Abstract
Alexandre Koyré’s views on Pascal have been published twice, in the proceedings of the “colloque de Royaumont”, éd. de Minuit, 1956, and in the Études d’histoire de la pensée scientifique. His speech in Royaumont is still famous, as he disturbed the French audience by questioning the genius of Pascal as a mathematician and the reality of the celebrated Rouen experiments, two largely admitted ideas in France. However, by this speech, he opened a new field, which had never clearly appeared before: the important part of the “art de persuader” in Pascal’s scientific works.
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Notes
- 1.
- 2.
J. Mesnard in Pascal 1964–1992, II, p. 494. Hereafter, I will refer to this edition by the acronym OC, followed by the volume number.
- 3.
The paper on Cavalieri was published a year before the conference on Pascal.
- 4.
Even the silences which marked the discussion were significant. In the discussion that followed the talk about “Pascal, scientist”, Marxist L. Goldmann , who usually specialized in interminable interventions, did not say a word.
- 5.
Both these editions are unsatisfactory as far as the Pensées are concerned. The Brunschvicg edition (Pascal 1904–1914) is based on a principle of thematic classification, which cancels out Pascal’s apologetic project. As for the Chevalier (Pascal 1954) edition, it is an attempt to reconstruct Pascal’s plan, mostly owed to the editor’s imagination. The Lafuma edition was published in 1951. The Sellier edition (Pascal 1991) and Le Guern edition (Pascal 1977) give us a more satisfactory version today. But they are based on completely different principles. Today, the only really satisfactory edition of Pascal’s Œuvres complètes is Jean Mesnard’s , by Desclée de Brouwer (Pascal 1964–1992).
- 6.
Koyré mainly thinks of Giordano Bruno’s writings.
- 7.
An echo of this discussion can be found in later studies, for example see Lanavère 1971, p. 82. See also Mesnard 1993, p. 89 . The place of this cosmological vision in the spiritual progress and conversion is stated in Pascal’s Écrit sur la conversion du pécheur, OC IV, pp. 40–44. I must add that the transcript of the debates is also interesting because it highlights the confusion which often creeps in the heat of the debates. It happened when it came to the argument of the wager, which the interlocutors agreed to nullify, on the pretext that the infinity of God is of a different nature from the mathematical infinite. Actually, the infinity of God only intervenes in the first part of the text in order to establish that the finite mind of men cannot comprehend God’s immensity. But from the moment when Pascal sets to determine what can reasonably be wagered, the only infinite which comes into his calculations is that of supernatural eternity, whose duration and worth can be expressed mathematically. Such a confusion is not rare during conferences.
- 8.
It is not completely certain that Koyré may not be somewhat bad-mouthing Pascal. Indeed, nothing allows us to suppose that by publishing his Lettre à M. ADDS (Arnauld, docteur de Sorbonne) on the equality of the parabolic arc and of the spiral arc, Pascal meant to “deal a bad blow to Torricelli”, to please Roberval , his “master and friend”, who was Torricelli’s rival in the invention of indivisibles.
- 9.
Koyré reckons it is “unusable”. In the 1950s, the restoration of the remaining machines, which showed that was not the case, had not yet taken place. Mourlevat (Mourlevat 1988) also showed that the secrets of the functioning of the Pascalines (especially the repartition of the weights of the inner parts) had not all been grasped at the end of the twentieth century.
- 10.
Dettonville was the pseudonym Pascal used for his works on the cycloid .
- 11.
Traité des Trilignes, Proposition II: “La somme des carrés des ordonnées à la base est double des rectangles compris de chaque ordonnée à l’axe et de sa distance à la base.” (OC IV, pp. 444–445).
- 12.
Like many others before him, Koyré assimilated l’hexagramme mystique to the théorème de l’hexagone, which says the intersections of the opposite sides of a hexagon inscribed in a conic section cross on lined-up points. Actually, René Taton (1964) and Jean Mesnard (1993) contested this identification: hexagon means that the figure has six sides, while hexagram means that it is comprised of six letters, which is not the same thing.
- 13.
Of course, we know that Fermat too had his own method for computing “partis”, which he compared with Pascal’s. But their correspondence shows that their principles were different.
- 14.
Koyré yielded here to the same tendency as Jesuit Henri Bosmans’s , who, for similar reasons, presented Jesuit André Tacquet as Pascal’s master when it came to indivisibles, arguing that Pascal did not know the geometrical homogenity law until he read Tacquet’s Cylindrica et annularia book, which shows that every demonstration by means of heterogeous indivisibles should be reduced to classical proofs. See Bosmans 1924, pp. 130–161, pp. 424–451. Father Tacquet’s treatise was printed twice: Cylindricorum et annularium libri IV (1651) were comprised of four books; in 1659, the Jesuit added a fifth one. The date is significant: the Society of Jesus was looking for a geometrician capable of winning recognition in the competition arranged by Pascal, as Father Lalouvère was being ridiculed. Book V focused on the problems of the centres of gravity, the most difficult problems posed by Pascal.
- 15.
- 16.
The 46 ft of the tube corresponded to 15,088 m then. The 32 ft of the water column represented 10,496 m.
- 17.
Roberval apparently did not witness for himself the Rouen experiments.
- 18.
Koyré reminds us that Robert Boyle already maintained in the seventeenth century that some of the experiments of the Treatise on the Equilibrium of Liquids were only mental experiments. He also doubted that it was possible to send a man 20 ft underwater. Indeed, it is even less likely that this same man should be sent in a cistern full of oil, as Pascal imagined in The Weight of the Air (OC II, p. 1078). However, the characteristics of the experiments of The Equilibrium of Liquids are not the same as those of the Rouen experiments.
- 19.
Actually, Pascal did not have a treatise up his sleeve in 1647.
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Descotes, D. (2018). Alexandre Koyré and Blaise Pascal. In: Pisano, R., Agassi, J., Drozdova, D. (eds) Hypotheses and Perspectives in the History and Philosophy of Science. Springer, Cham. https://doi.org/10.1007/978-3-319-61712-1_6
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