From de0c027888f5621100c910c4a93de18bd9915b15 Mon Sep 17 00:00:00 2001 From: oskar Date: Sat, 25 Apr 2026 03:07:07 +0200 Subject: [PATCH] MacBookPro.lan 2026-4-25:3:7:7 --- sources/0 - cours/LOGOS S2/.DS_Store | Bin 6148 -> 6148 bytes ...tre XII et ses cercles non-concentriques.md | 9 ++++----- .../fiche_lecture.pdf | Bin 241990 -> 247156 bytes 3 files changed, 4 insertions(+), 5 deletions(-) diff --git a/sources/0 - cours/LOGOS S2/.DS_Store b/sources/0 - cours/LOGOS S2/.DS_Store index 814a2bc8ba8f27cd813ef29bef76a8526e5bc2bb..1d8546a327ca1c42ad93585f71466ffd7a482680 100644 GIT binary patch delta 31 lcmZoMXffDulu5|M!azsCpjJnr+R)Mn$h0)re4R;G6abQ72%P`` delta 31 lcmZoMXffDulu5`yM?u%1R!5=Q(9#IVHZ-u% 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 71a34ee9..0aece766 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 @@ -1,4 +1,4 @@ --@camerini-lettre12tags: +--- aliases: title: La lettre XII et ses cercles non-concentriques subtitle: Fiche de lecture @@ -8,7 +8,6 @@ bibliography: /Users/oscarplaisant/devoirs/cours/sources/zotero/bibliographie/bi link-citations: true link-bibliography: true header-includes: | - \usepackage[left=2cm, right=2cm, top=2.5cm, bottom=2.5cm]{geometry} \usepackage{hyperref} \usepackage{centernot} \usepackage{enumitem} @@ -130,14 +129,14 @@ 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].[^imagination-pas-infinie] +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 +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. [^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'im +[^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] --- 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 a08fedc62a1d6c526243a266a0f06a7a11a78e3d..43b56e362e0a9faf777b4dd4ac8daa6c5328679e 100644 GIT binary patch delta 92536 zcmZs>V{@Qg)NUKwwvCQ$JL%ZAZQQYK+eXK>Z6_V4V|9`a_Veytr|O*AXMLJ~V9gri zn%CHGq^D?PRLY;?l8h`rxZo%kRz^4ASh$i<(ZN~Rm{aajX#p)6$Kx@~zCW6GRGfuB z)~81MwC5n;#^$(7K%h!_eo`>5hAOmamGU1M7W}eNa1l%3Msnpq9!ERSpUIL0`jbIZ;= z-C(gc@BELB6cFM=zT{Ec&3zjYpo{Fk`-0!W5%=O8UZ=GF4Fc*$20HPLKF zFRLLd2G-N^EO~kX{t*60;nl-lV3q_WQ3gY`OTJCEg^d1UO-Nrq&h0@=Q(N;{+KjBe zQ$8?dDeJ5Y(@FVESXfTuLHMA0p9XXYNm#seR!_;}95Bw!c}mAedVl?VnO+&v^WyPp zPUD%L4wnA-qk(&PN*LhuZS>D^57Qfr&Vu#P##SSkv`wW^6t2s6TH@;}o=(Hlp)LIJ 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