From 1507680ff4502b7a9a89cdc7543b265a53e5d548 Mon Sep 17 00:00:00 2001 From: oskar Date: Sat, 25 Apr 2026 04:07:07 +0200 Subject: [PATCH] MacBookPro.lan 2026-4-25:4:7:7 --- sources/0 - cours/LOGOS S2/.DS_Store | Bin 6148 -> 6148 bytes .../le savoir en mathématiques/.DS_Store | Bin 6148 -> 6148 bytes ...tre XII et ses cercles non-concentriques.md | 12 ++++++++- .../fiche_lecture.pdf | Bin 247156 -> 258834 bytes .../figures/cercles-non-concentriques.tikz | 24 +++++++++--------- .../figures/styles.tikzstyles | 4 ++- 6 files changed, 26 insertions(+), 14 deletions(-) diff --git a/sources/0 - cours/LOGOS S2/.DS_Store b/sources/0 - cours/LOGOS S2/.DS_Store index 1d8546a327ca1c42ad93585f71466ffd7a482680..814a2bc8ba8f27cd813ef29bef76a8526e5bc2bb 100644 GIT binary patch delta 31 lcmZoMXffDulu5`yM?u%1R!5=Q(9#IVHZ-u% delta 31 lcmZoMXffDulu5|M!azsCpjJnr+R)Mn$h0)re4R;G6abQ72%P`` diff --git a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/.DS_Store b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/.DS_Store index 4ab8969b5ef1a9e83868165ffeda3142ed1afdcd..6cdffae349cc6dc227312682e0db5fc249eb1dea 100644 GIT binary patch delta 93 zcmZoMXffEJ$;h~EvKC{Zt5|ilfsTSft&T#qp`{U!X=q?!P+QB%A*!rz9TcCPlbe^{ c!2kw~j1ZcE7fQpZ&drY)RoOPPa{T890P2Mjc>n+a delta 44 zcmZoMXffEJ$;h~4vKC_@heUO?u7Qq%?&O7xa*SP*4=~Czc5i;bsLHmPo#QV*04t0Q AfdBvi diff --git a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Fiche de lecture - La lettre XII et ses cercles non-concentriques.md b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Fiche de lecture - La lettre XII et ses cercles non-concentriques.md index 0aece766..4f083907 100644 --- a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Fiche de lecture - La lettre XII et ses cercles non-concentriques.md +++ b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Fiche de lecture - La lettre XII et ses cercles non-concentriques.md @@ -131,12 +131,22 @@ Dans la partie 8 de la *Lettre 12*, Spinoza donne une figure qu'il utilise comme L'enjeu, pour Camerini, est de comprendre et traduire correctement le commentaire accompagnant cette figure, qui se veut être une démonstration par l'exemple de la possibilité d'un tel infini. \say{L’intention de Spinoza est de montrer que les segments inégaux de ­ l’espace ­ compris entre deux cercles non ­ concentriques, bien que bornées entre un maximum et un minimum donc pas « sans fin », sont quand même dites infinies, dans un sens différent, puisque toutes ces variations ou inégalités ne peuvent pas être déterminées par un nombre fini.}[^3]. Il faut ici faire attention à la notion de *nombre*. En effet, pour Spinoza, le nombre (comme la *mesure* et le *temps*) est un auxilliaire de l'imagination. Le concept d'imagination est développé par Spinoza dans l'Éthique (notamment 2p17 et 2p18) et se distingue du sens contemporain en cela que l'imagination n'a rien de fantaisiste : elle est plutôt synonyme de "perception sensible", c'est-à-dire d'une perception qui passe par le corps (et par la mémoire)[^imagination-perception]. L'imagination n'est donc pas *en soi* cause d'erreurs[^imagination-erreurs]. Ce qu'affirme Spinoza, c'est que certaines choses ne peuvent être égalées par aucun nombre, autrement dit que *cette modalité d'imagination* qu'est le nombre ne permet pas de penser certaines choses pourtant limitées par un minimum et un maximum. Il affirme que les paradoxes ne viennent pas de cet infini, mais seulement de cette erreur que l'on fait de vouloir penser l'infini comme un nombre : \say{Si ­ l’on ­ confond le nombre, la mesure et le temps avec les choses elles- mêmes, dit Spinoza, on devrait admettre une série de paradoxes, dont de nombreux auteurs ont déduit ­ l’impossibilité ­ qu’il existe un infini en acte.} [@camerini-lettre12, p.8].[^imagination-pas-infinie] -Ainsi, dans la partie 8, Spinoza délivre deux arguments qui tendent à montrer que le nombre peut être impuissant malgré des limites. A chaque fois, il se réfère aux \say{Mathématiciens} pour soutenir ses arguments, qui sont géométriques. +Ainsi, dans la partie 8, Spinoza délivre deux arguments qui tendent à montrer que le nombre peut être impuissant malgré des limites. A chaque fois, il se réfère aux \say{Mathématiciens} pour soutenir ses arguments, qui sont géométriques. Dans un premier temps, c'est un argument négatif qui est utilisé : au lieu de positivement donner l'infini, il explique que les mathématiciens \say{ont découvert quantité de choses qui ne se peuvent expliquer par aucun nombre, ce qui prouve assez le défaut de tout nombre à tout déterminer}. Françoise Barbaras explique que cela est une référence implicite aux grandeurs incommensurables, que l'on sait être inexpliquables par des nombres (pas selon la conception contemporaine des nombres, mais selon la conception qu'en ont Spinoza et les philosophes modernes, héritée notamment d'Euclide)[^barbaras-incommensurabilite]. +Cet argument négatif montre une impuissance des nombres, et confirme que de l'impossibilité d'assigner un nombre on de doit pas conclure l'inexistence. Mais un second argument vient ensuite affirmer la présence d'un certain infini dans l'espace entre les deux cercles. +C'est la non-homogénéité de l'espace que veut nous faire remarquer, car en effet, les cercles étant non-concentriques, la distance entre les deux cercles varie ; c'est en cela que l'on peut trouver une *infinité de variations*. En même temps, ces variations sont limitées : elles sont contenues entre un maximum (la distance $AB$) et un minimum (la distance $CD$) et sont entièrement contenues dans l'espace entre les deux cercles (les circonférences sont les limites). +Ce n'est donc pas un espace infini (dans le sens d'indéfini, qui n'a pas de limites), mais bien un espace fini qui contient ces variations infinies. Le problème qui se pose est d'interpréter ce que sont ces variations (qu'est-ce qui varie, exactement, et quelle est la nature de cet espace entre les deux cercles ?) pour fournir une traduction fidèle à l'idée que Spinoza cherche à défendre. + +Le premier point de tension se tro + + [^3]: [@camerini-lettre12, p.8] [^imagination-perception]: C'est ce qu'affirment Russ Leo et Giovanni Liacata : \say{Quant au concept d’*imaginatio*, il faut toujours garder à l’esprit qu’il est ici synonyme de perception sensible, et qu’il ne s’agit donc pas seulement de la manière dont l’esprit projette une image relative à quelque chose qui n’est pas présent à nos sens : l’imagination ne correspond pas au sens contemporain de fantaisie. Il est donc légitime de dire que toute sensation est une imagination.} [@ethique-rovere, p.246 note 225] [^imagination-erreurs]: \say{[...] les imaginations de l’esprit, regardées en elles-mêmes, ne contiennent aucune erreur, autrement dit que l’esprit ne fait pas erreur parcequ’il les imagine [...]} [@ethique-rovere, p.245 2p17s] [^imagination-pas-infinie]: Spinoza est assez clair sur le fait que l'imagination est limités numériquement : il est impossible, pour l'esprit humain, d'imaginer en même temps un trop grand nombre de choses, sans les confondre. C'est même cette confusion qui fait naître les notions plus généralisées. À ce propos, voir Éthique 2p40s1, et la remarque de Filib Buyse : \say{[...] l'incapacité humaine de tenir ensemble, sans les confondre, un très grand nombre d'idées [...]} [@ethique-rovere, p.286 note 247] +[^barbaras-incommensurabilite]: \say{Ce premier argument porte donc sur l’incommensurabilité entre des \emph{choses} qui, n’ayant pas d’unité de mesure commune, ne peuvent être exprimées l’une en fonction de l’autre par \emph{aucun} nombre. On peut montrer – par exemple, par un raisonnement par l’absurde comme le font les mathématiciens anciens – l’impossibilité de trouver \emph{un} nombre par lequel pourrait s’exprimer le rapport entre diverses parties de la même figure. Si ces choses doivent néanmoins être considérées comme des grandeurs, leur grandeur ne peut être mesurée par aucun nombre.} [@barbarasSpinozaScienceMathematique2007 chap.6, Paragraphe 19] + + --- diff --git a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.pdf b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.pdf index 43b56e362e0a9faf777b4dd4ac8daa6c5328679e..937b5db6960037e872e5e583a41b8af7a0eeece3 100644 GIT binary patch delta 59215 zcmX`RV|1Pk&@CL>PGh#Qoiw(Srm>yI_7&TPyND+GRi1SUCCTXSa%QZ^2D&QyPQ$R9wpmTclWCq~aq?T!t5 zIeH2he82;P1939Lb>E+DYZ8laHZvLW5pQl+UyyIKZCsKVPv_I`AS%A(p2=Az(_%OKJ$cSvI*z7Q!?-6v6#kd z>nIa|Sy?n{^8lEO9i)ERRqc%q(az{NN7=SW=gWONC!cM(%RccJx_6zMqMOuIig9w& zv+CsKY4V7tf{xUgY}0ty!z&HQy3dZR=hYQmV3bDC62hfrV|frn$E=*Ely;!5ZeWjT zgdVamZP1v|N`2T*NHeUH@L5!MCPj z*fK5I7nE@<;Ts_>Tw(%k@AG?S^XH{+PgdYfJ<49vggsSl3PtWTPruMdv>Kxafa>fj&5PU{j9tc7nn z;7tuf;mdu@@JCAixpKz`MH?s5su@v%4TzKO0SIz>dAZ9_T8_GDaOT-Dp5nx*LKavd 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mathématiques/figures/cercles-non-concentriques.tikz +++ b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/figures/cercles-non-concentriques.tikz @@ -1,17 +1,17 @@ \begin{tikzpicture} \begin{pgfonlayer}{nodelayer} - \node [style=none] (1) at (2.5, 0) {}; - \node [style=none] (2) at (0, -2.5) {}; - \node [style=none] (3) at (-2.5, 0) {}; - \node [style=none] (4) at (0, 2.5) {}; - \node [style=none] (5) at (0, 0.5) {}; - \node [style=none] (6) at (0, -2) {}; - \node [style=none] (7) at (-1.25, -0.75) {}; - \node [style=none] (8) at (1.25, -0.75) {}; - \node [style=none] (9) at (0, -1.5) {C}; - \node [style=none] (10) at (0, -3) {D}; - \node [style=none] (11) at (0, 0) {B}; - \node [style=none] (12) at (0, 3) {A}; + \node [style=none] (1) at (2.25, 0) {}; + \node [style=none] (2) at (0, -2.25) {}; + \node [style=none] (3) at (-2.25, 0) {}; + \node [style=none] (4) at (0, 2.25) {}; + \node [style=none] (5) at (0, 0.25) {}; + \node [style=none] (6) at (0, -1.75) {}; + \node [style=none] (7) at (-1, -0.75) {}; + \node [style=none] (8) at (1, -0.75) {}; + \node [style=none] (9) at (0, -1.25) {C}; + \node [style=none] (10) at (0, -2.75) {D}; + \node [style=none] (11) at (0, -0.25) {B}; + \node [style=none] (12) at (0, 2.75) {A}; \end{pgfonlayer} \begin{pgfonlayer}{edgelayer} \draw [bend right=45] (4.center) to (3.center); diff --git a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/figures/styles.tikzstyles b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/figures/styles.tikzstyles index 76404ca8..5b655eeb 100644 --- a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/figures/styles.tikzstyles +++ b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/figures/styles.tikzstyles @@ -4,6 +4,8 @@ % \tikzstyle{NAME}=[PROPERTY LIST] % Node styles -\tikzstyle{new style 0}=[fill=green, draw=red, shape=circle] +\tikzstyle{new style 0}=[fill=white, draw=red, shape=circle] % Edge styles +\tikzstyle{grey}=[-, draw=red] +\tikzstyle{double_arrow}=[<->]