Source for Peano article written in symbolic logic

Question

L.E.J. Brouwer states in his 1912 address titled "Intuitionism and Formalism" that Peano

published one of his most important discoveries concerning the existence of integrals of real differential equations in the Mathematische Annalen in the language of symbolic logic; the result was that it could only be read by a few of the initiated and that it did not become generally available until one of these had translated the article into German.

I can only find this version but this is a French translation. Does anyone know where I can find Peano's original article written "in the language of symbolic logic" referenced by Brouwer?

Answer 1

Actually, Brouwer did refer to

Peano, G. (1890). "Demonstration de l'intégrabilité des équations différentielles ordinaires". Mathematische Annalen. 37 (2): 182–228.

which is exactly the version you linked.

This paper of 1890 is not the French translation of an article earlier written by Peano elsewhere, but an original paper written by Peano in French. According to Wikipedia, that paper gives a new proof of the fundamental theorem which guarantees the existence of solutions to certain initial value problems. Few years before (1886), Peano already published a paper with a proof of such a theorem, but the proof turned out to be incorrect.

Brouwer says that Peano's 1890 paper is written "in the language of symbolic logic" because if you read it, you can see that there are several theorems and proofs, and whole pages too, written using only the language of symbolic logic. See for instance pages 196-198 and 211-223.

The translation to German of Peano's 1890 paper is due to Mie, few years later:

Mie, G. (1893). "Beweis der Integrierbarkeit gewöhnlicher Differentialgleichungssysteme nach Peano". Mathematische Annalen, 43, pp. 553–568.

I presume that in the German version (which I have never seen) those theorems and proofs written in the language of symbolic logic by Peano are translated in German as well.

This recent paper by E. Luciano essentially confirms Brouwer's version on the initial "flop" of Peano's 1890 paper:

In these works Peano applied, for the first time, the methods and language of his mathematical logic; this use of symbolical procedures delayed the reception of his articles by the international mathematical community. Only after the translation into ordinary mathematical language by G. Mie in 1893 of Peano’s article “Démonstration de l’intégrabilité des équations différentielles ordinaires” [Peano 1890, pp. 182-228], did the importance of his results and the elegance of his proofs become recognized. [pp. 40]

Interestingly, Luciano also cites a letter from Peano to Jordan (in Italian) dating back to 1894, where he says that, according to him, his most relevant contribution in his 1890 paper is the formalization of his results in the language of symbolic logic, even though this was exactly the reason why that paper was initially ignored.