ 5
LA REDACTION et hen nn a Ee DPPC E RP aL We Te 7
Atvin JoHnson Prodromes d'un Monde Nouveau. .......... 11
Henri Focirrton PPE ae ae Pa aR eA 15
Jacgues Marrrain Communion et Liberté. ......0.0.00000..0. 18
PauL van ZEELAND Ampowa hal et Demain, o.oo 24
E. K. Ranp SOmatenaNOR, WHY OR ooo doccoseocccle oc ok 29
Micuer Rosrovrzerr L/’Orient et lg civilisation grecque: Doura-Europos
OU NING Oh LENA agg 43
Gitpert Curnarp L'Héritage de la Viberté. oo... cccceccecccscscssesssesssesee 60
Grorces Gurvircu La Philosophie sociale de Bergson. ...0.......ccc00... 81
ALEXANDRE Koyré Réflexions sur le mensonge. o..c...ccccccccccccccessessee 95
B. Mirxine-Guerzéviron 150° Anniversaire de la République Frangaise. 112
Craupe Lévi-Srrauss Guerre et commerce chez les Indiens de
eG BS SSSR ata nies tse aN ARAL 122
Jean Want Quelques mots sur l’activité intellectuelle en
Fo kh 38 angus YEE WARY 3 DCRR ese I IRA EON RE 140
Henri Laucrer Notes politiques sur la situation francaise. ........ 143
H. Fociron FR NES Sikicacbicsdlsssdshiesbovedlude: Leics lac ni euteas 153
Compte-rendus par
R. Bespatorr, Henri Fast, Henri Preyre, ANDRE SPIRE ...........cccccceccs. 155
Chronique de V’Ecole Libre des Hautes Etudes .........cccccccccccsccoccsseccceceecsssec 167
FASCICULE II
Jean Perrin We erfene des choses, iii le oa 181
Henri Roxin Méditation sur la Constitution belge. .............c000.-. 190
Gustave CouEN Epopée byzantine et épopée francaise. .............. 200
GrorGEsS SarRTON Peeve Ge Way BOReba eS a 218
Lion Herrmann Notes sur Vopinion francaise depuis Varmistice. .. 238
Pot Swincs Un exemple de coopération Scientifique. ............ 255
PauL ScHRECKER Le Probléme de la Révolution en philosophie
rt Si oak ROR OD ERNIE SOUER ORD {AOS Pati Ree SM Bee 270
B. S. CHiepner Economie de guerre, d’armement et de paix. ..... 29]
RENE vE Messrires Louis Cons: In Memoriam. ......0.00...................... 311
Paut River Fr, Boas: In Memoriam 0......6..cccccccccssccssseoseccosoeeee. 313
Compte-rendus par
Anpré Spire, CLaupe Lévi-Strauss, Léon Kocunirzxy ....................... 315
Chronique de l’Ecole Libre des Hautes Etudes ................... 333
DANS SES PROCHAINS NUMEROS
RENAISSANCE PUBLIERA NOTAMMENT
LES ARTICLES SUIVANTS:
Jean ALBERT Bépe
JEAN Benorr-Levy
Henri BoNNET
ROGER CAILLOIS
Henri GREGOIRE
Jacques HapAMARD
Juxren BoNFANTE
FrancoisE Dony
Reng ETIEMBLE
Henri Fast
RENE HIsLAIRe
Louts Mario
Henri MuLbLer
Jean WAHL
GERMAINE WEILL
Jean SYLVAIN WEILLER
MME pE WyzEwA
I. ZLOTOWSEKY
Cu. STERLING
R. JAKOBSON
Denis DE RouGEMONT
LIONELLO VENTURI
AucusTE VIATTE
AnTornE Bon
{. DELEVSKY
G. Levi Detra VIDA
Paris et Clemenceau.
Cinéma, art universel.
La Préparation intellectuelle des conquétes nazies.
Patagonie.
La Persécution comme system itique :
Juifs et les Chrétiens. :
La science et le monde moderne.
L’Origine des langues romanes.
Vices et vertus du personnage O’Neillien,
Gobineau, juge du fascisme.
La Liberté de la Presse.
Les Occasions perdues.
Le Corporatisme moderne.
De la naissance du frangais.
Métaphysique et poésie.
Montaigne d’aprés Léon Brunschvicg.
Utilisation de l'économie politique a des buts poli-
tiques.
Théodor de Wyzewa.
Le Cyclotron.
La peinture frangaise.
La grandeur des petites nations.
La sociologie du roman.
L’histoire et la critique d'art.
Le Canada et la Guerre.
Stephan Zweig et le Brésil.
La Boétie critique de la tyrannie.
Nationalisme et Internationalisme dans VIslam.
Compte-rendus par
2 rr ’ 7 - Dp f. : hw Pa r f Ld
E. Brxerman, H. Gricome, L. Kocunrrzxy, A. Koyré, C. Lévr-Srrauss
P. Scurecxer, J. SEZNEG, ETC.
En vente dans toutes les grandes librairies. En dépét a l’Ecole Libre
des Hautes Etudes et chez Brentano, 587 Fifth Avenue, New York.
Le prix de ce numéro
double comprenant les
fascicules 1 et 2 est de $2.00
f
: :
/t#4EC. MG 4027 / (Leer, Leecfa FuZecl
Yo
f fi - i A ne
(ALO KN pect tt | UG /Lt
f
t-
NICOLAS COPERNICUS
By Proressorn ALEXANDRE KOYRE
University of Paris, Ecole Libre Des Hautes Etudes
Reprinted from the Quarterly Bulletin of the Polish Institute
of Arts and Sciences in America, July, 1943
NICOLAS COPERNICUS’
By PROFESSOR ALEXANDRE KoyrE
University of Paris, Ecole Libre Des Hautes Etudes
The year 1543, the year of the publication of the De Revolutiont-
bus orbium Caelestium and of the death of its author, Nicolas
Copernicus, marks an important date in the history of human
thought.
One is tempted to consider it as that of the “end of the middle
ages and the beginning of the modern times,” because, much more
than the conquest of Constantinople by the Turks, or the discovery
of America by Christopher Columbus, it marks the end of a world
and the beginning of a new one.
Yet, perhaps this would still be a misvaluation: the cut made by
Copernicus does not mark the end of the Middle Ages alone. It marks
the end of a period which embraces both the Middle Ages and Antiq-
uity; for it is with Copernicus, and only since then, that man no
longer stands in the center of the World, that the Cosmos does not
revolve around him.?
* 2x 2K
It is rather difficult for us, to-day, fully to understand, to realize
and to appreciate in their overwhelming greatness the intellectual
effort, the daring and the moral courage embodied in the work of
Copernicus. In order to be able to do so, we would have to forget the
spiritual development of a couple of centuries; we would have to
force ourselves to go back to the naive and unquestioned certitude
with which common sense accepts the immediate evidence of the
immobility of the earth and of the motion of the skies.
Even that would not be sufficient. To this evidence we should be
able to add the influence of a threefold teaching: scientific, philo-
sophical, theological. A threefold tradition, a threefold authority of
1The following paper was read at the Copernicus celebration in the Polish
Institute of Arts and Science on May 3, 1943.
2 The heliocentric system, as everything or nearly everything else, originates, of
course, in the Greek thought (cf. Sir Thomas L. Heath, Aristarchos of Samos, London,
1913, and Pierre Duhem, Le Systéme du Monde, vol. I and II, Paris, 1913-17). Yet,
it never received recognition (a) because it never was developed into a real, workable
astronomic theory, and (b) because it could never meet the physical objections
against the motion of the Earth. On the importance of these cf. A. Koyré, Etudes
Galiléennes, Il, Paris, 1940, and “Galileo and the Scientific revolution of the X VIIth
century,” Philosophical Review, 1943.
ae ST ET FEISS OPER . — —
38 FRE” BES I REN ee ae ee ee REET pea ae =e
calculus, of reasoning, of revelation. Then, but only then, would
we be able to render to ourselves an account of the incomparable
boldness of the Copernican thought, which tore the Earth from its
foundations and hurled it in the skies.
* * *
If it is difficule for us—or even impossible otherwise than in
imagination—to realize the liberating effort of Copernicus, it is
just as difficult to grasp the depth and the strangeness of the im-
pression that the reading of his work could not fail to make on men
of his time; the destruction of a world that all, science, philosophy,
religion represented as centered upon man and created for him;
the crumbling of the hierarchical order which, opposing the sub-
lunar world and the skies, united them in and through this oppo-
sition itself ...
The impact was too great. The new world conception seemed
too crazy to be taken seriously. Besides, the book, as a whole, was
much too difficult for readers not trained in mathematics and as-
tronomy.* |
As Copernicus expressed it himself: mathemata mathematicis
scribuntur. Let us leave it to mathematicians. It’s only a new hypoth-
esis; new and old at the same time. A scheme for calculation, with
no more real importance than those of various astronomers till
then.® This is what, in spite of the Narratio Prima of Joachim Rheti-
cus, and thanks to Osiander’s clever introductory “‘letter to the
reader’’ prefixed to the work of Copernicus, was commonly thought
for about half a century or so. The Church didn’t stir; Melanchton
(and Luther) alone realized at once the bearing and the meaning
of the work.® |
3 The authority of the Bible weighed heavily against the heliocentric system and
prevented its universal recognition until the XVIIIth century. But in the times of
Copernicus — and until Galileo and Descartes—the opposition of the Aristotelian
philosophy and physics was at least as potent.
* Joachim Rheticus, the only disciple of Copernicus (cf. infra, p. 717) insists there-
fore that “the staff of the astronomer is mathematics, or geometry,” Narratio Prima,
p. 164 in E. Rosen, Three Copernican treatises, New York, 1938.
5 cf. infra p. 721. 2
6 Apelt, in his old but still valuable book, Die Reformation der Sternkunde, Jena
1842, p. 166, writes: “The new doctrine of the catholic canon, an essentially German
plant, just as protestantism itself, has been conserved and worked out chiefly by
protestants. . . . The destiny of the new astronomy was, in some sense, bound with
the destinies of protestantism.” I quote this phrase in order to point out what
nonsense can be written—even by a good historian—under the damaging and blinding
2
It is only later, much later, when it became obvious that the work
of Copernicus was not a matter for “mathematicians” alone; when
it became visible that the blow it dealt to the geocentrical and an-
thropo-centrical world was a mortal one; when, in the works of
Giordano Bruno, it had time to develop some of its metaphysical
and religious implications—that the old world reacted. A twofold
reaction: the condemnation of Copernicus and of Galileo, the at-
tempt to suppress the new world conception; the Pensées of Pascal,
an endeavour to reply.
x * *
It would be of deep, of priceless value for the history and the
phenomenology of human thought to be able to follow the de-
velopment, to reconstruct and to reconstitute the various steps, of
Copernicus’ thought. Alas, I must at once confess: this is an im-
possible task. Copernicus left no intellectual autobiography; his bio-
graphy by his pupil Joachim Rheticus, is lost; the few indications
he gives us in his proud and beautiful letter to Pope Paul the Third,
which constitutes the foreword to De Revolutionibus, are very scant
and, moreover, not very reliable. As for his opus itself, he presents
it to us—even in the Commentariolus—in a state of perfection that
is the despair of the historian.
Still, if we have to abandon the hope of writing the history of
Copernican thought, we must, at least, make an attempt at grasping
it in its historical meaning and truth . . . to bring it nearer to our
own thinking while avoiding every modernization of it. And, in
order to do so, we must try vot to see in Copernicus the forerunner
of Galileo and of Kepler and mo¢ to interpret him in the light of
later developments. 7
influence of national and religious prejudice. As a matter of fact, though Rheticus
and Kepler were protestants, protestantism had just as much to do with the new
astronomy as Germanism, that is, absolutely nothing. Indeed, while Catholic authorities
remained quiet until 1616, Luther condemned Copernicus as early as 1541 (cf.
Tischreden, vol. IV, p. 575) and Melanchton, who, in a letter to Bernardus Mithobius
(Oct. 16, 1541) declared that the attempt of Copernicus (whom he called Sarmaticus
Astronomus) “to move the Earth and to hold still the Sun’ was absurd, opposed
it in his Physics (Wittenberg, 1552, p. 60 sq. 99 sq.) and was followed by nearly all
the protestant divines. Thus the Physics of Comenius, reprinted through the whole
of the XVIIth century, violently opposed the new astronomy.
7 The conception of the “forerunner” is a very dangerous one. Though it is true,
that ideas have a quasi autonomous development, i.e. that ideas born in one mind
mature and bring fruit in another; though it is certain that, for later generations, the
older ones are interesting chiefly as their ‘“forerunners’’ and “ancestros,’ it is—or
should be—nevertheless obvious that nobody ever had, nor could have had, considered
himself as a “forerunner.’”” He could hope, of course, that later generations will solve
problems that he had to leave unsolved. But that is quite another thing.
This is a very important task,—a task which, in my opinion, has
been rather neglected until now. As a matter of fact, whereas we
have a number of good expositions of the astronomy of Copernicus,®
and whereas treasures of ingenuity and erudition were spent on
the problem of his biography,” or better to say, whereas innumer-
able efforts were spent in order to prove Copernicus to be a Pole or
a German (an interesting but still a subordinate problem*®), the
study of his physics has seldom been seriously attempted. And yet,
as Schiaparelli has already stated with his habitual insight,*? the
Copernican problem was above all a problem of physics and of
cosmology.
+ * x
Nicolas Kopernik was born at Torun, in Polish Prussia (Po-
morze), on February 19, 1473. His father, whose name too, was
Nicolaus, was a burgher of Krakéw, his mother Barbara Watzelrode,
a daughter of an old patrician Torun family.
As both of them died when Copernicus was 12 years old, he, as
well as his brother Andreas, was adopted by his uncle, Lucas Wat-
zelrode, his mother’s brother, who later (in 1489) became prince-
bishop of Warmia. Was Copernicus a Pole or a German? I must con-
fess that, to me, this question, or rather the importance given
tO it, appears somewhat anachronistic. Copernicus lived in a
time which, with some exceptions,1? was not yet poisoned by nation-
alism and nationalistic passions, which still enjoyed the blessings of
a common culture and of a common scientific language.1? Besides,
he lived in an Empire (medieval Poland was not a national state,
8 Cf. J. L. Dreyer, History of the Planetary Systems, Cambridge, 1906, A. Armitage,
Copernicus, London, 1938.
9 Thus the great work of Prowe, Nicolaus Copernicus, Berlin, 1813-4 deals with the
biography of Copernicus, the history of his time, but neglects the physical and
philosophical problems of the Copernican Revolution.
10 An exception are, of course, the magnificent works of Ludwik A. Birkenmajer;
Mikolaj Kopernik—Studya nad Pracami Kopernika oraz Materyaly Biograficzne, Czesé 1,
Krakéw, 1900; Mikolaj Kopernik—Jako Uczony i Twérca, Krakow, 1923, and Stromata
Coperniciana, Krakow, 1924.
11 Cf. G. V. Schiaparelli, I Precursori del Copernico nell’antichita, Milano, 1873.
»12 National opposition and national strife is not quite a new phenomenon; we en-
counter it, even during the Middle Ages, in Spain, in the Balkans, in Asia Minor,
etc. It is especially strong where it coincides with a religious opposition, as between
Christians and Moslems, or Orthodox and Catholics; sometimes it takes places even
without religious background, so in Bohemia between Czechs and Germans. Yet these
cases are rather infrequent.
13] would like to point out that Copernicus—and there was nothing unusual in
his case—began his studies in Krakéw, and continued them in Bologna, Ferrara and
Padova.
4
but an Empire), whose multi-national subjects, united by and through
common allegiance to the State (Res Publica) happily ignored min-
ority problems and rights—(which, by the way they fully enjoyed),
frequently intermarried and, generally speaking, got along pretty
well.
If we were able to put to Copernicus himself the question, “are
you a German or a Pole?” he certainly would not have understood
us, and probably would have answered that, of course he was
Polonus, meaning that he was a burgher of Torun, son of a burgher
of Krakow, a good Catholic, a canon of Frauenburg in Warmia, a
faithful subject of the Kingdom of Poland, and a bitter enemy of
the Teutonic Order. That, for his scientific work as well as for
intercourse with his peers, he used the language of science and
culture i.e. latin; but that, of course, when he had to deal with com-
mon people, he used their speech, Polish in Krakow and German in
Frauenburg.
If we would insist, and try to make him understand that we are
looking for something different, that we intend to explain his work
and his genius by his ‘nation’ or his “race,” he probably would
have become cross and would have informed us that the idea of
explaining the individual by the specific or the general is perfectly
stupid, that such a procedure is only valid when and where we
have to explain general (or specific) features of individual beings;
that it may be applied with good success in realms of nature which
lack of true individuality (e.g. minerals, plants, animals), but not
to man, who, as a spiritual substance, cannot be explained by fea-
tures and factors pertaining to his material being. I am afraid that,
if we would allow him to become somewhat anachronistic (as our-
selves), he would add that Taine’s theory according to which a
man or a work of genius can be “‘explained’’ by “race, environment,
and historical moment’ could only be invented and shared by bar-
barians utterly devoid of philosophical training.
Yet, as we cannot avoid being anachronistic, I will add that, as a
matter of fact, we have no reason whatever to suppose that Coper-
nicus was anything but a Pole. Besides, until the middle of the
XIXth century, nobody ever doubted it. And it is only since the
growing nationalism of European and, especially, of German thought
and historiography, that some German historians, ready to serve the
aims of German imperialism, have made a claim on Copernicus. A
>)
claim just as well founded as analogous claims with regard to
Leonardo da Vinci, Dante, Michel Angelo and so many others.
“ **
In 1491 we find Copernicus in the University of Krakow. We
need not speculate about the reasons which guided his choice: the
University of Krakow enjoyed a very high reputation at that time.*#
It was, as a matter of fact, since the downfall of Prague, the most
important of the Eastern Universities, a famous place of learning
and humanistic culture. Besides, Krakow was not far away from
Torun, and it is safe to assume that Copernicus still had relatives
in the birthplace of his father.
We lack information about the course of studies pursued by
Copernicus in Krakéw. Yet—though it is obvious that he made
a thorough study of astronomy there—we have no reason to doubt
that he followed the habitual curriculum of the Faculty of Acts,
including dialectics and philosophy. Copernicus, as a matter of fact,
is not a narrow specialist, an “astronomer’’ as Peurbach or Regio-
montanus, but a man deeply imbued with all the rich and complex
culture of his time, an artist, a classical scholar, a scientist, a man
of action: a Humanist in the best sense of this word.
Because of his astronomical studies, the biographers of Coper-
nicus admit that he enjoyed, quite particularly, the teaching of Albert
of Brudzewo (Brudzewski). Yet, Albert of Brudzewo, who in-
deed, for a long time taught astronomy with great success and dis-
tinction (in 1482 he wrote for his pupils a Commentary on the
Theorica Nova Planetarum by Peurbach)1° was by no means the
only Professor of astronomy in the University of Krakéw. On the
contrary, there were fourteen of them. Besides, since 1490, Albert
of Brudzewo did not teach astronomy any more, but lectured on
Aristotle’s De Caelo.
Albert of Brudzewo left Krakow in 1494 and the biographers
of Copernicus admit usually that Copernicus left it too about the
same time.
This is as it may be; in any case, in 1496 he went to Italy, to study
law at the University of Bologna. On January 6, 1497 we find his
name inscribed on the roll of the Natio Germanorum of the Uni-
14 Mathematical and astronomical studies were quite particularly flourishing in
Krakow.
15 This commentary, the first of the numerous commentaries of this very popular
textbook, was printed in 1495 in Milano.
6
versity. Which, by the way, does ot imply that Copernicus was, or
even considered himself, as a German. “Nationes’ of a mediaeval
university have nothing to do with nations in the modern sense of
the word!®; the German Nation (in Bologna), on the rolls of
which there is quite a lot of non-German names, was the ‘smart’
one and, as such, was usually joined by young Polish noblemen.
Copernicus, indeed, was not a nobleman but a commoner. Yet as the
nephew of a bishop, and of a high ranking one at that, he could
not decently join a socially less prominent “‘nation.”
Copernicus stayed in Bologna for about three years. He studied
astronomy, of course, though he seems already to have known
enough of it to be received by the famous astronomer, Domenico
Maria Navarra, non tam discipulus quam adjutor et testis observa-
tionum; but, at the same time, he studied a lot of other things: law,
medicine, philosophy; he learned Greek; he read Plato . . . Once
more, we must never forget that Copernicus is not an ‘astronomer’
but one of the most all-round minds of his time.
In 1500 he went to Rome (1500 was the year of the Jubilee which
attracted thousands of pilgrims to the capital of Christendom),
where, as his pupil Rheticus informs us, he gave a course of lectures
on mathematics; Rheticus, unfortunately, does not say what specifi-
cally he lectured about.
It seems that Copernicus did not crave going home. Yet it be-
came necessary to do so, in order to take possession of a canonry at
the cathedral church of Frauenburg, to which he had been elected,
owing to the protection of his uncle, Lucas Watzelrode.
In 1501 he is back in Poland; but not for a long time. After his
formal installation in the canonry he asks for leave, and, having
obtained it, returns to Italy. This time he goes to Padova, famous
for its schools of medicine and law. In 1503 he goes to Ferrara, but
does not stay there and, after being received Doctor utriusque iuris
(on May 31st), returns to Padova.
Copernicus seemed to be well pleased with his life in Italy. Alas,
all good things—even, and perhaps particularly, leaves of absences
—come to an end. Chapters do not like non-resident members and
16 The ‘“‘Nations” of a Medieval University (in the University of Paris there were
four “nations” among which we find the Burgundian and the Picardian “‘nations’’)
are rather to be compared with modern fraternities, endowed, moreover, with some
public functions.
7
Copernicus, though nephew of the Bishop, had to abide by the rule.
In 1506 he rejoins his diocese, never to leave it until his death.
x x **
The life that awaited Copernicus at home was not, as we may
be inclined to picture it to ourselves the life of a canon, the quiet
and easy life of thought and of prayer. Quite on the contrary, it
was a life of action. A mediaeval bishopric, and quite particularly
such a one as the bishopric of Warmia, was a political as much as
an ecclesiastic institution and had to do with worldly as much as
with religious affairs.17 And Copernicus who, for years, until the
death of Lucas Watzelrode, acted as his secretary (and his doc-
tor), entrusted among other things, with the economic administra-
tion of the bishopric—we owe to this activity his treaty on money*®
—didn’t have much time left for meditation, for study, for calcu-
lations . . . So it is only gradually, bit by bit, that his immortal
work grew and took shape. |
I said: meditation, calculus . . . not observations. We must not
think of Copernicus as spending his nights scrutinizing the skies
in order to discover some new facts, some new determinations of
the positions of the heavenly bodies. Copernicus is not a practical
astronomer. He is not Tycho Brahe. He made, of course, some ob-
servations; but very few. He gives us some determinations of his
own of the positions of the planets. Yet these are neither numer-
ous,!® nor very important. Perhaps, not at all. The greatness of
Copernicus—and I would like to stress that point—consists in his
having framed and developed a new theory, not in having provided
us with new facts. Indeed, his theory, or better to say, his system,
is based entirely on data already available then, chiefly on those of
Ptolomy. And, to say the truth, his system—a new interpretation of
these old data—at least insofar as we are concerned with calcula-
tion of observable phenomena—is no more in accordance with
them?° than that of Ptolomy which it endeavours to replace.
17 The bishopric of Warmia was an important political and even military position,
and churchmen had even to act as soldiers. Thus, during the war with the Teutonic
Order (in 1520) the episcopal city of Olsztyn was beleaguered by the troops of Albert
of Hohenzollern and stubbornly and skillfully defended by Copernicus, who, at this
occasion, acted as commander in chief.
18 De Monetae cudendae ratio, in 1526.
19 27 in all. Cf. Dreyer, op. cit. p. 316.
20 cf. Apelt, op. cit. p. 150: “If we ask: what practical advantages did astronomy
receive from the theory of Copernicus? we must reply: immediately, none whatsoever.
The system of Copernicus, such as it came out from the hands of its author is no
more in accordance with the skies than that of Ptolomy.”
8
Those of us who are not very well acquainted with the history of
astronomy will, probably, be slightly astonished. And yet it is a
fact that, for all practical purposes, the Prolomaic astronomy gave
a most satisfactory account of the observational data. We must never
forget (a) that, until Galilei who was the first man to use a (newly
discovered) optical instrument—the telescope—to look at the skies,
all astronomical observation were made with the naked eye and (b)
that, mathematically speaking, the astronomy of Prolomy is one of
the most wonderful achievements of the human mind. As a matter of
fact, its device of superposing and of combining of circular motions,
of epicycles and excentrics, enables it to represent — though, of
course, in a rather cumbrous way—almost any given curve and to
establish nearly as well as our modern theory of functions a mathe-
matical relationship between any given datas.
It is only from the point of view of cosmology, that is, only when
the astronomer tried to treat his circles and orbs as real objects in
real space that he encountered some difficulties; the circles and
orbs pertaining to different planets sometimes intersected and em-
braced each other, which looked rather bad im et per se, and more-
over, flatly contradicted the Aristotelian cosmology, which (worked
out long before Prolomy) persisted in using spheres and assigned
to each planet, and to the whole of its moving mechanism, a definite
spherical region of the Universe. That is the reason why, since the
revival of Ptolemaic astronomy, and especially in the second half
of the XVth century, the opposition between the “philosophers” and
the “mathematicians” gave birth (a) to attempts to harmonize the
systems of Aristotle and of Ptolomy and (b) to attempts to explain
away the whole problem by presenting the mathematical astronomy
as a merely mathematical device not concerned with reality.**
The central idea of his system seems to have been conceived by
Copernicus rather early, perhaps even before he left Italy. In the
21 This situation is not particular to Copernicus’ times. The development of
mathematical astronomy by the predecessors of Ptolomy and Ptolomy himself was ac-
companied by a growing conviction that their geometrical construction did not rep-
resent the physical truth, and that astronomy, which seemed not to be able to dis-
cover the real causes of the celestial phenomena, i.e. the real motions of the planets,
had to abandon this aim, and to content itself with a purely phenomenalistic theory,
which would enable the astronomer to gufey ra havopeva, salvare apparentias. The
same discussions are to be found in the arabic philosophical and astronomical literature
(e.g. Averroes flatly denies the physical reality of the circles and spheres of the
astronomers), and are well known to scholastics. Cf. Dreyers History of Planetary
Systems, London, 1906 and of course P. Duhems magnificent Le Systéme du monde,
Paris, 1913-1917.
?
letter-foreword of the De Revolutionibus Copernicus says that he
kept his work secret not for nine years (as the Pythagoreans pre-
scribed), but four times nine years. Of course that cannot be taken
literally, as concerning the book itself, only its main conception.
In that case it would mean that “four time nine years” were spent
in the elaboration and perfection of the theory. Copernicus under-
stood that it was of no use to formulate a new idea, or even, as it
was in his case, to try to revive an old one. He was perfectly aware
that, if he had to succeed, he had something quite different to do,
something that nobody had done before, i.e. to present a theory of
planetary movements, a theory just as complete, and just as work-
able, enabling prediction and calculation of observable celestial
phenomena, as that of Ptolomy or his mediaeval commentators and
followers. ?
We do not know exactly when Copernicus completed the elabora-
tion of the De Revolutionibus. Certainly not before 1530, perhaps
even some years later.
It seems that some time before the final working out of his system,
Copernicus wrote, and had circulated among his friends, a short
and schematic exposition of the new astronomy, the so-called Com-
mentariolus which remained unedited till 1876.°°
The Commentariolus which, from the point of view of astronomy,
that is, of the concrete arrangement of the movements of celestial
bodies and orbs, differs somewhat from the De Revolutionibus,** is
very interesting because it reveals to us at least some of the reasons
which guided and moved the thought of Copernicus.
Copernicus begins by pointing out that the astronomy of Calippos
and Eudoxos?® did not succeed in explaining the observable and
22 In his Commentariolus (cf. infra) Copernicus writes: “Let no one suppose that
I have gratuitously asserted with the Pythagoreans the motion of the Earth; strong
proof will be found in my exposition of circles.” (p. 59 of E. Rosen’s translation,
cf. infra, n. 23).
23 Nicolai Copernici de hypothesibus motuum coelestium a se constitutis Com-
mentariolus. An excellent English translation, with notes and a very interesting and
scholarly introduction was published, in 1939, by M. E. Rosen, cf. Three Copernicay
treatises, New York.
24 The system of the Commentariolus is “‘concentro-biepicyclic’’ whereas that of the
De Revolutionibus is “‘eccentro-epicyclic.’’ Cf. Aleksander Birkenmajer, “Le premier
systéme héliocentrique imaginé par Nicolas Copernic,” in La Pologne au VIle
Congrés International des Sciences historiques, Warsaw, 1933.
25 Calyppos and Eudoxos used only homocentric spheres. Their astronomy formed
the basis of the Cosmology of Aristotle.
IO
indubitable variations of the distances between the Planets and the
Earth; that the system of Ptolomy, though much more successful
concerning this point, failed in respect of another, namely, it did
not succeed in presenting the movements of the planets as composed
of uniform circular motions; and in order to save some kind of uni-
formity, he was compelled to introduce into his calculations the rather
dubious concept of “equant.’”?° This proceeding constitutes, from
the point of view of Copernicus, a somewhat dishonest device.**
Consequently, astronomy had to try out something else.
Seven “axioms” or “petitions” (axiomata vel petitiones: it is
interesting to note this Euclydian and Archimedian terminology)
present the chief characteristics of the new system.
The first and foremost of these axioms or petitions states the
necessity for building up a system of celestial movements “in which
everything would move uniformly around its proper center,* as the
rule of absolute motion requires.”
The second states that, ‘the center of the Earth is not the center
of the Universe, but only of gravity and of the lunar sphere.”
The third, that “all the spheres revolve about the sun as their
mid-point, and therefore the sun is the center of the Universe.”
The fourth and the fifth explain that the common motion of the
celestial phenomena is due not to the motion of the firmament but
to that of the Earth.
The sixth explains that the Sun stands still and that its apparent
motion is only the projection of the motion of the Earth; the seventh,
that the retrogradation and other peculiarities of the motion of the
planets are only apparent, not real motions, and that these appear-
26 In order to simplify the system and lessen the accumulation of circles and orbs,
Ptolomy let the planets move on their circles with a non-uniform velocity. Yet, in
order to preserve some kind of uniformity, he used only motions the angular velocity
of which, in respect to some point in the interior of the circle (mot its center) was
uniform. This point was called punctum aequans.
27 It is, probably, the conception of the eguant, combined with that of excentricity
of the orb of the Earth, which led Kepler to his discovery of the ellyptical character
of the planetary orbits. Yet, from his point of view, Copernicus was completely
right in stating that (Commentariolus, p. 1.) “Walde enim absurdum videbatur coeleste
corpus in absolutissima rotunditate non semper aeque moveri. . . . Yet Ptolomy
could not “save the appearances,” Nisi etiam aequantes quosdam circulos imaginarentur
.. . qua propter non satis absoluta videbatur huius modi speculatio neque rationali
satis concinna.”
28 Commentariolus, E. Rosen's translation, p. 76.
ances are due to the projection on the firmament of the annual
motion of the Earth.
Seven small chapters deal with the threefold movement of the
earth; they explain the order of the celestial orbs; they suggest the
advantage of referring the movement to the fixed stars, and not, as
commonly, to the equinoxial points (just because the latter are not
fixed, but—though very slowly—shift their positions) ; they describe
the mechanism of the planetary movements (the Moon, the superior
planets, Venus, Mercurius, Earth) and give an account of the dimen-
sions of the epicycles and orbs. All that without demonstrations and
proofs of any kind, the latter being reserved to the larger work,
majori volumunt.
It seems that Copernicus, though he persistently and obstinately
opposed the publication of his work, nevertheless made no secret
of his views. The Commentariolus seems to have circulated fairly
widely. Not only was it known to his immediate friends, but, ac-
cording to Tiraboschi,?® it found its way even to Rome, where the
Austrian Chancellor Johann Widmanstadt presented it to Pope
Clement VII in 1533 and explained to him the principles of the
new astronomical system. In Rome neither the Pope, nor anybody
else seems to have been very much struck by the new theory. It 1s
possible that the title of the little work with its use of the term
hy pothesis®® gave the impression that it was only a new, and some-
what extreme, mathematical construction which did not pretend to
give a description of the real world. It is possible that this was the
interpretation which Widmanstadt gave to the new theory. It is,
on the other hand, just as possible that the Pope and the cardinals
did not grasp its implications.
In any case, nobody raised any objections whatever. More than
that, some three years later, one of the members of the Roman curza,
the cardinal archbishop of Capua, Nicolas Schonberg, wrote to_
Copernicus (Nov. 1st, 1536) suggesting to him publication of his
discoveries and asked him to order that a copy (for which the
Cardinal offered to pay the expenses) be made of his work.
Copernicus did not follow the friendly advice of the Cardinal
29.N. Tiraboschi, Storia della Litteratura Italiana, Milano, 1824, vol. VII, p. 706,
quoted by Dreyer, op. cit. p. 317.
30 The term Aypothesis as employed by Copernicus is practically equivalent to
theory, and does not imply the non assertion of its truth. Cf. E. Rosen’s Introduction
to his translation of the Commentariolus, New York, 1939.
I2
of Capua. As far as we know, he did not even order the copy Schon-
berg asked for. In point of fact, the Cardinal of Capua was by no
means the first who urged him to publish his work. Quite on the
contrary, all his friends, and above all, “his very dear Tiedeman
Giese, Bishop of Kulm” had, for a long time, insisted on publication,
representing it to Copernicus as his duty toward science and man-
kind. But Copernicus could not decide. He knew better. He feared
calumniatorum morsus. And at 60, he obviously valued nothing more
than tranquility.
In the year 1539, a young professor of the University of Witten-
berg, Joachim Rheticus by name, came to Frauenburg. He had heard
about the new theories of Copernicus. He wanted to find out the
truth about them.
Well received by Copernicus, he stayed with him for about two
years, studying the manuscript of the De Revolutionibus, working
with the old man whom he always calls his Dominus Doctor Prae-
ceptor.
Joachim Rheticus was at once conquered and convinced. Con-
quered and seduced by the greatness of mind and the charm of
Copernicus’ personality; convinced and enticed by the beauty of his
work. And, in order that the light remaineth not under the bushel,
he started a bare couple of months after his arrival, and long before
he had completely mastered the new astronomy,** to compose a
short account of it which he sent to his master, Johannes Schoner.
The latter, just as quickly, had it printed.
In this report—that is the famous Narratio Prima—** which later
used to be printed in nearly all the editions of the De Revolutionibus,
we find besides an exposition of the Copernican Astronomy and
some very precious biographical data, a very curious astrological
explanation of the historical importance of the variation of the ex-
centricity of the orb of the Earth.**
The Narratio Prima insists on the fact, even more strongly than
Copernicus, that the new astronomy is true to the principle of the
31 “J have mastered the first three books, grasped the general idea of the fourth
and begun to conceive the hypotheses of the rest,” writes Rheticus to Schéner; cf.
Narratio Prima, p. 110 (Ed. Rosen).
82 The Narratio Prima is now available in an excellent translation of E. Rosen,
published in his Three Copernican treatises, New York, 1939; as for the Com-
mentariolus, 1 am quoting Rosen’s translation.
33 In the Copernican system the orb of the Earth has its center on a small excentric
circle, whose center is in the sun.
”~
14
uniform circular motion of the celestial bodies. Thus, explaining
the theory of the lunar motions Joachim Rheticus states (p. 135):
“here, in the case of the Moon we are liberated from an equant by
the assumption of this theory which, moreover, corresponds to ex-
perience and all the observations.” To this Rheticus adds: “my
teacher dispenses with equants for the other planets as well,” where-
fore (p. 136): “‘only on the basis of this theory could all the circles
in the universe be satisfactorily made to revolve uniformly and regu-
larly about their own centers and not about other centers—an es-
sential property of circular motion.”
For Rheticus the new astronomy is the revival of an old philoso-
phical lore. According to him, it is “following Plato and the Pytha-
goreans, the greatest mathematicians of that divine age, that my
teacher thought that in order to determine the cause of the phenom-
ena, circular motions must be ascribed to the spherical Earth.” (p.
147). Besides, ‘‘the ancients, not to mention the Pythagoreans, were
sufficiently clear about the fact (that) the planets evidently have the
centers of their deferents in the sun, as the center of the Universe.”
The Narratio Prima is rather helpful toward an understanding
of the teaching of Nicolaus Copernicus, and I shall have to quote it
frequently. But now let us come back to its historical astrology.
Rheticus—but, personally I have no doubt that it was Copernicus
speaking through his pen—** states that, when the excentricity was
at its maximum, “the Roman government became a monarchy; as
the excentricity reached its boundary and quadrant of mean value,
the Mohammedan faith was established; another great empire came
into being and grew very rapidly with the change in the excentricity.
A hundred years hence, when the excentricity will be at its minimum,
this empire will have completed its period. In our time it is at its
pinnacle from which equally swiftly, God willing, it will fall with
a mighty crash. We look forward to the coming of our Lord Jesus
Christ when the center of the excentric reaches the outer boundary
of mean value, for it was in that position at the creation of the
world. This calculation does not differ very much from the saying
of Elijah, who, under divine inspiration prophesied that the world
84Dr. E. Rosen points out that, in contradistinction with Rheticus, Copernicus
nowhere in his books, asserts a belief in astrology. Dr. Rosen is perfectly right. And
yet it seems—to me, at least—difficult to admit that Rheticus, who wrote his Narratio
with the knowledge and probably under the supervision of Copernicus, would have
dared to express these views if they were opposed to those of his master.
14
would endure only 6000 years, during which time nearly two revo-
lutions are completed. Thus it appears that this small circle is in
very truth the Wheel of Fortune, by whose turning the kingdoms of
the World have their beginnings and vicissitudes.” (p. 122)
This astrological exploitation of the new, heliocentric, astronomy
may appear astonishing to us. And even ludicrous. Yet we must not
forget that astrology belonged to the best established belief of that
time. Kepler himself shared it, not to mention Campanella.
* * *
The Narratio Prima met with considerable success. A new edition
was published in 1541 cura et studio of Achille Ganarus, a Basler
physician. The learned world was thus in possession of the first
elements of the doctrine.
The first reactions were rather favorable. Thus Erasmus Rein-
hold, Professor in the University of Wittenberg who, in 1542,
issued a reprint of the text book of Peurbach, expresses in its preface
the hope to see astronomy restored by Copernicus, whom he calls
“a new Ptolemy.’
The publication of the Narratio Prima made the withholding of
the De Revolutionibus senseless. We must not be amazed, therefore,
to see Copernicus, at last yielding to the urgings of his friends. The
priceless manuscript is entrusted to Tiedeman Giese. The latter
transmits it to Joachim Rheticus who has it printed by the famous
Nuremberg typographer, Johannes Petreius. Tiedeman Giese tells
us that Copernicus received the first copy of his work on his death-
bead, on May 24, 1543.
All that is fairly well known. We know too, that Joachim Rheticus,
appointed professor in the University of Leipzig in 1542, left the
supervision of the printing to his friend Andreas Osiander, a famous
—and somewhat heretical—Lutheran divine. We know further that
Osiander, who had a personal experience of the rabies theologorum
—and who recognized that there was some danger in the thesis
advocated by the new astronomy,— decided to shield it against
the ire of the theologians and the Aristotelians, and to take some
precautions. As a matter of fact, the boldness of Copernicus troubled
Osiander himself. The new world conception was, obviously, con-
trary to the scriptures and he was himself a good enough—though
heretic—Lutheran, to doubt their literal divine inspiration.
15
Thus, as early as 1541%°, he devised a rather elegant solution
of the difficulty by accepting a phenomenist theory of science.
Science, — and especially astronomy, — thinks Osiander has only
one purpose, which is to “save the phenomena,” salvare apparentias.
The goal and aim of the astronomer is not to find out the hidden
causes nor the real movements of the heavenly bodies,—which he
is unable to do—but to connect his observations by means of
hypotheses enabling him to calculate the (visible and apparent)
positions of the stars and the planets. These hypotheses, that of
Copernicus no more than those of others, make (or need not to
make), therefore, any pretension (or claim) for being true or even
verisimilar or probable; they are nothing more than calculatory
devices, and the best of them is not the truest but the simplest and
the most convenient.
This is what Osiander explains in a letter-preface ‘“To the reader
of this work,” which he prefixes without his signature to the text
of the De Revolutionibus, thus making the reader believe that its
author was Copernicus himself.
This very interesting and very modern looking piece of epis-
temology, very curious and very valuable from the point of view
of the history of philosophy and science,*® nevertheless had the mis-
fortune to be very severely judged by the friends of Copernicus.
Tiedeman Giese ascribes it to the envy and the cowardice of a
man who himself refuses to abandon his traditional views and be-
liefs and prefers to commit a real forgery, aggravating it by a
breach of confidence.
Tiedeman Giese wants Osiander to make a public declaration of
authorship. He asks the magistrate of Nuremberg to order the
suppression of the foreword. He even asks for the reimpression of
the first pages of the De Revolutionibus with an announcement that
the foreword is a forgery. Giese thinks that Joachim Rheticus
35 April 20, 1541 he wrote, on the same day, to Rheticus and to Copernicus him-
self, exhorting them to adopt the phenomenistic epistemology and, in order to placate
the theologians and the Aristotelians, to present the new world system as a purely
mathematical ““hypothesis.”” Copernicus answered with a refusal. The whole story
is told by Kepler in his—unfortunately unfinished and inedited—Apologia Tychonis
contra Ursum, printed for the first time by Frisch in his edition of Kepler’s Opera
omnia.
86 As I have mentioned already, the epistemology of Osiander is by no means new
and modern, but on the contrary, very old and trivial. Cf. Pierre Duhem, La théorie
physique, Paris, 1906.
16
should take the matter in hand. It is to him that he sends his com-
plaint to the magistrate.
It is probable that Joachim Rheticus saw things in a different
light from Leipzig than Tiedeman Giese saw them from Kulm. He
seems to have done nothing. Not only did he not assail Osiander,
nor did he contradict him,—but he even suffered the foreword to be
reprinted in the second, Basle 1566, edition of the De Revolutionibus,
an edition to which his own Narratio prima was added as introduc-
tion, without any mention of Osiander.
We must confess that, though they believed the foreword to
emanate from Copernicus himself, this declaration of phenomenist
faith did not deceive the initiated. They thought, simply, that Coper-
nicus took precautions.*?
As a matter of fact, Copernicus took very few, if any, pre-
cautions.*8 He joined to his book the letter he had received from
the Cardinal of Capoua some years before. He dedicated his work
to Pope Paul III. But in his own, very noble forewarding letter
(which Osiander did not publish), he insists proudly and unflinch-
ingly upon the rights of science and philosophy. Mathemata Mathe-
maticis scribuntur, he proclaims; the ignorant should better keep
silent. And the allusion to Lactantius who made himself ludicrous
by not wanting to believe in the rotundity of the Earth, ts a rather
broad hint: it is not enough to be a good Chrisian, or even a good
theologian in order to be qualified to discuss things astronomical.
In this forewarding letter Copernicus explains why he attempted
the elaboration of a new theory of planetary movements. It was the
disagreement among the mathematicians, the variance that prevailed
among them, the multiplicity of the astronomical systems ( Coper-
nicus quotes the systems of homocentric spheres, of epycicles, of
excentrics), as well as the failures of all of them to represent
exactly the apparent movements, or to remain faithful to the prin-
ciple of the uniform circular motion of the heavenly bodies, that
made him think that the “mathematicians” had either neglected some
essential principle, or, on the contrary, had introduced some false
assumption into their constructions. This would explain their failure.
But what was their error?
37 Thus Petrus Ramus reproached Copernicus for his lack of courage, wherefore
Kepler vigorously defended him. Cf. Kepler, Astronomia Nova, ed. Frisch vol. III,
p. 136. Gassendi mentions the facts in his Vita Copernici, Paris, 1654, p. 391.
88 In the body of his work he deals with the physical objections formulated by
Ptolomy against the motion of the Earth: cf. infra.
17
Copernicus informs us that in order to discover that error he
had read all the books of the philosophers dealing with this ques-
tion. He discovered that some of them believed in the movement
of the Earth. This gave him heart to try out this hypothesis him-
self, and to see if it did not furnish a better explanation of the
celestial phenomena. As a matter of fact, he found that such was
precisely the case, and that, moreover, one obtained in this way
a perfectly well ordered Universe.*®
It had been the error of the mathematicians to have made the
Earth the center of the world and of the celestial movements.
M. Dreyer, the author of one of the best modern histories of
astronomy, remarks in this connection (p. 312): According to this
statement Copernicus first noticed how great was the difference of
opinion among learned men as to the planetary motions, next he
noticed that some had even attributed some motion to the Earth
and finally he considered whether any assumption of that kind
would help matters. We might have guessed as much even if he had
not told us.
M. Dreyer who, obviously, has slight confidence in the sincerity and
outspokenness of Copernicus’ writing to the Pope, thinks that the
information given to us by the former does not enable us to give
an answer to the question: What urged Copernicus to place the
sun in the center of the word? Was he influenced by his reading of
the ancient philosophers? Does he owe the first idea of his system
to Aristarchus of Samos? Or else did he work out the heliocentric
astronomy first and then find in the writings of the ancients en-
couragement and corroboration ?*°
It is true that the account of Copernicus is somewhat reserved and
reticent. And yet, if he does not give us the history of his thought,
he gives us, nevertheless, some precious, though scanty, indications
about its incentives and its motives.
Copernicus, as a matter of fact, tells us, and very clearly so, his
objections to all the other systems of ancient and medieval astron-
omy: it is, in the first place, the fact that they are unable to remain
89 N. Copernicus, De Revolutionibus. Preface: “The order and the magnitude of
the stars and their orbs and the heaven itself are so connected that in no part can
anything be transposed without confusion to the rest and to the whole Universe.”
40 Aristarchos of Samos is not mentioned in the printed work. Yet, in the MS his
name follows those of Philolaos and Hiketas.
18
faithful to the principle of the uniformity of the circular motion
of the heavenly- bodies, which in Copernicus’ opinion means that
they are physically impossible. It is, in the second place, the fact
that they give us a disconnected and irrational picture of the
Universe.
ies
In the body of his book, Copernicus, in setting forth the difficulties
inherent in the theory of the movements of Venus and Mercury,
gives an account of a theory, mentioned by Martianus Capella, ac-
cording to which both planets center their movements around the
Sun, or, more simply, revolve around the Sun. He adds that if any-
body were to follow this hint, he would make the Sun the center of
the movements of Saturn, Jupiter and Mars, and would have found
the true explanation of their movements. Is this perhaps a reminis-
cence of the path his thought had followed?
In the Narratio prima J. Rheticus says that it was the great varia-
tions in the brightness of the planet Mars . . . which no geocentric
theory could explain that convinced Copernicus that this planet
did not revolve around the Earth, but had the center of its move-
ments in the Sun. This seems to point to the same trend of thought.
And yet, if Copernicus had reasoned according to this pattern, he
would have developed the system of Tycho Brahe.** Not his own.
It may be, as Apelt and Dreyer point out, that Copernicus noticed
that the movement of the sun along the zodiac played a very im-
portant part in the astronomy of Ptolemy; particularly, that the
period of revolution of the deferent of the inner, was equal to one
year and that of the epicycles of the outer to the synodic period.*?
Joachim Rheticus seems to confirm this assumption. He says in his
Commentariolus (p. 139) that “Under the commonly accepted prin-
ciples of astronomy, it could be seen that all the celestial phenomena
conform to the mean motion of the sun and that the entire harmony
of the celestial motions is established and preserved under its con-
41 In Tycho Brahe’s astronomy the planets revolve around the sun, and the whole
system revolves around the immobile Earth. From the point of view of calculations—
which deal only with relative positions and motions—there is absolutely no difference
between this system and that of Copernicus. The reason why Tycho Brahe imagined
this device seems to be the fact that the Copernicans were unable to refute the
physical objections against the motion of the Earth.
42 Cf. Dreyer, op. cit., p. 312: “It must have struck him as a strange coincidence
that the revolution of the sun round the zodiac and the revolution of the epicycles’
centers of Mercury and Venus round the zodiac should take the same period, a
year, while the period of the three outer planets in their epicycles was the synodic
period, i.e. the time between two successive oppositions to the sun.”
19
trol. Hence the sun was called by the ancients leader, governor of
nature, and king.” (p. 139). It was not very difficult to deduce from
this statement that the above mentioned circles were nothing else
than the projection of the orbital motion of the Earth around the
Sun; and, perhaps, to back this discovery by the contention that,
in order to exercise his power and leadership the Sun had no need
to travel around the world; just as “the Emperor does not hurry
from place to place to impose his rule and authority on his realm”’
(zd.); and finally, to affirm that, after having created the Sun
To whose rhythm the gods move, and the world
Receives its laws and keeps its pace ordained
“God stationed in the center of the stage this governor of nature,
king of the entire Universe, conspicuous by its divine splendor’
(p. 142).
All that is possible. Copernicus, as well as Rheticus, is full of
Pythagorism.
Copernicus objects to the Astronomy of his time because of its
great complication. It is better to admit the movement of the Earth,
says he, though it may appear absurd, than to let one’s mind be
distorted and torn asunder by the nearly infinite multitude of circles
and orbs of the geocentric astronomy. And, as a matter of fact, when
we see the schematic picture of his system of the Universe, we are
taken in by its apparent simplicity and beauty. Yet, this impression
is not quite correct. The number of circles in the astronomy of
Ptolemy was not as large as he says. And they were by no means
absent in that of Copernicus. There were 42 cycles in the system
of Ptolemy. And there are 34 in the Copernican. Eight cycles is all
we gain. Those who thought that the gain was not big enough for
the price cannot be blamed.
Strange as it seems, Copernicus does not particularly insist in the De
Revolutionibus on the real gain of his system: on its physical systema-
tization and simplification, on the fact that a great number of
particular movements of the celestial bodies are, from now on, ex-
plained as the apparent result of one and only one real movement,
namely the movement of the Earth. Nor does he insist on the fact
that the role of the Sun or of the solar period in all of the planetary
motions is from now on explained in a perfectly easy and natural
way.
20
Yet if Copernicus fails to do so, his pupil does it for him. Rheticus
does not only reproach the Ptolemaic system for its endless invention
of spheres but opposes to it: “the remarkable symmetry and inter-
connection of the motions and spheres, as maintained by the as-
sumption of the foregoing hypotheses, are not unworthy of God's
workmanship and not unsuited to these divine bodies” (p. 145).
Rheticus does not stop with that. He sees a deep meaning and a
confirmation of the Copernican astronomy not only (as Copernicus
himself) in the fact that the speed—or the slowness — of the
planetary movements correspond to their distance from the Sun, but
even in the fact that this astronomy reduces their number from seven
to six: There are, in the Copernican world, no more than “six moOv-
ing spheres which revolve about the sun, the center of the universe.”
And Rheticus adds (p. 146, 7), “Who could have chosen a more
suitable and more appropriate number than six? By what number
could anyone more easily have persuaded mankind that the whole
Universe was divided into spheres by God the Author and Creator
of the World? For the number six is beyond all others in the sacred
prophesies of God and by the Pythagoreans and other philosophers.
What is more agreeable to God’s handiwork than that his first and
most perfect work should be summed up in the first and most
perfect number ?”
Another objection of Copernicus to the Ptolemaic astronomy
—a philosophical one—appears at first glance to be very strong.
Copernicus says—and, of course, he is quite right—that it 1s absurd
to want to move the Jocus and not the /ocatum, and that, therefore,
the starry sky which, according to Aristotle, is the locus of the Unt-
verse, must be considered as unmoved.
This seems to us a perfectly well reasoned out argument. Indeed,
we feel that it is contrary to reason (and even, perhaps, to common
sense) to let the whole immense (or, for us, infinite) Universe re-
volve around a tiny speck of dust. We feel convinced. But the Aris-
totelian (or Ptolemaic) is not. His Universe, though pretty large,**
43 The Universe of Copernicus is immensum, that is immeasurable; yet not infinite.
It is much larger than the Universe of Ptolemy (though this, too, was rather large)
because Copernicus must explain why—if the Earth does move on its orbit around
the sun—the (fixed) stars appear always in the same position; in other terms, why
there is no paralax? Copernicus answers by assuming that the dimensions of the
sphere of the fixed stars is “in no proportion” with that of the orb of the Earth,
and therefore, literally, immeasurable. No wonder that this answer did not appeal
to his contemporaries. We must not blame them: we must admire the boldness
of Copernicus.
oe I
is by no means immense (and he objects to its—from his point of
view—motiveless extension by Copernicus**) ; he feels that there is
a fundamental, qualitative, opposition between the heavy, inert
Earth and the imponderable heavenly spheres: to move the first an
external, material motor of a tremendous power would be needed;
the motion of the latter, on the contrary, is a sequel of their perfec-
tion, of their nature itself. Therefore, concludes the Ptolemaic from
the self same premises as Copernicus, the mobile sphere is mot the
locus of the Universe, and. thus, we must admit above it another
one, which is the true, immobile sphere (the eighth, or ninth, or
tenth .. .)
The proofs that Copernicus advances for his system are curious.
In fact, they do not prove anything at all. From the point of view
of his adversaries they are worthless. His refutation of the physical
objections of the Ptolemaics against the motion of the Earth are,
too, rather feeble. Withal, they are of a tremendous historical im-
portance.
Copernicus shows us that, from the optical point of view, it is
impossible to decide whether it is the observer or the observed who
are in motion. Quite right, would the Prolemaic answer; the well
known relativity of motion*® implies doubtlessly that the motion of
the Earth is optically possible. But it implies at the same time—
always from the optical point of view—that it does not present any
advantage as compared with its immobility.
To the physical objection that the rotation of the Earth would
engender a tremendous centrifugal power which would blow it to
pieces, Copernicus replies that the self same objection could be
raised against the motion of the skies, the more so as the velocity
of their motion is infinitely greater than that of the Earth.
As a matter of fact, from the point of view of the Ptolemaic,
Copernicus is wrong, because the motion of the heavenly spheres,
considered as imponderables, is of a quite different nature from that
of the ponderable Earth, and could not give birth to a centrifugal
force. Besides, the revolution of the skies being for them a natural
44 Once more we must not blame Copernicus for that, but on the contrary, admire
him more because, as a matter of fact, no proof was possible without an extensive
use of optical instruments and without an elaboration of a new physics, i.e. not
before the middle, or even the: end, of the XVIIth century.
45 On the theories of space and motion cf. P. Duhem, Le mouvement absolu et
le mouvement relatif, Paris, 1905.
22
motion, cannot be the cause of an effect which would endanger
their conservation and being.
We must not smile at these arguments.*® From the point of view
of the Aristotelian physics they are perfectly valid. Besides, Coper-
nicus himself makes use of them in order to show that, if the
Earth revolved around its axis, it would be a natural motion, where-
fore none of the effects deduced (hypothetically) by Ptolemy, on
the assumption that this motion would be a violent one and contra
naturam, would, as a matter of fact, take place.
We see that Copernicus—as everybody until Galileo and Des-
cartes—accepts the distinction between natural and violent motions;
he only asserts that the same laws apply to the Heavens and to the
Earth and, by doing this, he lays the ground for that deep-reaching
transformation of human thought to which History has given the
name of Copernican Revolution.
But this we shall see more clearly by glancing at the Copernican
dynamics.
‘oe.
The dynamics of Copernicus is by no means “modern.” Never-
theless, an abyss separates it from that of his contemporaries, be-
cause, spontaneously and unhesitatingly he applies the geometrical
point of view to the Universe. Even his esthetics is a geometrical
one: the esthetics of geometry, or more exactly, of geometrical
optics. His physics, too—though he never says so expressis verbis,
and perhaps does not even recognize it clearly and distinctly—is
a geometrical physics.
Not quite, of course. Copernicus still uses a “physics,” that is a
theory of nature, or better to say, a theory of natures; and yet the
geometrization of his thought is deep and strong enough to trans-
form completely the fundamental Aristotelian notion of form itself.
Thus, when and where medieval and classical physics talked
about form, they usually meant: substantial forms; Copernicus, on
the contrary, has geometrical form in mind.
The implications, as may be seen readily, are numerous and far-
reaching. For instance, whereas for ancient physics it was the specific
46 For the discussion of these arguments cf. my N. Copernic, Des Révolutions des
Orbes célestes, 1.1., texte, traduction, notes, Paris, 1933 et my Etudes Galiléennes,
v. III, Paris, 1940.
23
nature of a definite substantial form (and, of course, of the corre-
sponding matter) which determined the kind of natural movement
pertaining to a body (rectilinear for the sublunar, circular for the
heavenly bodies), it is its geometrical form which plays that réle for
Copernicus. If the celestial bodies move around themselves, it is not
because they have a specific nature, it is simply because they are
spherical.
Copernicus seems to believe that the spherical shape,—the geo-
metrically most perfect form that all natural bodies seek for this
reason — naturally engenders the most perfect, the most natural
movement, i.e. the circular one. Thus (a) the same reasoning en-
ables and even obliges us to ascribe to the Earth the same circular
motion with which the planets are endowed (and this is the reason
why Copernicus dwells at such length and with such a profusion
of arguments upon the sphericity of the Earth which nobody in his
time doubted, and which—if it were not so tremendously important
—could therefore be treated as a matter of common knowledge)
(b) the same laws of motion which apply to the planets, are valid
also for the Earth, (c) partaking of the same circular form, and
following the same laws of motion, the Earth no longer stands in
Opposition to the moving heavenly bodies as a world apart—an
Underworld—but forms with them a single and unique Universe.
The geometrization of the concept of form placed the Earth
among the stars, and, so to say, lifted it into the skies.
We understand now why Copernicus attributes such an impor-
tance to the rule or principle of the uniform circular motion and
considers it as the basis of his whole celestial mechanics.
It was, for him, the only means to put the machina mundi into
motion. In the dynamics of Copernicus—a curious dynamics, as
we are seeing, a dynamics which he had, perhaps, inherited from
Nicolaus of Cues,** the (circular) movement is caused by (or due
to) the (spherical) form of the bodies. The bodies turn around be-
cause they are round, without an external (or even internal) motor.
Put a round body (a sphere) into space, and it will turn around.
Place an orb into it: it, too, will revolve around itself, without having
any need either of a motor to keep up its movement, or of a physical
center which would support it. And this is the dynamical reason
47 Cf. Riccioli, Almagestum Novum, Bononiae, 1651, and L. Birkenmajer, Mikotaj
Kopernik, Krakéw, 1900, p. 461.
24
why, having expelled the Earth from the center of the movements
of the World, Copernicus can leave it empty.
It is a fact that, if Copernicus places the Sun in the center of the
Universe, he does not place it in the center of the celestial move-
ments. The sun does not play any role in the celestial mechanics of
Copernicus. Its role is quite different. It is purely optical. It lights,
or gives light, to the Universe—and that is all.
Yet I am quite wrong in saying: that is all. For the function per-
formed by the sun, the function of illuminating and lighting the
Universe, is, for Copernicus, of extreme and supreme importance.
It is this function which explains and secures the place that it holds
in the World: first in dignity and central in position. It is in order
to give light to the Universe that the sun, this lam pada pulcherrima,
is placed in its center—a position that is, obviously, the most fitting
for this end. And this is the reason—the true reason—which in-
spired the thought and the soul of Copernicus. It is not a purely
scientific reason. It is much more than that.
Old traditions, the tradition of the metaphysics of light (meta-
physics which during the entire Middle Ages bears and accompanies
the study of the geometrical optics), Platonic and New Platonic or
Pythagorean reminiscences and revivals (the visible sun representing
the invisible one, the sun being the master and king of the visible
world and thus representing God) can alone—at least in my opin-
ion,—explain the emotion with which Copernicus speaks about the
Sun. He adores it, and almost deifies it.*®
People who, like Digby and Bruno, and others, have linked the
Copernican astronomy with a kind of heliolatry, who, at the same
time have felt themselves raised into the skies, were by no means
infidel to the inspiration of the great Polish thinker.
Copernicus, as I have said it so often and as Dreyer has said it
long before me, is not a Copernican. He is not a “modern.” His
Universe is not the infinite space of the classical physics. It has
limits, just as that of Aristotle. It is larger, of course, much larger,
48 N. Copernicus, De Revolutionibus, cap. X ‘For who could in this most beau-
tiful temple place this lamp in another or better place than that from which it can
at the same time illuminate the whole? Which some not unsuitably call the light of
the world, others the soul of the ruler. Trismegistus calls it the visible God, the
Electra of Sophocles the All seeing. So indeed the Sun, sitting on the royal throne,
steers the revolving family of stars.”
25
so large as to be immeasurable (immensum), and yet finite, con-
tained in, and limited by, the sphere of the fixed stars. The sun is
in its center. And, around the sun rise the orbs (which bear and
carry the planets), orbs just as real as the crystalline spheres of the
medieval cosmology.*® The orbs revolve because of their form and
carry with them the wandering planets, which are set in them as
jewels are set in their mount. ...
Splendid order, luminous astro-geometry, magnificent cosmo-
optics, which replaces the astro-biology of the Ancients.
* *+*. *
The ways of Spirit, as the ways of God, are quaint and curious.
And truly great minds are only inflamed and inspired by infinite
goals. uf
49 As I have already stated (cf. Supra p. 713, mn. 21; p. 720) not all astronomers
believed in the physical reality of their spheres, orbs, and circles. Tycho Brahe, for
instance, did not. Copernicus, on the other hand, certainly did. This may appear strange
to us, and we may feel inclined to ask: how could he believe in the orb of the Earth?
Yet Kepler confirms my interpretation (Cf. Kepler, Opera Omnia, VII, p. 181). Once
more, we must not modernize the thought of Copernicus. Besides, we must not forget
that even Descartes found no difficulty whatever in this conception and felt himself
compelled, in order to explain the movements of the Earth and of the planets, to admit,
for dynamic reasons, the existence of some kind of orbs (which he called tourbillons).
26
’ : Be:
ge Ce desk, FUE, Jeezrr, Qtatromtetk fH
CI Ne
GALILEO AND THE SCIENTIFIC REVO-
LUTION OF THE SEVENTEENTH
CENTURY
ALEXANDRE KOYRE
Reprinted from THE PHILOSOPHICAL Review, July, 1943
Reprinted from THE PuiLosopHicaL REvIEW, July, 1943
GALILEO AND THE SCIENTIFIC REVOLUTION
OF THE SEVENTEENTH CENTURY
ODERN science did not spring perfect and complete,- as
Athena from the head of Zeus, from the minds of Galileo
and Descartes. On the contrary, the Galilean and Cartesian revolu-
tion—which remains, nevertheless, a revolution—had been pre-
pared by a strenuous effort of thought. And there is nothing more
interesting, more instructive, nor more thrilling, than to study the
history of that effort; to write the story of the human mind deal-
ing obstinately with the same everlasting problems, encountering
the same difficulties, struggling untiringly with the same obstacles,
and slowly and progressively forging for itself instruments and
tools, new concepts, new methods of thinking, which will enable it
to overcome them.
It is a long and thrilling story ; too long to be told here. Yet, in
order to understand the origin, the bearing and the meaning of the
Galileo-Cartesian revolution, we cannot dispense with throwing
at least a glance backwards, on some of the contemporaries and
predecessors of Galileo.
Modern physics studies, in the first line, the motion of ponderous
bodies, i.e., the motion of bodies which surround us. Thus it is
from the effort to explain the facts and the phenomena of common,
everyday, experience—the act of falling, the act of throwing—that
proceeds the trend of ideas which leads to the establishment of
its fundamental laws. Yet it does not proceed therefrom exclu-
sively, or even principally, or in a direct way. Modern physics
does not originate from earth alone. It comes, just as well, from
the skies. And it is in the skies that it finds its perfection and end.
This fact, the fact that modern physics has its “prologue” and
its “epilogue” in the skies, or, to speak a more sober language,
the fact that modern physics takes its origin from the study of
333
334 THE PHILOSOPHICAL REVIEW [Vor. LIT.
astronomical problems and maintains this tie throughout its his-
tory, has a deep meaning, and carries important consequences. It ex-
presses the replacement of the classic and medieval conception of
the Cosmos—closed unity of a qualitatively determined and
hierarchically well ordered whole in which different parts (heaven
and earth) are subject to different laws—by that of the Universe,
that is of an open and indefinitely extended entirety of Being, gov-
erned and united by the identity of its fundamental laws; it deter-
mines the merging of the Physica coelestis with Physica terrestris,
which enables the latter to use and to apply to its problems the
methods—the hypothetico-deductive mathematical treatment—de-
veloped by the former; it implies the impossibility of establishing
and elaborating a terrestrial physics, or, at least, a terrestrial me-
chanics, without a celestial one; it explains the partial failure
of Galileo and Descartes.
Modern physics, which, in my opinion, is born with, and in, the
works of Galileo Galilei, looks upon the law of inertial motion as
its basic and fundamental law. It does so quite correctly, for
ignorato motu ignoratur natura, and modern science aims at the
explaining of everything by “number, figure, and motion”. True,
it was Descartes, and not Galileo—as I believe I have established
in my illfated Galilean Studies'—who for the first time fully under-
stood its bearing and its meaning. And yet Newton is not wholly
incorrect in giving full credit for it to Galileo. As a matter of fact,
though Galileo never explicitly formulated this principle—nor
could have—his mechanics, implicitly, is based upon it. And it is
only his reluctance to draw, or to admit, the ultimate consequences
—or implications—of his own conception of movement, his reluc-
tance to discard completely and radically the experiential data for
the theoretical postulate he worked so hard to establish, that pre-
vented him from making the last step on the road which leads
from the finite Cosmos of the Greeks to the infinite Universe of
the Moderns.
The principle of inertial motion is very simple. It states that
a body, left to itself, remains in its state of rest or of motion as
long as it is not interfered with by some external force. In other
*A. Koyré, Etudes Galiléennes, Paris, 1940.
No. 4.] GALILEO AND THE SCIENTIFIC REVOLUTION 335
words, a body at rest will remain eternally at rest unless it is
“put in motion”. And a body in motion will continue to move, and
to persist in its rectilinear uniform motion, as long as nothing
prevents it from doing so.?
The principle of inertial motion appears to us perfectly clear,
plausible, and even, practically, selfevident. It seems to us pretty
obvious that a body at rest will remain at rest, 1.e., will stay where
it is—wherever that may be—and will not move away on its own
accord. And that, converso modo, once put in motion, it will con-
tinue to move, and to move in the same direction and with the
same speed, because, as a matter of fact, we do not see any reason
nor cause why it should change either. All that appears to us not
only plausible, but even natural. Yet it is nothing less than that.
In fact, the “evidence” and the “‘naturalness” which these concep-
tions and considerations are enjoying are very young: we owe
them to Galileo and Descartes, whereas to the Greeks, as well as
to the Middle Ages, they would appear as “evidently” false, and
even absurd.
This fact can only be explained if we admit—or recognize—
that all these “clear” and “‘simple” notions, which form the basis
of modern science, are not “clear” and “simple” per se et in se,
but only as a part of a certain set of concepts and axioms, apart
from which they are not “‘simple” at all. This, in turn, enables us
to understand why the discovery of such simple and easy things
as, for instance, the fundamental laws of motion, which today are
taught to, and understood by, children, has needed such a tremen-
dous effort—and an effort which often remained unsuccessful—by
some of the deepest and mightiest minds ever produced by man-
kind: they had not to “discover” or to “establish” these simple
and evident laws, but to work out and to build up the very frame-
work which made these discoveries possible. They had, to begin
with, to reshape and to re-form our intellect itself; to give to it a
series of new concepts, to evolve a new approach to being, a new
concept of nature, a new concept of science, in other words, a new
philosophy.
?Sir Isaak Newton, Philosophiae Naturalis Principia Mathematica;
Axiomata sive leges motus; Lex I: Corpus omne perseverare in statu suo
quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus
impressis cogitur statum ille mutare.
Se
336 THE PHILOSOPHICAL REVIEW _[Vot. LIU.
We are so well acquainted with, or rather so well accustomed
to, the concepts and principles which form the basis of modern
science, that it is nearly impossible for us to appreciate rightly either
the obstacles that had to be overcome for their establishment, or
the difficulties that they imply and encompass. The Galilean con-
cept of motion (as well as that of space) seems to us so “natural”
that we even believe we have derived it from experience and
observation, though, obviously, nobody has ever encountered an
inertial motion for the simple reason that such a motion is utterly
and absolutely impossible. We are equally well accustomed to the
mathematical approach to nature, so well that we are not aware
of the boldness of Galileo’s statement that “the book of nature is
written in geometrical characters”, any more than we are conscious
of the paradoxical daring of his decision to treat mechanics as
mathematics, that is, to substitute for the real, experienced world
a world of geometry made real, and to explain the real by the
impossible.
In modern science, as well we know, motion is considered as
purely geometrical translation from one point to another. Motion,
therefore, in no way affects the body which is endowed with it ;
to be in motion or to be at rest does not make any difference to,
or produce a change in, the body whether in motion or at rest.
The body, as such, is utterly indifferent to both. Consequently, we
are unable to ascribe motion to a determined body considered in
itself. A body is only in motion in its relation to some other body,
which we assume to be at rest. We can, therefore, ascribe it to
the one or to the other of the two bodies, ad libitum. All motion
is relative.
Just as it does not affect the body which is endowed with it, the
motion of a body in no way interferes with other movements that
it may execute at the same time. Thus a body may be endowed
with any number of motions, which combine to produce a result
according to purely geometrical rules; and, vice versa, every given
motion can be decomposed, according to these same rules, into any
number of component ones.
Yet, all this notwithstanding, motion is considered to be a State,
and rest another state, utterly and absolutely opposed to the former,
No. 4.] GALILEO AND THE SCIENTIFIC REVOLUTION 337
so that we must apply a force in order to change a state of motion
of a given body to that of rest, and vice versa. 7
It is therefore perfectly evident that a body in a state of motion
will persist in this state forever; and that it will no more need a
force or a cause by which to explain, or to maintain, its uniform,
rectilinear movement, than it will need one by which to explain
or to maintain its rest. ; :
Thus, in order to appear evident, the principle of inertial motion
presupposes (a) the possibility of isolating a given body from all
its physical environment, (b) the conception of space which
identifies it with the homogeneous, infinite space of Euclidian
geometry, and (c) a conception of movement—and of rest—
which considers them as states and places them on the same
ontological tevel of being. :
No wonder that these conceptions appeared pretty difficult to
admit—and even to understand—to the contemporaries and prede-
cessors of Galileo; no wonder that to his Aristotelian adversaries
the notion of motion as a persistent, substantial relation-state
appeared just as abstruse and contradictory as the famous sub-
stantial forms of the scholastics appear to us; no wonder that
Galileo Galilei had to struggle before he succeeded in forming that
conception, and that great, but somewhat lesser, minds, such as
Bruno and even Kepler, failed to reach that goal. As a matter of
fact, even today, the conception we are describing is by no means
easy to grasp, as anyone who ever attempted to teach physics to
students who did not learn it at school will certainly testify.
Common sense, indeed, is—as it always was—medieval and
Aristotelian.
We must now give our attention to the pre-Galilean, chiefly
Aristotelian, conception of motion and of space. I will not, of
course, endeavor to give here an exposition of Aristotelian physics ;
I will only point out some of its characteristic features as opposed
to the modern; and I would like to stress, because it is fairly
widely misappreciated, that the Aristotelian physics is a ind
thoroughly thought out, and very coherent, body of i OR
knowledge, which, besides having a very deep philosophica
‘ —_ ne en Oe
en el Se ° ee
338 THE PHILOSOPHICAL REVIEW [Vor. LIT.
foundation, is, as stated by P. Duhem and P. Tannery,? in pretty
good accordance—a much better one, indeed, than the Galilean—
with the experience, at least with the commonsense experience, of
our everyday life.
Aristotelian physics is based on sense-perception, and is therefore
decidedly non-mathematical. It refuses to substitute mathematical
abstractions for the colorful, qualitatively determined facts of
common experience, and it denies the very possibility of a mathe-
matical physics on the ground (a) of the nonconformity of mathe-
matical concepts to the data of sense-experience, (b) of the inabil-
ity of mathematics to explain quality and to deduce movement.
There is no quality, and no motion, in the timeless realm of figure
and number.
As for motion—xivys1g—or rather “local motion”—Aristotelian
physics considers it a kind of process of change—in contradis-
tinction with rest, which, being the goal and the end of motion,
is to be recognized as a state.t Motion is change (actualization or
decay) and consequently a body in motion changes not only its
relations to other bodies, but, at the same time, undergoes itself
a processus of change. Motion, therefore, always affects the body
which endures it, and, consequently, if a body is endowed with
two (or more) movements, these movements interfere with each
other, impede each other, and even are, sometimes, incompatible
with each other. Besides, Aristotelian physics does not admit the
right, nor even the possibility, of identifying the concrete world-
space of its well ordered and finite Cosmos with the “space” of
geometry, no more than it admits the possibility of isolating a given
body from its physical (and Cosmical) environment. In dealing
with a concrete physical problem it is, therefore, always necessary
to take into account the world order, to consider the realm of being
(the “natural place”) to which a given body belongs by its nature;
and, on the other hand, it is impossible to try to subject these
different realms to the same laws, even—and perhaps especially—
to the same laws of motion. E.g., heavy things descend whereas
3 .
OME nba Le ha dabted = Monde I (Paris, 1915) 194 sq; P. Tannery
rincipes de ique”, Mémoi lentt at
1926) phe 9 p Dp a Dynamique , Mémoires scientifiques VI (Paris,
or Aristotle rest, being a deficienc watio, i
t Fa cy, privatio, is on a lower ontolo
level than motion, actus entis in potentia inquantum est in potentia. —
No. 4.] GALILEO AND THE SCIENTIFIC REVOLUTION 339
light ones ascend; terrestrial bodies move in right lines, celestial
ones in circles, and so on.
It is evident, even from this brief account, that motion, con-
sidered as processus of change (and not as state), cannot go on
spontaneously and automatically, that it requires, for its persist-
ence, a continuous action of a mover or cause, and that it stops
dead as soon as this action does not exercise itself upon the body
in motion, i.e., as soon as the body in question is separated from
its mover. Cessante causa, cessat effectus. It follows therefrom,
with absolute necessity, that the kind of motion which is postulated
by the principle of inertia is utterly and perfectly impossible, and
even contradictory.
And now we must come to the facts. I have said already that
modern science originated in close connection with astronomy ;
more precisely, it takes its origin in, and from, the necessity of
meeting the physical objections formulated by some of the leading
scientists of the time against the Copernican astronomy. As a
matter of fact, these objections were nothing less than new: quite
to the contrary, though presented sometimes in a slightly modern-
ized form, as by replacing the throwing of a stone of the older
argument by the firing of a cannon ball, they were fundamentally
identical with those that Aristotle and Ptolemy raised against the
possibility that the earth moves. It is very interesting, and very
instructive, to see them discussed and rediscussed by Copernicus
himself, by Bruno, Tycho Brahe, Kepler, and Galileo.*
Divested from the imaginative clothing which they gave them,
the arguments of Aristotle and Ptolemy can be boiled down to the
statement that, if the earth were moving, this movement would
affect the phenomena occuring on its surface in two perfectly
definite ways: (1) the tremendous velocity of this (rotational)
movement would develop a centrifugal force of such a magnitude
that all the bodies not connected with the earth would fly away,
and (2) this same movement would cause all bodies not con-
nected, or temporarily disconnected with it, to lag behind. There-
fore, a stone falling from the summit of a tower would never land
°Cf. my Etudes Galiléennes, III, Galilée et le principe d’inertie, Paris,
1940.
340 THE PHILOSOPHICAL REVIEW [Vot. LIT.
at its foot, and, a fortiori, a stone (or a bullet) thrown (or shot )
perpendicularly into the air would never fall back to the place
from which it departed, because, during the time of its fall or
flight, this place would be “quickly removed from below it and
rapidly moved away”.
We must not smile at this argument. From the point of view of
the Aristotelian physics it is perfectly sound. So sound that, on the
basis of this physics, it is utterly irrefutable. In order to destroy it
we must change the system as a whole and evolve a new concept
of movement: The concept of movement of Galileo.
As we have already seen, motion for the Aristotelian is a process
which affects the moved, which takes place “in” the body in
motion. A falling body moves from A to B, from a certain place
situated above the earth, toward the latter, or, more eiinctSy,
towards its center. It follows the straight line which Lisiiciisek
these two points. If during this movement the earth revolved
around its axis, it would describe, in respect to this line (the line
leading from A to the center of the earth) a movement in which
neither this line, nor the body which follows it, take any part
whatever : the movement of the earth does not affect the body
which is separated from it. The fact that the earth beneath it
This conception may appear strange to us. But it is by no means
absurd: it is exactly in that way that we represent ourselves the
movement—or propagation—of a ray of light. And it implies that
if the earth were moving, a body thrown from the top of a ihipeie
would never fall at its foot ; and that a stone, or a cannonball shot
vertically in the air, would never fall back to the place here it
went from. It implies, a fortiori, that a stone or a ball falling from
the top of the mast of a moving ship will never fall at its foot.
What Copernicus himself has to reply to the Aristotelian is very
poor, He argues that the unhappy consequences deduced by this
No. 4.] GALILEO AND THE SCIENTIFIC REVOLUTION 341
latter would follow, indeed, in the case of a “‘violent’’ movement.
But not in that of the movement of the earth, and to the things
that belong to the earth: for them it is indeed a natural movement.
This is the reason why all these things, clouds, birds, stones, etc.,
etc., partake in the movement, and do not lag behind.
The arguments of Copernicus are very poor. And yet they bear
the seed of a new conception which will be developed by later
thinkers. The reasonings of Copernicus apply the laws of “celestial
mechanics” to terrestrial phenomena, a step which, at least implic-
itly, involves abandoning the old, qualitative division of the Cosmos
into two different worlds. Besides this, Copernicus explains the
apparently rectilinear path of the falling body by its participation
in the movement of the earth; this movement, being common to the
earth, to the body, and to ourselves, remains for us “as if it were
non-existent”.
The arguments of Copernicus are based on the mythical con-
ception of a “community of nature” between the earth and
“earthen” things. Later science will have to replace it by the
concept of the physical system, of the system of things sharing
the same movement; it will have to rely upon the physical and not
only upon the optical relativity of motion. All of which is im-
possible on the basis of the Aristotelian philosophy of motion and
makes it necessary to adopt another philosophy. As a matter of
fact, as we shall see more and more clearly, it is with a philo-
sophical problem that we are dealing in this discussion.
The conception of physical or, rather, mechanical system, which
was implicitly present in the arguments of Copernicus, was worked
out by Giordano Bruno. By a stroke of genius Bruno saw that it
was necessary for the new astronomy to abandon outright the
conception of a closed and finite world, and to replace it by that
of an open and infinite Universe. This involves the abandonment
of the notions of “natural” places and motions as opposed to non-
natural, violent ones. In the infinite universe of Bruno, in which
the Platonic conception of space as “receptacle” (yopa) takes the
place of the Aristotelian conception of space as envelope, all
“places” are perfectly equivalent and therefore perfectly natural
for all bodies. Therefore whereas Copernicus distinguishes be-
tween the “natural” moyement of the earth and the “violent”
342 THE PHILOSOPHICAL REVIEW [Vo.. LII
ee of the things upon it, Bruno expressly assimilates them.
a appens on the earth if we suppose it in movement has
as he explains, its exact counterpart in what happens on hi ,
Bibi on the surface of the sea; and the movement of a aiech
ee — oe upon the movement on the earth than the
mt € ship on those of the things that are in the ship.
consequences deduced by Aristotle would only take place if
No. 4.] GALILEO AND THE SCIENTIFIC REVOLUTION 343
repeats imperturbably the old Aristotelian objections (though in a
somewhat modernized presentation) ; nor even on Kepler, who,
though influenced by Bruno, deems himself obliged to return to
those of Copernicus, replacing, indeed, the great astronomer’ s
mythical conception of the community of nature by a physical con-
ception, that of the force of attraction.
Tycho Brahe flatly denies that a bullet falling from the top of
the origin, i.e., the place of departure, of the moving bod
external to, and not connected with, the earth. a
Bruno states that the place of origin as such does not plav a
role in the determination of the motion (the path) of ea a
body, that what is important is the connection—or lack of oeing
tion—of this “place” with the mechanical system. It is even
Oe ca ae
ible—horribile dictu—for the selfsame “place” to pertain to two
or more systems. Thus, for instance,
one of them on the top of the mast o
the mast of a moving ship will come down at its foot. He affirms
that, quite on the contrary, it will lag behind, and lag behind the
more the faster the ship is moving. Just as cannonballs, shot verti-
cally in the air, would never—on a moving earth—be able to
come back to the cannon.
Tycho Brahe adds that, if the earth were moving, as Copernicus
wants it, it would never be possible to send a cannonball to the
same distance to the east and to the west: the extremely rapid
movement of the earth, if it were shared by the ball, would
impede its own movement and even, if the ball had to move in a
direction opposite to that of the movement of the earth, render it
utterly impossible. The point of view of Tycho Brahe appears to
us pretty strange. Yet we must not forget that to him the theories
of Bruno seemed utterly unbelievable and even exaggeratedly
anthropomorphic. To pretend that two bodies, falling from the
same place and going to the same point (the center of the earth),
will follow two different paths, describe two different trajectories,
for the reason that one of them was associated with the ship,
whereas the other was not, means for the Aristotelian to pretend
if we imagine two men,
f a ship passing under a
bridge, and the other on that bridge, we may imagine, further, that
at a certain moment, the hands of both of them will be ” the nan
place. If, at that moment, each of them shall let a stone fall ke
stone of the man on the bridge will fall down (and in the cas,
i stone of the man on the mast will follow the movement of
ag ip, and (describing, relatively to the bridge, a peculiar curve )
all at the foot of the mast. The reason for this different behavior
explains Bruno, is simply the fact that the last stone, having shared
the movement of the ship, retains in it a part of the “moving virtue”
which has been impressed into it.
5 a Oe a a ee 2 ee RIPON tg ER a et
| As we see, Bruno substitutes for the Aristotelian dynamics the
nea atiee of the Parisian nominalists. It seems to him
at this dynamics provides a sufficient basis for his construction
: reer which, as history has shown us, was an error. It is true
at the conception of the impetus, virtue, or power, which animates
th
oe body, produces its motion, and uses itself up in this
Production, enabled him to refute the arguments of Aristotle: at
;
oi some of them. Yet it was not able to meet all of them: still
ess was it able to carry the structure of modern science
The arguments of Giordano Bruno appear to us perfectly
Pha Yet in his time they made no impression whatever;
neither on Tycho Brahe, who in his polemics with tiene
PEL,
that the bullet in question remembers its past association, knows
where it has to go, and is endowed with the power and the ability
to do so. Which, in turn, implies that it is endowed with a soul.
Besides, as we have already mentioned, from the point of view
of the Aristotelian dynamics—as well as from the point of view
of the dynamics of the impetus—two different movements always
impede each other, which is proved by the well known fact that
the speedy motion of the bullet (in a horizontal flight) prevents it
from moving downwards and enables it to stay in the air much
longer than it would be able to do if we simply let it fall to the
bottom.
In short, Tycho Brahe does not admit the mutual independence
344 THE PHILOSOPHICAL REVIEW [Vor. LII.
of motions—nobody did till Galileo ; he is therefore perfectly righ
not to admit the facts, and the theories, which imply it f begs
ae position taken by Kepler is of a quite particular interest and
por ance. It shows us, better than any other, the ultimate
philoso phical roots of the Galilean revolution. From : purely scien
tific point of view, Kepler—to whom we owe, inter alia oa ‘aii
term imertia—is, undoubtedly, one of the foeinost st not -
foremost—genius of his time: it is needless to insist upon his out-
standing mathematical gifts, equalled only by the intrepidity of
his thought. The very title of one of his works Physica sais
is a challenge to his contemporaries. And yet, philosophical i
is much nearer to Aristotle and the Middle Ages than to Gali
and Descartes. He still reasons in terms of the Cosmos: for it
motion and rest are still opposed as light and darkness ‘as bein
and privation of being. Consequently, the term inertia ists ce
him the resistance that bodies Oppose, not to change of state .
for Newton, but only and solely to movement; therefore, just like
Aristotle and the physicists of the Middle Ages, he des cause
or a force to explain motion, and does not need one to explai
rest ; just like them, he believes that, separated from the has :
deprived from the influence of the moving virtue or power iota
in motion will not continue their movement, but, on the betes
will immediately stop. Therefore, in order to explain the fact dea
on the moving earth, bodies, even if they are not attached to it
by material bounds, do not “lag behind”, at least not perceptibly ;®
that stones thrown upwards come down to the spot they si
thrown from; that cannonballs fly (nearly) as far to the west as
to the east, he must admit—or find out—a real force which bind
them to the earth, and pulls them along. Dey
This force is found by Kepler in the mutual attraction of all
material, or at least of all terrestrial, bodies, which means for all
practical purposes, in the attraction of all terrestrial dani by th
earth. Kepler conceives all these things as bound to the ite i
‘innumerable elastic chains; it is the traction of these chains Dwi
explains that clouds, vapors, etc., stones, and bullets, do not sta
immobile in the air, but follow the earth in its apwericlies and ae
fact that these chains are everywhere explains, in Raters bok
* Cf. ibid, 172-94.
. ae smd <a | _ .
~ J Pm el. Rn, ot 4
eee ee ae Pa om... : “
Seiedaetiine ae a o
No. 4.] GALILEO AND THE SCIENTIFIC REVOLUTION 345
the possibility of throwing a stone or firing a cannon against its
movement: the attracting chains pull the bullet to the East as well
as to the West and thus their influence is nearly neutralized. The
real movement of the body (the cannonball shot vertically) is, of
course, a combination or mixture of (a) its own movement and
(b) that of the earth. But, as the latter is common to all the
examined cases, it is the former only that counts. It is therefore
clear (though Tycho Brahe did not grasp it) that, while the length
of the path of a bullet shot to the east and of another shot to the
west differ, as measured in the space of the universe, neverthe-
less their paths on the earth are the same or nearly the same.
Which explains why the same force, produced by the same amount
of powder, can throw them to the same distance in both directions.
The Aristotelian or Tychonian objections against the movement
of the earth are thus satisfactorily disposed of. And Kepler points
out that it was an error to assimilate the earth to the moving ship:
in fact, the earth “magnetically attracts” the bodies it transports,
the ship does not. Therefore, on a ship we need a material bond,
which is perfectly useless in the case of the earth.
We need not dwell upon this point any longer: we see that
Kepler, the great Kepler, the founder of modern astronomy, the
same man who proclaimed the unity of matter in the whole uni-
verse and stated that ubi materia, ibi geometria, failed to establish
the basis of modern physical science for one and only one reason:
he still believed that motion is, ontologically, on a higher level of
being than rest.
If now, after our brief historical summary, we turn our atten-
tion to Galileo Galilei, we shall not be surprised that he, too, dis-
cusses at great, and even at a very great, length, the timeworn
objections of the Aristotelians. We shall, moreover, be able to
appreciate the consummate skill with which, in his Dialogues on the
two greatest world systems, he marshalls his arguments and pre-
pares for the final assault on Aristotelianism.
Galileo is well aware of the tremendous difficulty of his task.
He knows perfectly well that he has to deal with powerful ene-
mies : authority, tradition, and—worst of them all—common sense.
It is useless to present proofs to minds not able to grasp their
value. Useless, for instance, to explain the difference between
346 THE PHILOSOPHICAL REVIEW [Vor. LII. No. 4.] GALILEO AND THE SCIENTIFIC REVOLUTION 347
linear and radial velocity (the confusion between which is the Thus necesse determines esse. Good physics is made a priori.
whole basis of the first of the Aristotelian and Ptolemaic objec- Theory precedes fact. Experience is useless because before any
tions) to people not accustomed to mathematical thinking. You experience we are already in possession of the knowledge we are
must begin by educating them. You must proceed slowly, step by seeking for. Fundamental laws of motion (and of rest), laws that
step, discussing and rediscussing the old and the new arguments ; determine the spatio-temporal behavior of material bodies, are laws
you must present them in various forms; you must multiply of a mathematical nature. Of the same nature as those which
examples, invent new and striking ones: the example of the rider govern relations and laws of figures and of numbers. We find
throwing his spear in the air and catching it again; the example and discover them not in Nature, but in ourselves, in our mind,
of the bowman straining his bow more and less and thus giving in our memory, as Plato long ago has taught us.
to the arrow a greater or a lesser speed; the example of the bow And it is therefore that, as Galileo proclaims it to the greatest
placed on a moving carriage and able to compensate the speed of dismay of the Aristotelian, we are able to give to propositions
the carriage by a greater or lesser speed given to his arrows. In- which describe the “symptoms” of motion strictly and purely
numerable other examples which, step by step, lead us, or rather mathematical proofs, to develop the language of natural science,
his contemporaries, to the acceptance of this paradoxical, unheard to question Nature by mathematically conducted experiments,“ and
of point of view, according to which motion is something which to read the great book of Nature which is “written in geometrical
persists in being in se et per se and does not require any cause, or characters”.
force, for its persistence. A hard task. Because, as I have already The book of Nature is written in geometrical characters: the
said, it is not natural to think of motion in terms of speed and of new, Galilean, physics is a geometry of motion, just as the physics
direction instead of those of effort, of impetus, and of momentum. of his true master, the divus Archimedes, was a geometry of rest.
But, as a matter of fact, we cannot think of motion in terms of Geometry of motion, a priori, mathematical science of nature....
effort and impetus: we only can imagine in this way. Thus we How is it possible? The old, Aristotelian objections against the
must choose: either to think or to imagine. To think with Galileo, mathematization of nature by Plato, have they, at last, been dis-
or to imagine with common sense. proved and refuted? Not quite. There is, indeed, no quality in the
For it is thought, pure unadulterated thought, and not experi- realm of number, and therefore Galileo—as, for the same reason,
ence Or sense-perception, as until then, that gives the basis for the Descartes—is obliged to renounce it, to renounce the variegated,
“new science” of Galileo Galilei. qualitative world of sense-perception and common experience and
to substitute for it the colorless, abstract Archimedian world. And
as for motion. .. there is, quite certainly, no motion in numbers.
Yet motion—at least the motion of Archimedian bodies in the
infinite homogeneous space of the new science—is governed by
number. By the leges et rationes numerorum.
Motion is subjected to number; that is something which even
the greatest of the old Platonists, the superhuman Archimedes
Galileo is perfectly clear about it. Thus discussing the famous
example of the ball falling from the top of a mast of a moving
ship, Galileo explains at length the principle of the physical rela-
tivity of motion, the difference between the motion of the body
as relative to the earth, and as relative to the ship, and then,
without making any appeal to experience, concludes that the mo-
tion of the ball, in relation to the ship, does not change with the
motion of the 1 hi iri ; are
; : atter. Moreover, when his empirically minded *« Experiment—in contradistinction to mere experience—is a question we
Aristotelian opponent asks him, “Did you make an experiment ?” put to Nature. In order to receive an answer we must formulate it in some defi-
nite language. The Galilean revolution can be boiled down to the discovery
Galileo proudly declares: “No, and I do not need it, as without of that language, to the discovery of the fact that mathematics is the gram-
any experience I can affirm that it is so, because it cannot be other- mar of science. It is this discovery of the rational structure of Nature which
gave the apriori foundations to the modern experimental science and made
= 33
wise . its constitution possible.
348 an THE PHILOSOPHICAL REVIEW
himself, did not know, something which was left to discover to
this “marvelous Assayer of Nature”, as his pupil and friend
Cavallieri calls him, the Platonist Galileo Galilei.
The Platonism of Galileo Galilei (a problem discussed by me
elsewhere’) is, indeed, quite different from that of the Florentine
Academy, just as his mathematical philosophy of nature is differ-
ent from their neo-pythagorean arithmology. But in the history of
philosophy there are more than one Platonic school, more than one
Platonic tradition, and it is still a question whether the trend of
ideas represented by Iamblichus and Proclus is more or less
Platonic than the trend represented by Archimedes.®
I will not discuss this problem here. Yet I must point out that
for the contemporaries and pupils of Galileo, as well as for Galileo
himself, the dividing line between Aristotelianism and Platonism
was perfectly clear. In their opinion the opposition between these
two philosophies was determined by a different appreciation of
mathematics as science, and of its role for the constitution of the
science of Nature. According to them, if one sees in mathematics
an auxiliary science which deals with abstractions and is, there-
fore, of a lesser value than sciences dealing with real being, such
as physics, if one affirms that physics can and must be built directly
On experience and sense-perception, one is an Aristotelian. If, on
the contrary, one claims for mathematics a superior value, and a
commanding position in the study of things natural, one is a
Platonist. Accordingly, for the contemporaries and pupils of Gali-
leo, as well as for Galileo himself, the Galilean science, the Galilean
philosophy of Nature, appeared as a return to Plato, a victory of
Plato over Aristotle.
I must confess that, to me, this interpretation seems to be per-
fectly sensible.
ALEXANDRE KoOyreE
Ecorre Lispre pes Hautes Erupes
"Cf. my article, “Galileo and Plato”, in the Journal of the History of
Ideas, 1943.
*For the whole doxographic tradition Archimedes is a philosophus
platonicus.
THE LIAR
—
ALEXANDRE KOYRE
Reprinted from
PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
Vol. VI, No. 3, March, 1946
Made in United States of America
Made in United States of America
Reprinted from PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
Vol. VI, No. 3, March, 1946
THE LIAR
The Cretan, Epimenides, said ‘All Cretans are liars.’”’ But Epimenides
is a Cretan, therefore he is a liar and, consequently, his assertion is false.
Ergo, Cretans are not liars—and this implies that Epimenides did not lie
but spoke truly. Accordingly ....
The paradox of the Liar, it seems, was popular among the Greeks. In
the Middle Ages its popularity did not wane; medieval logicians unfailingly
mention it, and propose solutions for the ‘‘insoluble’’ sophism.’ Slowly,
it was put aside and was asleep? when, in our times, Lord Russell noticed
that its logieal structure was identical with that of the mathematical
paradoxes which he discovered. The Greek sophism was, on this occasion,
elevated to the rank of an, antinomy.
*
ca a
In the twentieth century, the logico-mathematical paradoxes played an
important réle, as is well known, in the evolution of mathematical or, more
precisely, metamathematical thought. It was their discovery which
determined the “crisis of the foundations” of mathematics; and we owe the
rich development of symbolic logic, the intuitionism of Brouwer, the axio-
matics of Zermelo and Hilbert to the desire to solve or to avoid them.*
In his brilliant and important paper, A. Fraenkel® says that this discovery
has had a “terrifying” effect. The most secure foundations of science,
indeed, of reason itself, seemed to be undermined.
Today it is different —No longer does the mathematician feel himself in
danger. ‘It was recognized rather soon that the paradoxes were not of a
purely mathematical nature.’’® Moreover, “now we know that the authen-
tically mathematical theorems and disciplines are not touched by the
antinomies; that the fear of Poincare that the mathematicians in their
attempt to found the classical analysis and the theory of aggregates had
built a wall around mathematical concepts—a wall which protects them
1V. Alexander Riistow, Der Ltigher, Diss., Erlangen 1907 (Lpz. Teubner, 1908) ;
Ch. Baldwin, Dictionary of Philosophy, s.v. Insolubtlia.
2B. Russell, Principles of Mathematics, I, cap. IX, I. pp. 96 ff. App B. pp. 525
ff., Cambridge, 1903; Principia Mathematica, 2 Vol. I, pp. 8 ff.; 23 ff.; 41 ff.; 64 ff., etc.
Cambridge, 1925.
3 Cf. bibliography of Riistow, op: cit.; Cf. also Jorgensen, Treatise of Formal Logic,
3 v. Copehhagen, 1931; J. Cavaillés, Remarques sur la formation de la théorie abstraite
des ensembles, Paris, 1937; and Méthode axiomatique et formalisme, Paris, 1937.
‘Cf. Heyting, Mathematische Grundlagenforschung, Berlin, 1934.
5 A. Fraenkel, ‘“‘Le probléme des antinomies et son développement récent,’’ Revue
de Métaphysique et de Morale, 1939.
6Jb., p. 227. Cf. also the report by M. Jean Cavaillés on M. R. Poirier’s book,
Le Nombre, Paris, 1938 in the Revue de Métaphysique et de Morale, 1939.
344
Tue LIAR 345
from external dangers, but leaves inside unsuspected elements of decomposi-
tion—was unfounded. We know how to restrict the operations in order to
avoid the antinomies, and it has been recognized that the mathematician
never penetrates the dangerous area, because it is, for him, without any
interest whatever. The warning given by the antinomies has been, never-
theless, of lasting value, showing, in the first place, the necessity for a
systematic limitation of mathematical operations and, furthermore, for a
reform of the traditional Aristotelian logic. Therefrom logic received an
astonishing impulse and developed itself in an extremely fecund way,
following a direction that has been foreseen only by Bolzano and Leibniz.’’?
So all is for the best in this best possible world. Still, the uneasiness
continues—the threat was not destroyed, it was only avoided. The math-
ematician has contained the scourge; he has built a fence around it.
Nevertheless he is still in jeopardy. In the No Man’s Land of pure logic,
the Liar,. negotium perambulans in tenebris, hides out and continues in his
role of the ghostly Sword of Damocles.* Hence, it is not a cause for aston-
‘shment that the discussion of the problem has not been abandoned.’
7K. Grelling, Der Einfluss der Antinomien auf die Entwicklung der Logik im 20.
Jahrhundert. Travaux du [Xe Congrés International de Philosophie (Congrés
Descartes), fasc. VI, p. 9., Paris, 1937: ‘‘Das Problem der Antinomien...hat...
wie mir scheint, auf den Gang der Entwicklung dér Logik in unserem Jahrhundert
einen beherrschenden Einfluss getibt, der sich bis in die letzten Jahre verfolgen
lisst und wohl auch heute noch nicht ganz aufgehort hat.” Jbid., p. 15: ‘Wie
Hilbert selbst an verschiedenen Stellen hervorhebt, war der Wunsch, die Logik und
Mathematik von Antinomien zu reinigen, der Hauptbeggrund fiir die Aufstellung
seines Lehrgebandes.’’ According to Mr. Grelling (ibid., p. 9.)—the solution of
antinomies is accomplished in three steps. 1) Russell founds the theory of types
with the axiom of reductibility. 2) Ramsey divides antinomies into two groups.
The first group receives its solution from the simple theory of types; alone, the
enlarged groupe requires the axiom of reductibility. 3) Hilbert founds the meta-
mathematical theory of the proof, which the Polish logicians elaborate into a metho-
dology. Gédel discovers arithmetisation and proves the existence of insoluble
propositions. Tarsky shows that the concept of truth can be defined without contra-
diction only in meta-language. Carnap generalizes this result, and it thus comes
about that syntactic antinomies are of no harm to science. According to Mr. Grelling
(op. cit. p. 17), “‘die Ueberwindung von Antinomien zu den wissenschaflichen Ruh-
mestaten unseres Jahrhunderts.’’ Cf. also K. Grelling, “The Logical Paradoxes,”’
Mind, vol. XLV (1936), p. 485.
8 H. Behmann, Zu den Widerspriichen der Logik und der Mengenlehre,’’ Jahres-
bericht der deutschen Mathematiker Verenigung, vol. 40, 1931), p. 38; speaking of
solutions to paradoxes says that: ‘Sie alle sich damit begniiden . . . dem entscheid-
enden Punkt in mehr oder weniger weitem Bogen aus dem Wege zu gehen, die Wider-
spriiche zu vermeiden, statt zie im eigentlichen Sinne aufzulésen.”’
° Ch. Perelman, Une solution des paradozes de la logique et-ses conséquences pour la
conception de l’infini, Travaux du [Xe Congrés de Philosophie (Congrés Descartes),
fasc. VI, p. 206, Paris, 1937. ‘‘Plusieurs solutions ont été proposées pour sauver des
paradoxes la théorie des ensembles, telle qu’elle a été dévoloppée par Cantor et par
346 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
Although much ingenuity has gone into the study of the paradoxes, no
completely satisfactory solution has been achieved. Indeed, in my Soinion
no genuine progress has been made in this direction (with the Rendiitions
perhaps, of F. M. Ramsay’s analysis), since Lord Russell’s attempts ts
solve it. Russell was, in my judgment, already in possession of the basic
elements of the answer. But his belief in the virtue of formalization and
symbolization, and his contempt for traditional logice—which landed him
in the labyrinth of the theory of types—barred the way to his unfoldment
of that answer. I do not share these Russellian prejudices and, accord-
ingly, I shall analyze them without translation into symbols. For anti-
nomies neither merit the honor of a symbolic translation nor the euphemism
of the name itself. They are just plain sophisms, for the most part re a
reformation of logic is not necessary to solve them.!° The iaieiyis of
identity suffices, 1.e., the phrases and terms used should have a clear and
certain meaning, and not be shifted in the progress of the argument
It would be a work of supererogation to narrate the history of the dis-
ses successeurs ayant conservé le concept naif de ‘classe’ ou ‘d’ensemble.’ C
diverses solutions ont pour but de limiter la théorie des ensembles ‘classi we if de
sorte que l’on obtienne un systéme déductif exempt de contradictions et Sed = a
que possible. Cependant tout le ‘monde se rend parfaitement compte du eee :
arbitraire de ces limitations. En évitant la contradiction on parvient, cert : “<a
cette fagon & formuler une condition suffisante pour que les aniinmeins ne he :
duisent plus, mais cette condition suffisante n’est nullement nécessaire. Il en ‘a ak
deux conséquences regrettables: d’une part, ces limitations Snot im se :
écartent des propositions dont |’affirmation ne présente aucun SARA Rn d’a : :
part, comme ces régles limitatives ne constituent pas des conditions cor’ tpi *
nécessaires pour éviter les antinomies, il est impossible de comprendre pour each
leur transgression entrainerait, dans chaque cas, des contradictions dans le s iiiin ;
1° Ch. Perelman, ‘‘Les Paradoxes de la logique,’”? Mind, vol. XLV (1936), 205
remarque, par contre: “‘Voici de probléme posé par ces antinomies: on su oe it:
les hypothéses dont on part sont parfaitement valables pour la lovigiis Gee aie
et que, malgré leur iégitimité, on parvient 4 en déduire des conséquences Siatradis.
toires. On en conclut qui’il faut restreindre les régles de la logique classi aur
tolerent ces hypothéses nous entrainnant dans d’inextricables antinomies si o
modifie; on impose des conditions supplémentaires A la construction de pro is ti
valables. On cherche a remédier aux antinomies par telle ou telle sd icistins al
régles de la logique classique, ce qui malheureusement, entraine d’ordinaire Vobli
tion de sacrifier d’autres propositions logiques ou mathématiques précieuse all aa
et qui deviennent d’innocentes victimes de l’oeuvre de purification entre ; “i a
pitié. Si lon veut sauver ces propositions, dont personne n’avait ies ait
contesté ni la légitimité ni la fécondité, on en est réduit A des ex oe ge adi
moins ingénieux et rarement convaincants . . . ce ne sont pas les kd de 7 i a
classique qu’il faut rendre responsables des paradoxes, mais bien les kins inns
de ces régles, commises en posant les hypothéses qui ménent aux Htc
x ee
THe LIAR 347
covery and the analysis of the logico-mathematical paradoxes; and it is
unnecessary to study each and every one of them: this would be both use-
less and impossible. It would be impossible because one may construct
them freely and ad libitum: the pattern of paradoxes is simple—it is the
pattern of the causa sut or of the suicide. It would be useless, because
most of them are formed on the basis of that pattern. I shall discuss only a
few, but the few which are important—especially that of the Liar.
*
7. *
The paradox of the Liar may be presented in a number of different forms.
However, the most important are: (a) the Epimenides form, which heads
this article; (b) the simplified and condensed form: If I say that I am lying,
do I lie or do I speak the truth? These two forms are not equivalent, and
it is interesting, therefore, to analyze them in turn.
The Liar appears as a typical antinomic judgment: the truth of the
asserted proposition entails its falsehood; its falsehod, in turn, entails its
truth. But, importantly, the reasons why its pretensions to be one must
be rejected are not the same in both cases. The Epimenides is not an
antinomy, it is a self-contradictory judgment, a counter-sense”; the J am
lying is not an antinomy because it is not a judgment.
A. Epimenides
To grasp the structure of this form, attention must be given to, first, the
meaning of the proposition asserted by Epimenides and, secondly, the fact
that it is Epimenides who asserts it.
Consider first the meaning of the proposition, “All Cretans are Liars.”’
Epimenides does not thereby wish to convey any appreciation of the moral
character of the Cretans. Indeed, if his assertion carried this meaning and
had this purport, the major ‘All Cretans are liars’? coupled with the minor
‘“Epimenides is a Cretan’ would give the conclusion ‘‘Epimenides is a
liar.’ This conclusion would be unobjectionable, the reasoning would find
‘ts end then and there, exactly as the case would be if Epimenides had
characterized the Cretans as ‘‘braves” or “cowards,” ‘sober men”’ or
“drunkards.” The syllogism would be perfectly legitimate, exactly as
the case would be if Socrates, from the general proposition that all men are
mortal, and the fact that he is a man, deduced his own mortality. The
fact that Epimenides himself characterizes the Cretans as liars does not
change the situation. A man can be a liar and admit it, without ceasing
11 The reasoning would also end if Epimenides had said: ‘‘All Cretans always tell
the truth.”
348 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
to be one; and without creating by nis avowal an antinomy or even a
paradox.
In order to create a paradox and establish a kind of reasoning which can
go on forever, or better, which is not able to stop at a conclusion, the sen-
tence, ‘‘All Cretans are liars,’’ must be differently interpreted, namely, as
a logical and not as a moral judgment. The meaning must be, “All Cre-
tans lie always,” i.e., all judgments or all assertions made by Cretans are
false. )
All this, of course, goes without saying; but, as it will be shown herein-
after, to dot all the i’s and to cross all the t’s, is of supreme importance to a
correct analysis of the problem. The implicit meaning of each assertion
must be made explicit, for thought is unstable and volatile—it glides easily
and without notice from one intention to another.”
Thus, ‘‘All statements made by a Cretan are false,’”’ we admit, is what
Epimenides wants to say. This assertion affirms the essential and uni-
versal falsehood of each and every judgment made by a Cretan and, as a
proposition, it is formally unimpeachable. If Epimenides were an Athe-
nian or a Spartan and not a Cretan, the sentence, ‘“The Spartan, Epimen-
ides, says that the Cretans always err,’”’ would not be paradoxical. It
would, of course, be a false assertion, for even the almighty Cartesian God
could not create a being who would always be in error. Nevertheless, this
falsehood would be material, not formal.
Consider next that it is Epimenides who asserts it. Epimenides is
neither a Spartan nor an Athenian; he is a Cretan. Therefore, from the
major, ‘‘All Cretans, etc.’”? and the minor, “‘Epimenides is a Cretan”’ it
follows:—‘‘Epimenides lies always,” i.e., “‘All the assertions of Epimenides
are false.’’ But this last proposition, taken as a major, together with ‘‘the
assertion ‘all Cretans, etc.’ is an assertion of Epimenides,’” entails the
conclusion,—the assertion ‘all Cretans, etc.’’ is false.
But this conclusion is equivalent to the assertion, Not all the Cretans
are liars, i.e., the statements of Cretans are not all and necessarily false.
We must conclude from this that there are certain Cretans who speak the
truth, i.e., that certain judgments made by Cretans are (or can be) true.
However, it does not follow therefrom that Cretans are always truthful,
and that all the judgments of the Cretans are true always.
Thus, we are not entitled to the conclusion that Epimenides is a truthful
Cretan, and consequently that his assertion about the Cretans is true.
On the contrary (and be it as it may as to other Cretans), as Epimenides’s
statement is certainly false, Epimenides is without doubt a liar—which is
the unique and only conclusion we can draw from what he says!
12 Mr. Perelman very justly observes (op. cit., p. 207) how much the formalization
favors this gliding.
THe LIAR 349
The proposition, ‘‘Epimenides the Cretan says, ‘all Cretans, etc.,’”
considered in its entirety, is necessarily false; for, either the Cretans are
not all (and always) liars, or it is false that Epimenides has said it. Or,
again, if he did say it, he could not be a Cretan.
Thus, the composite proposition, ‘‘Epimenides, etc.” is false in that it
contains incompatible members, subassertions that cannot be true _ to-
gether and at the same time. Then, what is it? A witty story, a “‘coun-
ter-sense,’’ a sophism: but not an antinomy.
To Epimenides the assertion, ‘‘All Cretans, etc.” is forbidden. He can-
not make it. In his mouth it suffers a perversion, it becomes a contre-sense,
a self-contradiction. However, this case is not unique. If someone said,
“The boat that I travelled on was lost with all hands,’”’ we could, and should,
doubt either the truth of the assertion or the truthfulness of the speaker,
orboth. Certainly,to extend these doubts to a doubt of the validity of the
laws of logic, is an exaggeration. It is curious and even strange, perhaps
(but not incomprehensible or contradictory), and it has not been sufficiently
noticed, that some propositions may not be uttered by everybody, that
certain verbs may not be used in the first person. It is not permissible, for
example, truly to say, “‘I am silent,” ‘‘I am absent” or ‘‘I am dead.”’ Nor
is it permissible meaningfully to say, “‘I am Jying.”’
)
B. “I am lying”
The meaning of the assertion “I am lying”’ is not quite identical with the
meaning of the assertions “I am silent’ or ‘I am dead.”’ The latter are
self-contradictory statements, but the former is not self-contradictory—it
is meaningless. This is old lore; and long before Lord Russell'* recognized
it anew, the medieval logicians were fully aware that this utterance, taken
verbatim, means nothing at all, therefore, being no judgment, is neither
true nor false.
Although this was widely admitted in the Middle Ages, none the less
the meaninglessness of “I am lying’ has often been doubted, even denied.
Let us look into it more closely.
At first sight, it appears that the assertion “‘I am lying” is meaningful.
This error arises because, in the last analysis and in general, language ex-
presses our thought in a very imperfect and incomplete manner. We
seldom say what we mean, or mean what we say. Moreover, we do not
often know what we mean and intend to say. Besides, the words we speak,
the sentences we hear, take their complete and full meaning only in and
through the context—we do not say or hear everything. Consequently,
in order to interpret the words we hear we have to reconstitute and to re-
store the whole of the intended meaning; since, however, we are accus-
13 Principia Mathematica, I, p. 39 sq., cf. Riistow, op. cit.
350 PHILOSOPHY AND PHENOMENOLOGICAL KESEARCH
tomed to meaningful speech to hearing sentences that have a meaning
(or at least, that pretend to have one), nothing is more difficult for us than
to apprehend a pure nonsense. We give a meaning even to what has none.”
Accordingly, when someone says “‘I am lying’ we interpret this utter-
ance, we substitute, we add, we qualify. We understand the sentence as
meaning either “I have been lying”’ or, ‘I sometimes lie” or “TI often lie,”
which can be true or false and, in any case, is a perfectly correct statement;
or even “I am always lying,’ a judgment of the type of Epimenides,—self-
contradictory, but therefore meaningful.
Yet, the expression “‘I am lying” means or pretends to mean something
else, something quite different, which does not extend its application to the
past or to the future, but confines itself to the present: This expression
claims to mean “‘I am lying now, in this moment”’ or, “It is in this moment
that Iam making a false assertion” or, ‘“The assertion that I am making
in this moment is false.”
But, as Russell has rightly pointed out,!® this expression contains not
one but two assertions, namely, (a) there is an assertion that I am making
in this moment, and, (b) this assertion is false. Now, where is the assertion
(a) to which the qualification ‘‘false’’ is applied in the assertion (b)? Obvi-
ously, there is no such thing; the assertion which is declared to be false
simply does not exist. The problem may be elucidated by comparing this
assertion with the assertions ‘‘I am silent”’ or “‘I am dead.”’
If I say, “I am silent,” or ‘I am dead,” I say something that can be as
“X is silent,’”’ or ‘“X is dead’’; for example, ‘‘Epimenides is silent” or ‘‘Epi-
menides is dead.’’ Here we deal with authentic judgments—something
is said about something; a predicate is asserted about a subject. Even
were I to substitute myself for the subject we would still have an authentic
judgment, though a necessarily false one, for in this case it is impossible to
link the subject to the predicate—it is impossible to speak (as I am speak-
ing) being silent or dead.
_ But if I say “I am lying” the objectivation reveals a much more complex
structure, viz., ‘“‘The assertion Y that the person X is making, is false,”
e.g., “The assertion Y which Epimenides is making, is false.”’ Still, this can
14 Even when we speak ‘“‘in order to say nothing.”’
15 Just as we put order and logic into our dreams.
16 Cf. Principia Mathematica, I, p. 30 sq. As a matter of fact, if I say: ‘“‘the
expression written between the ( ) is true or false,’’ that assumes that something
is written there. Or, if nothing is written there, we have no judgement; unless the
formula is interpreted as meaning 1) there is a judgment written between the ( )
and 2) that this judgment is false. In that case we shall have a false assertion,
because its first term is false.
THe Liar 351
be an authentic judgment if Epimenides, in this moment, genuinely makes
an assertion; and, correspondingly, our judgment will be true or false
according to the falsehood or truth of this assertion. Here everything is
perfectly correct: a predicate is asserted about a subject. But, if Epi-
menides does not make any assertion, the subject about which we speak,
the subject of our judgment, does not exist. In its place there is a void—
something (falsehood) is predicated of nothing.
Yet (as was sometimes advocated by logicians), the non-existence of the
subject does not prevent a proposition to be meaningful: it prevents it
from being true only. For example, if I were to say ‘““The king of France is
living in Versailles’ or ‘‘is bald,” this proposition would be false, since
there is no king of France; nevertheless it would be perfectly meaningful.
In the same manner the judgment ‘‘The assertion being made by Epi-
menides is true (or false),”’ or ““The proposition written on the blackboard
is false (or true)’ does not become meaningless if it turns out that Epi-
menides does not make an assertion, or that nothing is written on the black-
board—it becomes false. It is to be observed, however, that from the
falsehood of one of these propositions, we have no right to conclude to the
truth of its opposite: i.e., from the fact that it is not true that the king of
France lives in Versailles, it does not follow that he lives elsewhere; nor
does it follow from the fact that it is not true that the sentence written on
the blackboard is false, that this sentence is true. If no sentence is written
on the blackboard, this affirrlation would be just as false as the previous
one, the validity of the law of excluded middle to the contrary notwith-
standing.
Now, the expression ‘‘I am lying”’ (equivalent to ‘‘I am making a false
statement’’), may be interpreted to mean, ‘“The statement that I am mak-
ing is false.”” But here there is no statement, Y, to which this judgment
could be applied, therefore the judgment will be a false one. However, no
paradox arises. If, for example, I were to say instead, ‘“The song I am
singing is a French one,” that statement too would be false, for no song is
now being sung by me—(it’is impossible to speak and to sing at the same
time), the qualification ‘““French’”’ possesses no object to which it can be
applied. Similarly, it is impossible to make two judgments, namely, a
judgment, and also a judgment about this judgment—that it is false or
true. Further, if from the fact “It is false that I am singing a French song,”’
it cannot be concluded that I am singing an English one, so too, from the
fact that ‘It is false that the statement Y that I am making is false,”’ one
cannot conclude that I am making a true statement. The proposition—
“The statement Y that I am making is true’’—is equally, and for the same
reasons, as false as the, first one.
352 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
Yet it is claimed that the expression “I am lying”’ leads to a paradox.
It pretends to be a judgment about itself, that is to say, it claims to be its
own subject. In this case (to be carefully distinguished from the preced-
ing one) it becomes nonsense, a ‘‘meaning’’ impossible to realize, or, what
amounts to the same thing, it is an expression which falsely pretends to
have a meaning.
It is self-evident that a judgment cannot be its own subject. This im-
possibility was clearly perceived by Russell.’7 Quite unnecessarily, how-
ever, he raised this fact to the rank of a principle, the famous ‘“‘vicious
circle principle,’’ which (although quite mistakenly) rules out every appli-
cation of a judgment to itself.* Nevertheless, as it is not yet the com-
munis opinio of the logicians, let me quote at some length the excellent
analysis by C. K. Langford’? of the situation which would arise if a judg-
ment were to become its own subject.
““Let us take, to Legin with, what is perhaps the simplest and best known
example in connection with which we get a logical paradox; namely, that in
which we consider what significance the words ‘‘I am speaking falsely’’ or,
perhaps better, ‘“This proposition is false’? can have, where, if we had a
17 Cf. Principia Mathematica, I., p. 171: ‘‘A proposition can never be about itself.’’
18 As an example of difficulties and confusion produced by the non-distinction of
the two meanings of the ‘‘I am lying”’ analysed by us, we shall quote B. Russell,
“Les paradoxes de la logique,’’ Revue de Métaphysique et de Morale, vol. XIV (1906),
p. 643: ‘‘Nous pouvons maintenant résoudre le Paradoxe de l’homme qui dit: ‘je
mens.’’ Ce jugement est susceptible de diverses interprétations; la plus simple
est: ‘Il y a une proposition p que j’affirme et qui est fausse.’’ Ce jugement contient
une variable apparante p; il n’énonce done pas une proposition définie, au sens que
nous avons donné au mot ‘proposition.’ Cette énonciation peur étre fausse si
j’afirme une proposition p, qui est vraie, ou si je n’affirme pas de proposition. La
premiére hypothése entraine la contradiction. La second n’est possible que si une
énonciation générale n’affirme pas une proposition déterminée. C’est cette derniére
hypothése que nous adoptons. Donc l’énonciation de l’homme qui dit: ‘je mens’ est
fausse, non parce qu’il énonce une proposition vraie, mais parce que tout en faisant
une énonciation, il n’énonce pas une proposition. Ainsi quand il dit qu’il ment, il
ment, mais on ne peut pas en conclure qu’il dit la vérité. Il ne peut pas vouloir
dire: ‘je fais en ce moment une énonciation qui est fausse,’ parce qu’il n’y a pas
moyen de parler d’énonciations en général; on peut parler d’énonciations de proposi-
tions contenant une, deux, trois variables apparentes, mais non de propositions
en général. Si l’on veut dire ‘je fais une énonciation fausse contenant n variables
apparentes,’ il faut dire quelque chose comme ceci: ‘il y a une fonction proposition-
nelle g (X11, X2-+- Xx) telle que j’affirme que ¢ (Xi, X2.--- X,) est vraie pour n’importe
quelles valeurs de X1, X2 --- Xn, et cela est faux.’ Cette énonciation contient
n + 1 variables apparentes, savoir X,, X,--- X,et¢. Donec elle nes’applique pasa
elle-méme. De cette maniére nous évitons tous les paradoxes du type de |’Epimé-
nide, puisque pour toute énonciation proposée, nous pouvons montrer qu’elle ne
s’applique pas 4 elle-méme.”’
19 C, Lewis and C. Langford, Symbolic Logic, New York-London, 1892, pp. 438 ff.
THe LIAR 353
genuine statement, we should have one that was its own subject. In the
expression “‘this proposition is false,”” the words “this proposition’ pretend
to designate the whole statement as well as the subject, since these would
be the same; and it is clear, therefore, that we can represent the situation
in the following way. Let P be the name of a proposition, and let the propo-
sition of which it is the name be “‘P is false,” so that we can write
P = P is false
It looks as if these words expressed a genuine statement, and yet, in view of
certain considerations, it would seem that this could not possibly be the
case; so that we have two incompatible appearances, both claiming assent.
If P names a proposition, then it could be replaced by its meaning, and we
should have ‘‘(P is false) is false,’’ that is, P is true. But, if in turn P were
replaced by its meaning in “‘P is true,’’ we should have ‘‘(P is false) is true,”
that is, P is false. Thus, not only would P imply its own contradiction,
but this contradiction would in turn imply it. That is to say, one should
have both P < ~ P and ~ P < P and this is what is known as a vicious
circle. So if P stood for a proposition it would have to stand for one that
was both true and false: from which it follows, of course, that P does not
stand for a proposition at all.”
Yet the contradiction, the vicious circle or the vicious regression, 1S by
no means relevant. Exactly the same situation would arise if instead of
writing P = P is false, we would write
P = Ps true.
In this case, exactly as in the former one, we would have “an infinite se-
quence of more and more complicated expressions, each of which requires
explanation before its import becomes definite; so that no one of the expres-
sions can be significant unless the sequence terminates, which it does not
do... owing to the fact that the sequence of substitution never ends; and
so never ends in any undefined expression. What has happened is, of
course, that” the symbol P has no meaning at all.
*
* *
Thus, the statement “I am silent’”’ has both a predicate and a subject;
the vice is that it is impossible to link them together. Therefore, it is a
false judgment. However, and on the one hand, the statement “T am
singing a French song,” has a predicate, but it lacks an existent mahyooks
it too, is a false judgment. On the other hand, the expression ‘ r am
lying,’ has no subject and, accordingly, it is not a judgment. Concisely
put: every proposition must have a subject; no proposition can be its own
subject.
354 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
The validity of this rule has sometimes been contested. It has been
urged” that the expression ‘‘The phrase that I am uttering is false,”’ is not
any more destitute of meaning than the expression ‘‘The phrase that I am
uttering is composed of English words’’—a sentence which, concededly,
not only has a meaning but is even true. Here, however, the sentences
are not analogical. It is not true that the latter sentence is its own sub-
ject, any more than the sentence ‘“The words I am uttering are English
words.” These propositions are not about themselves, but about their
verbal contents or their verbal forms. Such propositions are as legitimate
as propositions about ‘‘the movements I am executing.”’
It is not the temporal coincidence of the judgment and its subject, but
its claim to identify them, which empties the expression ‘‘I am lying”’ of
meaning. It attempts to put the judgment within itself or in its own
interior.
Although sentences such as, “‘I am speaking”’ ‘“‘I am singing”’ have legiti-
mate structures and clear meanings,” it is not so as to ‘‘I am lying.”” More-
over, the negative moment within the notion of “lying” (falsehood )—
which play so preponderant a réle in the apparently paradoxical structure
of the Epimenides and entailed its self-contradiction—plays no réle in “‘I
am lying.’”’ Indeed, the proposition ‘I am speaking the truth,” and even
the neutral one “‘I am making a judgment”’ are just as objectionable on the
same grounds.
I maintain, therefore, (with B. Russell) that the expression “the proposi-
tion that I am uttering is false (or true)” is meaningless. The meaning
which it seems to have is an illusion. The longer the sentence, the more
easily we succumb to that illusion. For sentences are atomistically con-
structed of meaningful parts (words), and we start off with an unclear
understanding and vague impression of a meaning of the whole. This
impression of meaning endures, although the effort to unite the parts
would disclose that it is not a meaningful whole. As Husserl, and Plato
before him, pointed out, the effort to realize what is meant by a sentence,
the earnest effort needed to effectuate the intentional contents of the
thought, is postponed or avoided as long as possible, and consequently it
is seldom, if ever, made, and this initial illusion of meaning is never dis-
sipated.
When objectionable or paradoxical expressions are presented in the form
of symbols—particularly where, instead of pointing directly to itself it does
so by means of a long circuit (and the longer the better), in which every
20 Cf. R. Poirier, Le Nombre, Paris, 1938. The term “‘phrase’’ is used here in a
vague sense, and should not be understood as meaning: ‘‘judgment.’’ To be entirely
exact, it would have been necessary to say, as a matter of fact, ‘“‘the words which Iam
pronouncing are French words.”’
21 The first one is even necessarily true, and the second necessarily false.
—
THe LIAR 355
step in and of itself is legitimate and understandable—the illusion that we
deal with meaningful statements is especially strong. For an example of
such a circle, I quote the ‘‘very elegant form” given to the Liar by the well-
known Polish logician, Professor Lucasievicz:”
“Let the letter Q be an abbreviation for the phrase: ‘the proposition
occupying the 12th line of this page.’ Then let us write:
(1) Q ts a false proposition.
By counting the lines we can verify:
(2) Q is identical with the proposition (1).
As definition of the concept ‘false’ we assume, in accordance with M.
Perlman, Def.: P is a false proposition is equivalent to non-P. By sub-
stituting Q for the variable P in this definition, we get:
(3) Q is a false proposition is equivalent to non-Q.
The first member of this equivalence (printed in italics) is our proposi-
tion (1). Thus we have:
(4) The proposition (1) is equivalent to non-Q.
But in virtue of (2) the proposition (1) can be replaced by Q. Thus
results the contradiction:
(5) Q is equivalent to non-Q.
The operations performed by us in this deduction are all legitimate in
classical logic, i.e., according to classical logic they lead from the premises
to a true conclusion. We have substituted the constant Q for the variable
P in the definition of a false proposition and we have replaced the proposi-
tion (1) by (4) by the description Q (this letter was introduced only for the
sake of typological brevity) whose identity with the proposition (1) can be
verified by the reader himself... .”
Thus, Grelling writes: ‘“The paradox of the Liar does not presuppose
anything but the rules of classical logic, the definition of falsehood, and an
easily verifiable empirical proposition.”’
Now, I submit, it is perfectly clear that the use of the letters P and Q—
the substitution of “Q”’ as an “abbreviation” for a certain proposition or
expression—is not only useless but even worse than useless. The letters
substituted in lieu of the proposition enable the reader to follow the subse-
quent reasoning, the prospective operations, without obligation to account
to himself for the meaning of the proposition with which he deals. The
steps which beguile him into the region of meaninglessness are thereby
made more difficult to recognize. -
On the one hand, we are entitled to write: ‘“The proposition occupying
the 12th line of this page is false.” This expression can stand for a true or
false proposition, for it depends upon what we find or do not find on the
12th line. On the other hand, we can write this expression itself on the
12th line of the page—and even fill the whole page with it. This expres-
22 Cf. K. Grelling, ‘““The Logical Paradoxes,’”’ Mind, 1936, p. 485 ff.
356 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
sion, written on the 12th line, will then indirectly point to itself and raise
the claim to be its own subject. The fact that this claim is expressed in a
circuitous and not in a direct way, does not make its fulfillment any more
possible than in the case of the simpler direct form. Nothing is changed
logically: the expression written on the 12th line is as objectionable as the
expression ‘“‘I am lying.” It is no cause of wonderment, therefore, that,
when the rules of classical logic (rules made for meaningful propositions
and judgments) are applied to it, there is obtained a paradox, even an an-
tinomy. Consider more closely the “elegant form”’ Professor Lucasievicz
has given to the Lzar.
Q is said to be an abbreviation of “The proposition occupying the 12th
line of this page.” The formula (1) says: “‘Q is a false proposition,’ which
means: “The proposition occupying the 12th line of this page is a false proposi-
tion.” The formula (2) is “Q is identical with the proposition (1).”’ But
this is quite false. Q is not identical with the proposition (1), and Q is
not a proposition. Q is an abbreviation for an expression forming only
the subject of the proposition (1). Q does not stand for “The proposition
occupying the 12th line of this page is a false proposition,”’ but only stands
for “The proposition etc....”’ In other words, Q does not mean “‘Q is a
false proposition.’’ Therefore Q cannot be identical with the expression
written on line 12. Or, vice versa, if it is, then the expressifon written on the
12th line is not ‘“The proposition occupying the 12th line of this page is a
false proposition,’’ but only ‘The proposition occupying the 12th line of
this page.’ Which expression is not a proposition at all. It is therefore
impossible to operate with it as if it were one. The paradox—if only we
are careful enough not to change the meaning of our symbols—does not
arise. If, on the other hand, we substitute for the original meaning of Q
the “meaning” “‘Q is false,’’ we have no right to identify it with Q. Fi-
nally, if we start from the identification of Q and “Q is false,” ie., Q and
non-Q, we must not wonder that we come to contradictions. And we have
no right to incriminate the rules of classical logic.
*
x %
We must now turn to another attempt—that of Professor A. P. Ushenko
—to improve the presentation of the Liar and thus to vindicate its legit-
imacy. In his article, ‘“A New Epimenides’”* Professor Ushenko writes:
—_——— ————- — —
All propositions written within
the rectangle of Fig. 1 are false.
Fig. 1 Fig. 2
28 Cf. A. P. Uchenko, ‘‘A New Epimenides,?? Mind, 1937, p. 545 ff.
THe LIAR 357
“Let the expression within the rectangle of Fig. 1 be called A. Either
A is a proposition, or not. Suppose A is a proposition, then either it is
true or false. But if A is true, then it cannot be dealing with any other
proposition than itself (since there are no others within the rectangle),
and therefore it is false. But if it is false, then the only proposition within
the rectangle, viz. A, is true. Now this a vicious circle, and the familiar
resolution would be to the effect that A is meaningless and only appears
to be a significant proposition.
‘But then, if A is not a proposition, there are no propositions within the
rectangle at all. The statement ‘It is false that there are propositions
within the rectangle of Fig. 1’ is true. But if it is true, then the statement
“Tt is false that there are true propositions within the rectangle of Fig. 1”
isalsotrue. But this statement is the same as A, since, ‘“~ (4x) -fx-~gx”’
is the same as “(x)-fxgx.’’ Hence, if A is not a proposition, A is true; but
since nothing but a proposition can be true, if A is not a proposition, then
A is a proposition. A vicious circle reappears.”
Professor Ushenko’s presentation of his analysis is interesting and in-
genious. Alas, again, it seems to show that symbolization does not bring
forth, necessarily, more clarity and precision in our thinking.
Indeed, from the fact (or proposition) that there are no propositions
written in the rectangle 1, Professor Ushenko deduces (rightly) that “‘It
is false that there are true propositions within the rectangle of Fig. 1;”
and therefrom, with the aid of symbolisation, he deduces that ‘All proposi-
tions written within the rectangle of Fig. 1 are false.” It is rather strange
that Professor Ushenko does not notice that from the fact that there are no
propositions within the rectangle 1, we can deduce, just as rightly, that
“There are within the rectangle 1 no false propositions,” and, therefore,
that “It is false there are no false propositions within the rectangle of Fig.
1,” which, according to him, would imply that “All propositions written
within the rectangle of Fig. 1 are true. We would, then, have the super-
paradox of being able to deduce two obviously incompatible statements
from a single, and true proposition. ... But if this reasoning were to be
accepted as correct, then, from the fact that no numbers are written within
the said rectangle and that, therefore, no even (or odd) number is written
within it, we would be able to deduce that all numbers written in the
rectangle are odd, or even, and, therefore, odd and even,in the same time
and so forth. We would be able to deduce a great many interesting things.
It is even possible that from the fact that no cat has two tails we would be
able to deduce that all cats have three... .
Professor Ushenko, as a matter of fact, forgets to take into account
the existential purport of his statements. He does not seem to notice
that the existence, or the non-existence of the object we are speaking about
358 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
(or: the subject of a proposition) does make a difference and that positive
judgments about non-existent objects are all false. It is, therefore, not
true, but false that all propositions written etc. are false; and it is just as
false that they are true.
Professor Ushenko continues: ‘‘Observe that with reference to Fig. 2
the statement ‘There are no true propositions within the rectangle of Fig.
2’ will be recognized as a true proposition precisely because there are no
propositions within the rectangle of Fig.2. But the meaning of this propo-
sition has no reference to, and therefore, should not depend on, the place
or date ofits formulation. If it is meaningful and true as written above,
it should not cease to be true and meaningful when one chooses to write
it within the rectangle of Fig. 2.’ Here too we are forced to disagree with
him. The meaning of a proposition, even if it has no explicit reference to a
date or place, depends quite often on the place and date of its formulation
because it refers to them implicitly. We have already seen that some verbs
cannot be used in the present tense, some others not even in the past one.
There are things that I can say about ‘“‘you,” or “he,” but not about “I,”’
terms such as ‘‘this,’’ ‘“‘here,” “now,” etc. cannot be understood without a
reference to date and place. Besides, if we admit Professor Ushenko’s
contention that the meaning—and the truth—of the proposition ‘There
are no propositions within the rectangle 2” does not change, and will not
cease to be meaningful and true if we write it within the rectangle 2, we
must admit that, even if we do so, there still will be no propositions written
within the said rectangle. ...
x *
Let us examine now another famous “antimony,” that of Berry.* I
must confess that, for my part, I cannot admit of its being anything but a
pure and simple sophism, built according to one of the classical modes of
sophism, which consists in taking as dictum simpliciter something which
is only dictum secundum quid.
The Berry paradox is formed in the following manner:* ““The number of
syllables in the English names of finite integers tend to increase as the
integers grow larger and must gradually increase indefinitely, since only a
finite number of names can be made with a finite number of syllables.
Hence the names of some integers must consist of at least nineteen syl-
—-—
24] shall not study the Richard paradox which is perfectly analogous, nor the
paradox of the barber, etc. Cf. my ‘‘Ensemble and Category,”’ to be published in
this journal.
2 Cf. Jérgensen, III, 132 sg. Cf. Russell-Whitehead, Principia Mathematica,
Vol. I, p. 63.
THe LIAR 359
lables and among these there must be a least. Hence ‘the least integer
not nameable in fewer than nineteen syllables’ must denote a definite
integer; in fact 111 777.% ‘‘One hun/dred and el/ev/en thou/sand se/ven
hun dred and se/ven ty se/ven” (19 syllables) is ‘the least integer not
nameable in fewer than nineteen syllables’ (18 syllables). But ‘the least
integer not nameable in fewer than nineteen syllables’ can be named in
eighteen syllables, which is a contradiction.”” Undoubtedly. And yet
it is doubtful if the existence of this ‘‘contradiction” entitles us to proclaim
the doom of classical logic and the imperious necessity to reform it. The
contradiction, as a matter of fact, could be avoided on less onerous terms.
Thus, for instance, we could, in the first of the two expressions or “‘names,”’
drop the two ‘“ands’’, obviously superfluous. We would, in this way,
save two syllables and the contradiction would disappear. But I shall
not insist. That would be too cruel.
As for the “‘paradox”’ itself, it seems rather obvious that its existence is
based entirely on an equivocation, or still worse, on a complete lack of
precision and even of determination in the use of the term“‘nameable.”’
Nameable how? In what language? By what means? As long as this
is not told, nothing is told.
It is evident that there would be no contradiction (and even nothing
unusual) in the fact that a number “‘nameable” in 19 syllables in English
could be “named” in 15 syllables in French and in only two in Chinese.
Even if we were told that ‘‘to name” means to name in English and in
words, this specification would not give to the term ‘“‘to name”’ 4 precision
permitting an unambiguous use. It is clear that the reader of Berry com-
pletes involuntarily and unconsciously his lax and unprecise expression.
He believes that we have to deal with proper or common ‘‘names’’ of the
numbers and, therefore, he accepts his method of classification. It is
quite certain that the “proper names” of the numbers (of which every
number has one and only one) can be ordered according to their length
(in syllables or even in letters). But it is at the same time just as certain
that this classification applies only to ‘‘names’”’ properly so-called. There
is therefore nothing paradoxical nor even astonishing in the fact that a
given number whose “‘proper name” contains 7 syllables can at the same
time be designated by an expression which is no “name” and which con-
tains a different, larger or smaller, number of syllables.
Now this is just what Berry is doing. He starts by classifying the
(proper) “names’’ of the integers, thus creating in the mind of the reader
the—false—impression that the term “‘to name’”’ is used by him in a certain
determined and univocal sense. Then, suddenly and without warning,
he changes the meaning of the term and extends it to any kind of designa-
tion. No wonder that this ambiguous use of the term produces an ap-
pearance of contradiction.
360 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
The objection will probably be raised that my solution is much too easy
and too simple, and that the paradox arises from the fact that Berry uses
for “naming” the numbers the classification itself that he is establishing.”
This, of course, is quite particularly objectionable and sophistic; yet, in
my opinion, this is not the decisive point.
The paradox arises from the fact that Berry uses the term “to name”
in two quite different acceptations: the first time in the very precise sense
of ‘“‘to name by a proper name,” because otherwise he would not be able to
establish his classification of integers; and a second time in the perfectly
general and indetermined meaning of “to denote by whatever means,”
because otherwise he would not be able to claim that he has ‘‘named”’ the
number 111,777 by denoting it by the means of the classification of “proper
names.”
Let us repeat once more: to say, “to name,” ‘“‘to denote,” “to determine”’
without saying how and by what means is to say nothing whatever, because
in this case all and everything can be “named” or “denoted.” Indeed,
if in order to “name” a number we are entitled to denote it “by whatever
means,” by the means of its “proper name”’ as well as by any other means,
for instance as the n™ prime number, or as the n power of m, or as the
sum, quotient, product or difference of m and n, or even as the number of
verses, syllables or letters of the Bible, the Iliad or the Koran, etc., etc.,
etc., the classification proposed by Berry would become, obviously, im-
possible. To the question: is it possible, or not, to “name” a certain num-
ber in less than 7 syllables, it would be impossible to give a determinate
answer because the question would have no determinate meaning. And
if, furthermore, in the process of “naming,’’ we gave ourselves the right
to create new “names’’ new manners and patterns of “naming,” the very
idea of such a classification would lose any meaning whatever.
In order that it may have one, in order that the question, “Is it or is it
not possible?’’ may be answered by a “‘yes”’ or a “no,” it is first of all neces-
sary to give a precise meaning to the terms we are using, to determine the
means we are entitled to employ for the “naming.” Then, our classifica-
76 B. Russell, Principia Mathematica, I, pp. 66 f., proposes a solution based on
the theory of types (cf. above, p. 352): “5. The paradox about ‘the least integer
not nameable in fewer than nineteen syllables embodies, as is at once obvious, a
vicious circle fallacy. For the word ‘“‘nameable’’ refers to the totality of names,
and yet is allowed to occur in what professes to be one among names. Hence there
can be no such thing as a totality of names, in the sense in which the paradox speaks
of ‘‘names.”’ It is easy to see that in virtue of the hierarchy of functions, the theory
of types renders a totality of names impossible. But on no stage can we give a
meaning to the word ‘“‘nameable”’ unless we specify the order of names to be em-
ployed; and any name in which the phrase ‘“‘nameable by names of order » occurs is
necessarily of a higher order than the n**. Thus the paradox disappears.”’
THE LIAR 361
tion having been established, nothing stands in the way of our using it as a
new means of denoting, a new means which is added, to or substituted for,
the previously employed means. The fact that some operations, impos-
sible to execute as long as we are employing the means N become easily
executable if we add to them a new one, the N + 1, involves no contradic-
tion. Thus, a problem, insoluble as long as we use only the rule and the
compass, may quite easily be solved with the aid of conic sections.
*
~ ~
Berry’s paradox is the result of an equivocation and imprecision in the
use of the term “to name.” If, on the contrary, we specify it every time
that it is employed, we shall find ourselves before the following statements:
let us make a classification of integers according to the length (in syllables)
of their “‘proper names.’’ Among those, the “proper names” of which have
at least 19 syllables, there is at least one. This integer is 111,777. We
can also denote or name it as: the least integer whose ‘“‘proper name’”’ has
at least 19 syllables. It is obvious that this last expression is not a “proper
name”’ and, therefore, irrespective of the number of syllables, of which it is
composed, it cannot be compared with the first one. Thus no contradiction
whatever can possibly result from the fact that an expression of the second
type may be shorter than that of the first one.
To deny it, and to pretend that we are confronted with a paradox would
be the same as to pretend that there is a paradox (or a contradiction) in the
fact that, having classified the books in our library according to the length
of their titles (In words), we can denote or ‘“‘name”’ a certain volume by the
expression: “the first volume (or the smallest, or the largest) the title of
which has at least a hundred words.”
*
* *
Let us now return to the Epimenides. In our analysis of the assertion
‘All Cretans are liars,’’ we have found and submitted that this assertion
(in contradistinction to the “I am lying’’) is meaningful but self-destructive.
We have made a distinction, that is to say, between the cases in which, on
the one hand, a proposition pretends to reflect directly upon itself, i.e , to
be its own subject; and, on the other hand, the differently constituted
sentence which formulates or expresses a general or universal proposition
that can be applied to itself as a particular.
It is the failure to distinguish these two cases that is at the root of Rus-
sell’s theory of types; and also of the corresponding semantic theories of
Carnap and Tarski of a hierarchy of languages and meta-languages.
The distinction which I have made, a distinction which is nothing else
362 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH
but Husserl’s distinction between nonsense and counter-sense,?’? enables
us to avoid all these painful consequences, to subject logic to its own rules,
to count numbers, and to write the grammar of a given language in this
language itself.
As I will show in a later publication,?8 this distinction, which, by the way,
is indispensable for the possibility of the theory of types itself—in order
that it should not rule itself out—leads us to the resolute abandonment of
the extentionalist (class extension) interpretation of logic, and by way of
consequence to a solution of all the logico-mathematical paradoxes dis-
covered by and since Bertrand Russell.
ALEXANDRE KOYRE.
SORBONNE, Paris.
27 ““Unsinn” and “‘Widersinn.”’? Cf. E. Husserl, Logische Untersuchungen, Vol. I,
pp. 112 ff.; Marvin Farber, The Foundation of Phenomenology, pp. 120 ff.; 324 ff.,
Cambridge (March), 1943.
28 “Ensemble and Category.”
