L’état présent des recherches assidus sur les manuscrits mathématiques de Marx: 2

Il y avait aussi des étudiants anglophones du sujet au point de vue historique, peut-être le meilleur parmi eux étant l’américain de famille serbe, Alexander Vucinich (qui a passé, comme Votre Serviteur, assez de temps à Berkeley). À 2000 — il est mort deux années plus tard — il donnait ses vues à la fois sans bornes et trenchantes au journal le plus prestigieux des quelles dévotés à l’histoire des mathématiques [A. Vucinich, “Soviet Mathematics and Dialectics in the Stalin Era,” Historia Mathematica, 2000, vol. 27, pp. 54-76, pages cités 56 & 57]

[Communist Party ideologue Ernst] Kol’man added further to the debate [de la relation dialectique propre aux mathématiques], attacking skeptics who concluded that, because of its concern with formal properties of quantitative measurement rather than with substantive analysis, mathematics stood above dialectics in nature. He wrote in 1932 that Engels deserved credit for the discovery of “dialectical laws in arithmetic and, primarily, in algebra and higher mathematics,” which helped him to oppose the efforts of “bourgeois philosophers” to reduce mathematics to “formal logic” and to treat it as a product of “pure thought.”

Kol’man criticized Friedrich Adler, the author of Marksizm i estestvoznanie, who asserted that it was possible to create “an algebra of dialectics,” but that all efforts to lay the foundations for a “dialectics of algebra” were destined to fail. . . .
Kol’man called for a concerted effort to create a unified Marxist orientation in the foundations of mathematics with mathematicians waging war on all “outdated” theories. First of all, he said, mathematics must be totally integrated into socialist construction, dialectical materialism, and Soviet politics. As their immediate task mathematicians must must clarify the dialectic of continuity and discreteness as categories [accent le mien; c’est-à-dire les manuscrits mathématiques de Marx — MM] of mathematical analysis, link probability theory with other branches of mathematics, reorient mathematics to make it more responsive to practical needs, synchronize logical and historical treatments of mathematical theories, and wage a widely-based attack on logicism, intuitionism, and other ‘idealistic’ orientations in the foundations of mathematics.

In a proper presented at the Second International Congress of Historians of Science, held in London in 1931, Kil’man argued that modern mathematics was dominated by two general orientations, one emphasizing the study of continuities in natural processes and the other concentrating on the study of discrete phenomena. He [considered] that differential calculus dealt exclusively with continuity and that set theory, particularly as advanced by Luzin and [the Moscow mathematical school], recognized only the discrete nature of phenomena. In his opinion the two orientations, left to their own resources, and continuing to subscribe to an idealistic philosophy, could not achieve a unified mathematical orientation. Although he thought that Marxist theory, relying on the dialectical method, was well equipped to handle the problem of unity, he neither made nor suggested moves in that direction. [une phrase de 15 mots omise]

[Junior CP ideologue and successor to E. Kol’man as official editor of Marx’s mathematical manuscripts] S. A. Ianovskaia, in full agreement with Kol’man, argued that the real cause of crisis in the foundations of mathematics must be sought in the one-sided preoccupation of scholars with the formal aspects of their science and their near-total disregard of substantive content drawn from real life. She thought the foundations of mathematics could perform a socially useful role only by establishing harmonious relations between the theoretical postulates of dialectical materialism and the practical needs of socialist construction.

The publication of Marx’s “mathematical manuscripts” in 1933 [c’était seulement une première ébauche, de peut-être quarante pages — MM] marked an important event in the relations of dialectical materialism to mathematics.

Nous voyons voir, Chers Lecteurs, un exercise typique dans de l’argumentation par contradiction naive. C’est à dire, on dit A est vrai; au même temps et à la même degré on dit ne-pas-A est vrai; et en fin, tout qu’on veut dire est vrai. Cette argumentation se trouve au fond des mystifications variées; en place de la traitement conscient du Maître, qui nous expliquait comme à comprendre des lacunae et contradictions comme indicateurs extérieures d’un phénomène pas encore visible, les penseurs bourgeois — et comme ils ressentent la terme! — emploient le fait de contrediction pour une opportunité à démanteler quasi complètement la nécessité de la logique.

Dans cette texte M. Vucinich nous dit que the publication of Marx’s mathematical manuscripts marked an important event in the relations of dialectical materialism to mathematics. Eh bien, continuons avec sa présentation: ses mots prochains sont

The task of interpreting the paper went to Ianovskaia, who made use of this opportunity to establish herself as the chief Marxist spokesperson for modern developments in mathematics. She presented Marx’s papers as a model application of dialectical materialism to mathematics and as a stimulus for future work on a broader and more modern Marxist orientation in the foundations of mathematics. In her opinion Marx attacked “all efforts” to base the foundations of mathematics on absolute — ahistorical — foundations and on a symbolism reflecting philosophic idealism.

Cité par M. Vucinich ici est K. Marx, The Mathematical Manuscripts of Karl Marx, trans. by C. Aronson and M. Meo [London: New Park], 1983; cette référence a été la deuxième à notre oeuvre dans la littérature anglophone.   La première [je me vois comme homme honnête, alors je donne la citation complète verbatim] était dans une note supplémentaire de Irving Anellis [il est nommé comme membre de la groupe éditoriale], “Russell and Engels: Two Approaches to a Hegelian Philosophy of Mathematics,” Philosophia Mathematica, An International Journal for Philosophy of Modern Mathematics, 1987, 2 (2): 151-179, de p. 173:

A bibliography of calculus books read by Marx is given by S. A. Janovskaja [on emploie la transliteration allemande, ne pas l’anglaise] in her posthumously published edition of K. Marx, Matematicheskie Rukopisi (Moscow, 1968).  This list, however, is incomplete.  See the English translation by C. Aronson [depuis défunt] and M. Meo, Mathematical Manuscripts of Karl Marx (London, New Park, 1983, pp. 241-242, “Index of Sources Consulted by Marx”.  Unfortunately, this translation is rather poor.

La référence par M. Vucinich était possible en premier plan parce que j’ai transmis (par la poste) à lui un exemplaire de mon oeuvre, avec une requête polie pour une énoncement de sa signification pour la champs des études russes et soviétiques (j’admet que le mot d’un Vucinich m’assisterait).  La réponse par carte postale était immediate mais brève: “Thank you for sending me a copy of Marx’s mathematical manuscripts.  It is good to have it in English.”

Comme j’expliquera un peu plus tard, cette réplique laconique me semble de l’importance significative.  Pour le présent, continuons avec la citation de Vucinich.

Marx’s mathematical papers prepared Ianovskaia for a general critique of mathematical idealism from a position of dialectical materialism.  She noted that idealistic philosophy was particularly attracted to mathematics

[Surely a solecism here: it is not standard English to say “philosophy was particularly attracted to mathematics,” and a host of expressions in common use are available which convey the concept, such as “philosophy was attractive to mathematicians,” unambiguously.]

and that some Soviet mathematicians demonstrated idealistic inclinations.  She claimed that mathematics deals with phenomena that are empirical, quantitative, material, historical, and dialectical, although she provided no examples illustrating the work of dialectics in the growth of mathematical knowledge.

Marx’s “mathematical manuscripts” advanced two sweeping ideas: they asserted categorically that even the most abstract mathematical theories carried indelible imprints of the social values and styles of thought of their time;

— ah, un moment por favor, Monsieur Vucinich!  Pouvez-vous me dire comment c’est possible “[to] assert categorically that even the most abstract mathematical theories carried indelible imprints of the social values. . . of their time” sans aucune mention quelconque des ces ‘social values’?  J’ai traduit les manuscrit mathématiques alors, et ce n’est pas nécessaire à relire la texte à constater définitivement qu’il n’y existe point de discussion — pas un mot, chers Lecteurs — de société ou de ses valeurs.

Si on demande, qui croit qu’il y a thèse dans les manuscrits mathématiques sur l’importance de société au progrès des mathématiques? — peut-être ce n’est pas Monsieur Vucinich personnellement; peut-être il répète simplement les avis des commentateurs soviétiques.  Le fait reste que la thèse est fausse.

and they created the distinct impression that mathematics was, in a sense, an historical discipline sensitive to changes in its own symbolism, substantive foci, and underlying philosophies.

Voici dans la présentation de M. Vucinich une autre locution forte équivoque; est-il possible en fait “[to] advance two sweeping ideas”, une desquelles est simplement une “distinct impression”?  S’ils avancent la “sweeping idea” c’est certainement beaucoup plus qu’une “distinct impression”.

C’est un jeu académique banal que M. Kucinich ici nous donne: avancer une thèse définitive, et puis reculer devant les consequences de la même thèse.  Une “sweeping idea” “advanced” par les manuscrits mathématiques est prononcé, mais c’est dans la prochaine phrase seulement une “distinct impression”; comme j’ai écrit plus haut, A et ne-pas-A sont les deux vrai, et simultanément.

Et lorsque M. Vucinich nous dit quelque chose claire, comme j’attremperai à démontrer, c’est fausse.

At the time of the publication of Marx’s mathematical manuscripts, there was considerable discussion about the primary significance of the historical approach to “Marxist mathematics”, but no significant changes could be detected.

“detected”, chers Lecteurs, par qui?  Mais cette manière équivoque n’importe.  Voici — les mots immédiatement prochains — la conclusion de M. Vucinich sur les manuscrits mathématiques.

Although the Soviet Union produced rich literature on the history of mathematics from ancient Mesopotamian and Egyptian times to the most recent developments, only a small fragment was written from Marxist theoretical positions [on cite  A.P. Iushkevich en 1948].  No general or systematic study of the role of Marxism in mathematics was undertaken during the Stalinist phase of Soviet history.

Nous revenions au sujet de M. Iushkevich et ses oeuvres au troisième part.

About M. Meo

Worked as translator, museum technician, truck lumper, lecture demonstrator, teacher (of English as a Second Language, science, math). Married for 25 years, 2 boys aged 18 & 16 (both on the Grant cross-country team). A couple of scholarly publications in the history of science. Two years in federal penitentiary, 1970/71, for refusing the draft.
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