From e2a9e1ce3358aed26e2c885bff7acf86d3ed2bda Mon Sep 17 00:00:00 2001 From: oskar Date: Sat, 25 Apr 2026 02:07:07 +0200 Subject: [PATCH] MacBookPro.lan 2026-4-25:2:7:7 --- ...tre XII et ses cercles non-concentriques.md | 26 +- .../le savoir en mathématiques/Makefile | 8 +- .../fiche_lecture.aux | 48 + .../fiche_lecture.dvi | Bin 0 -> 41572 bytes .../fiche_lecture.fdb_latexmk | 215 ++++ .../fiche_lecture.fls | 390 ++++++ .../fiche_lecture.log | 1071 +++++++++++++++++ .../fiche_lecture.out.ps | 25 + .../fiche_lecture.pdf | Bin 220821 -> 241990 bytes .../fiche_lecture.tex | 332 +++++ 10 files changed, 2105 insertions(+), 10 deletions(-) create mode 100644 sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.aux create mode 100644 sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.dvi create mode 100644 sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.fdb_latexmk create mode 100644 sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.fls create mode 100644 sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.log create mode 100644 sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.out.ps create mode 100644 sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.tex 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 33a2ed3e..71a34ee9 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 @@ -1,6 +1,4 @@ ---- -up: -tags: +-@camerini-lettre12tags: aliases: title: La lettre XII et ses cercles non-concentriques subtitle: Fiche de lecture @@ -48,6 +46,7 @@ header-includes: | \usepackage{csquotes} \usepackage{figures/tikzit} + \newcommand{\figref}[1]{Figure\,\ref{#1}} --- \setlength{\parindent}{4ex} \setlength{\parskip}{0ex} @@ -120,17 +119,25 @@ C'est sur la seconde distinction, et sur l'exemple fourni par Spinoza (la figure $$*\,*\,*$$ -Dans la partie 8 de la *Lettre 12*, Spinoza donne une figure qu'il utilise comme exemple pour étayer sa seconde distinction des les infinis. Il veut donc \say{montrer la différence entre ce qui est dit infini parce ­ qu’il ­ n’a pas de limites et ce qui est dit infini parce que ses parties dépassent tout nombre} [@camerini-lettre12, p.7]. Pour cela, une figure est introduite, donc voici la reproduction : +Dans la partie 8 de la *Lettre 12*, Spinoza donne une figure qu'il utilise comme exemple pour étayer sa seconde distinction des les infinis. Il veut donc \say{montrer la différence entre ce qui est dit infini parce ­ qu’il ­ n’a pas de limites et ce qui est dit infini parce que ses parties dépassent tout nombre} [@camerini-lettre12, p.7]. Pour cela, une figure est introduite, reproduite dans la \figref{fig:cercles-non-concentriques}. -\begin{figure} -\resizebox{3cm}{!}{\input{figures/cercles-non-concentriques.tikz}} -\label{fig:cercles-non-concentriques} -\ +\begin{figure}[h] + \center + \resizebox{3cm}{!}{\input{figures/cercles-non-concentriques.tikz}} + \caption{La figure des cercles non-concentriques} + \label{fig:cercles-non-concentriques} +\end{figure} -Le premier 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. +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] +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 + +[^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 --- @@ -143,3 +150,4 @@ $$*\,*\,*$$ # Critique # Bibliographie + diff --git a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Makefile b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Makefile index 36e316de..5174e351 100644 --- a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Makefile +++ b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Makefile @@ -1,8 +1,14 @@ -all: +all: pdf + +pdf: pandoc -f markdown+smart -t latex -o fiche_lecture.pdf \ --standalone --citeproc \ Fiche\ 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\csllabelwidth}{\strut#1\strut}} +\newcommand{\CSLIndent}[1]{\hspace{\cslhangindent}#1} +\setlength{\emergencystretch}{3em} % prevent overfull lines +\providecommand{\tightlist}{% + \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} +\usepackage[left=2cm, right=2cm, top=2.5cm, bottom=2.5cm]{geometry} +\usepackage{hyperref} +\usepackage{centernot} +\usepackage{enumitem} +\setlistdepth{9} +\setlist[itemize,1]{label=$\bullet$} +\setlist[itemize,2]{label=$\bullet$} +\setlist[itemize,3]{label=$\bullet$} +\setlist[itemize,4]{label=$\bullet$} +\setlist[itemize,5]{label=$\bullet$} +\setlist[itemize,6]{label=$\bullet$} +\setlist[itemize,7]{label=$\bullet$} +\setlist[itemize,8]{label=$\bullet$} +\setlist[itemize,9]{label=$\bullet$} +\renewlist{itemize}{itemize}{9} + +\setlist[enumerate,1]{label=$\arabic*.$} +\setlist[enumerate,2]{label=$\alph*.$} +\setlist[enumerate,3]{label=$\roman*.$} +\setlist[enumerate,4]{label=$\arabic*.$} +\setlist[enumerate,5]{label=$\alpha*$} +\setlist[enumerate,6]{label=$\roman*.$} +\setlist[enumerate,7]{label=$\arabic*.$} +\setlist[enumerate,8]{label=$\alph*.$} +\setlist[enumerate,9]{label=$\roman*.$} +\renewlist{enumerate}{enumerate}{9} + +\usepackage[french]{babel} +\usepackage[T1]{fontenc} +\usepackage[ + left = \flqq{}\,,% + right = \,\frqq{},% + leftsub = \flq{}\,,% + rightsub = \,\frq{} % +]{dirtytalk} +\usepackage{csquotes} + +\usepackage{figures/tikzit} +\usepackage{bookmark} +\IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available +\urlstyle{same} +\hypersetup{ + pdftitle={La lettre XII et ses cercles non-concentriques}, + pdfauthor={Oscar Plaisant}, + hidelinks, + pdfcreator={LaTeX via pandoc}} + +\title{La lettre XII et ses cercles non-concentriques} +\usepackage{etoolbox} +\makeatletter +\providecommand{\subtitle}[1]{% add subtitle to \maketitle + \apptocmd{\@title}{\par {\large #1 \par}}{}{} +} +\makeatother +\subtitle{Fiche de lecture} +\author{Oscar Plaisant} +\date{} + +\begin{document} +\maketitle + +\setlength{\parindent}{4ex} +\setlength{\parskip}{0ex} + +\section{Introduction (contexte)}\label{introduction-contexte} + +\section{Résumé}\label{ruxe9sumuxe9} + +\begin{itemize} +\item + Présentation de la lettre +\item + Point de vue exégétique +\item + Point de vue historique +\item + Conclusion +\item + :( L'article ``La \emph{Lettre XII} et ses cercles non-concentrique -- + Spinoza et l'infini actuel entre Descartes et Leibniz'' présente une + analyse philosophique et historique du texte de la \emph{Lettre XII} + de Spinoza. +\end{itemize} + +\subsection{\texorpdfstring{Présentation de la \emph{Lettre +XII}}{Présentation de la Lettre XII}}\label{pruxe9sentation-de-la-lettre-xii} + +La \emph{Lettre XII} de Spinoza addressée à Lodewijk Meyer, un ami +proche de Spinoza\footnote{\say{Une grande amitié les lia, qui ne se démentit jamais}. + (\citeproc{ref-spinoza-pleiade}{Spinoza 2022})}. La lettre précédente +étant perdue, on ne peut que supposer les questions auxquelles elle +réponds. Il est cependant probable que Spinoza y réponde à des questions +de Meyer à propos des \emph{Principia Philosophiae +Cartesianae}\footnote{\say{il est très probable qu'il avait demandé à Spinoza quelques explications supplémentaire sur l'ouvrage} + (\citeproc{ref-camerini-lettre12}{Camerini, n.d., 2}) affirmation qui + vient de + (\citeproc{ref-barbarasSpinozaScienceMathematique2007}{Barbaras 2007, + 127}). Notamment, les dates et les sujets correspondent, et Meyer cite + des passages de la lettre dans la préface.}\footnote{Ce livre de + Spinoza propose de démontrer la philosohpie cartésienne sous une + nouvelle méthode : + \say{[Spinoza rédige] dans l'ordre synthétique ce que Descartes avait exposé dans l'ordre analytique, et le [démontre] à la manière ordinaire des géomètre.} + (\citeproc{ref-spinoza-pleiade}{Spinoza 2022, 174})}. Camerini propose +la division du texte de la lettre dans 12 parties qu'il intitule +ainsi\footnote{Cette division est la même que celle proposée dans + (\citeproc{ref-spinoza-pleiade}{Spinoza 2022, 1075--81})} : + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\tightlist +\item + Salutations initiales à Meyer ; +\item + Introduction à la question de \- l'infini et les trois distinctions ; +\item + Différences entre substance et modes, éternité et durée ; +\item + Divisibilité et \- composition ; +\item + Quantité abstraite et quantité dans \- l'intellect ; +\item + Temps, mesure et nombre ; +\item + Exemple de \- l'heure (temps et durée) ; +\item + Exemple des cercles non \- concentriques (nombre) ; +\item + Application de \- l'exemple à la matière (physique) ; +\item + Résumé des \- conclusions tirées ; +\item + Crescas et démonstration aristotélico-scolastique de \- l'existence de + Dieu ; +\item + Salutations finales. +\end{enumerate} + +\[*\,*\,*\] Dans un premier temps, Camerini présente la partie 2 de la +lettre en expliquant les distinctions opérées par Spinoza sur les +différentes notions de d'infini. Voici le texte français de cette +deuxième partie\footnote{Cette traduction est celle donnée par Camerini, + à laquelle j'ai ajouté le mot \say{Car} pour relier deux morceaux, ce + qui suit la traduction de Bernard Pautrat + (\citeproc{ref-spinoza-pleiade}{Spinoza 2022, 1076}).} : + +\begin{displayquote} +La question de ­ l’Infini a toujours semblé à tout le monde la plus difficile, et même inextricable, parce ­ qu’ils ­ n’ont pas distingué entre ce dont ­ l’être infini suit de sa nature, autrement dit de la force de sa définition, et ce qui ­ n’a aucune fin [\emph{nullos fines habet}], non pas par la force de son essence, mais par celle de sa cause. Ensuite, parce ­ qu’ils ­ n’ont pas distingué entre ce qui est dit infini parce ­ qu’il ­ n’a aucune fin, et ce dont nous ne pouvons pas égaler [\emph{adequare}] ni expliquer les parties par aucun nombre, même si nous en ­ connaissons le maximum et le minimum. Enfin, parce ­ qu’ils ­ n’ont pas distingué entre ce que nous ne pouvons que ­ comprendre [\emph{intelligere}], mais non pas imaginer, et ce que nous pouvons aussi imaginer. Car ils auraient clairement ­ compris [\emph{intellexissent}] quel Infini ne peut être divisé en parties, autrement dit ne peut avoir de parties, et quel au ­ contraire est divisible et cela sans ­ contradiction. Ils auraient également ­ compris en outre quel infini peut être ­ conçu ­ comme plus grand ­ qu’un autre, sans aucune implication [\emph{sine ulla implicantia}], et quel au ­ contraire ne peut ­ l’être. +\end{displayquote} + +Ce passage décisif (et central pour le reste de la lettre\footnote{\say{le centre de gravité de toute la lettre est représentée par le point 2, c'est-à-dire les trois distinctions [...]} + (\citeproc{ref-camerini-lettre12}{Camerini, n.d.}).}) présente trois +distinctions, trois couples de conceptions opposées de l'infini : + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\tightlist +\item + L'infini par son essence ; l'infini par sa cause. +\item + L'infini en tant que sans limites ; l'infini en tant que + \emph{exprimable par aucun nombre} malgré la présence de limites +\item + L'infini de l'imagination ; l'infini de la compréhension + {[}\emph{intelligere}{]}. +\end{enumerate} + +Il est notable que Spinoza ne cherche pas à hiérarchiser ces différentes +notions d'infini : il n'en pause aucune comme mauvaise ou fausse, il ne +sélectionne pas les \say{bons} concepts de l'infini. Il cherche bien +plus à réduire la confusion entre plusieurs concepts qui se cachent dans +le mêm nom d'infini\footnote{Camerini dit : + \say{Spinoza ne semble pas vouloir opérer une sélection entre ce qui est infini et ce qui ne ­ l’est pas. [Il] ne veut pas distinguer entre un vrai et un faux, un bon et un mauvais infini [...]. Son objectif, au ­ contraire, semble être plutôt ­d’analyser les situations ­ d’équivocité,­ c’est-à-dire les cas où deux choses différentes sont appelées par le même nom.} + (\citeproc{ref-camerini-lettre12}{Camerini, n.d.})}\footnote{Cela peut + être relié à une démarche plus large de la part de Spinoza et de son + entourage : + \say{L’exploration du lexique disponible à l’expression humaine passionne Spinoza et ses amis au point qu’ils seraient aujourd’hui considérés comme des linguistes : Meyer a publié un dictionnaire de néerlandais, Koerbagh un dictionnaire du droit (latin/néerlandais)… [...] Les préoccupations du groupe concernent principalement, au fond, la difficulté d’exprimer correctement les choses (idées, corps, passions, etc.) avec une précision satisfaisante. Qu’ils abordent ce problème en poètes (comme Meyer et Bouwmeester), en médecin (Sténon), en théologiens (les Koerbagh) ou en métaphysicien (Spinoza), il s’agit toujours de déterminer des manières de désigner et d’articuler des éléments de réalité et d’en faire circuler la connaissance de manière non ambiguë.} + (\citeproc{ref-ethique-rovere}{Spinoza {[}1677{]} 2021, 470} note 403)}. +En particulier, il affirme : - l'existence d'un infini actuel (dans +l'infini par sa cause), ce qui s'oppose notamment à la conception +aristotélicienne de l'infini\footnote{\say{Spinoza affirme [...]­ l’existence ­ d’un infini causé en acte – ­ contredisant ainsi ­ l’une des pierres angulaires de ­ l’argumentation aristotélicienne, pour laquelle ­ l’infini ­ n’est donné ­ qu’en puissance.} + (\citeproc{ref-camerini-lettre12}{Camerini, n.d.})} - que la présence +de limites ne rend pas nécessairement déterminable (autrement dit, il +nie l'implication \(\text{limité} \implies \neg\text{infini}\)) - qu'il +peut y avoir un infini plus grand qu'un autre - que notre entendement +peut comprendre l'infini, à condition de réguler (parfois limiter) +l'imagination (certains infinis sont imaginables, d'autres seulement +compréhensibles par des raisonnements) + +\%\% Ces trois distinctions proposées par Spinoza s'inscrivent chacune +dans une histoire de la pensée de l'infini (il s'insipre de Hasdaï +Crescas\footnote{\say{[...] Spinoza semble suivre de très près ­ l’argumentation anti-aristotélicienne développée par le penseur médiéval Hasdaï Crescas} + (\citeproc{ref-camerini-lettre12}{Camerini, n.d., 6})}, de problèmes +comme le paradoxe de Galilée\footnote{\say{La seconde distinction [...] remonte [...] au problème du ­ continu de ­ l’Axiome ­ d’Euclide et au paradoxe de Galilée} + (\citeproc{ref-camerini-lettre12}{Camerini, n.d., 6})}\ldots). \%\% + +C'est sur la seconde distinction, et sur l'exemple fourni par Spinoza +(la figure des deux cercles non-concentriques et son commentaire) que +Camerini se concentre. + +\[*\,*\,*\] + +\begin{figure}[h] + \center + \resizebox{3cm}{!}{\input{figures/cercles-non-concentriques.tikz}} + \label{fig:cercles-non-concentriques} + \caption{La figure des cercles non-concentriques} +\end{figure} + +Dans la partie 8 de la \emph{Lettre 12}, Spinoza donne une figure qu'il +utilise comme exemple pour étayer sa seconde distinction des les +infinis. Il veut donc +\say{montrer la différence entre ce qui est dit infini parce ­ qu’il ­ n’a pas de limites et ce qui est dit infini parce que ses parties dépassent tout nombre} +(\citeproc{ref-camerini-lettre12}{Camerini, n.d., 7}). Pour cela, une +figure est introduite, reproduite dans la Figure +\ref{fig:cercles-non-concentriques}. + +Le premier 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. + +\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center} + +Dans son article, Camerini nous propose d'étudier la \emph{lettre sur +l'infini} selon deux points de vue : d'abord ``exégétique'', en essayant +--- par le prisme des traductions française du passage des cercles non +concentriques --- de mieux cerner la conception de l'infini actuel selon +Spinoza ; ensuite historique et philosophique, pour comprendre comment +la position de Spinoza s'inspire mais se détache de celle de Descartes, +mais aussi comment elle s'inscrit dans l'histoire du concept d'infini +actuel. + +\[*\,*\,*\] + +\section{Critique}\label{critique} + +\section*{Bibliographie}\label{bibliographie} +\addcontentsline{toc}{section}{Bibliographie} + +\protect\phantomsection\label{refs} +\begin{CSLReferences}{1}{1} +\bibitem[\citeproctext]{ref-barbarasSpinozaScienceMathematique2007} +Barbaras, Françoise. 2007. \emph{Spinoza : La science mathématique du +salut}. CNRS Philosophie. CNRS Éditions. +\url{https://books.openedition.org/editionscnrs/48687}. + +\bibitem[\citeproctext]{ref-camerini-lettre12} +Camerini, Matteo. n.d. \emph{La {Lettre XII} Et Ses Cercles +Non-Concentriques}. + +\bibitem[\citeproctext]{ref-ethique-rovere} +Spinoza. (1677) 2021. \emph{Éthique}. Maxime Rovere. Flammarion. + +\bibitem[\citeproctext]{ref-spinoza-pleiade} +Spinoza. 2022. \emph{Œuvres complètes}. Pléiade. Gallimard. + +\end{CSLReferences} + +\end{document}