BR TO LEON CHWISTEK, 21 OCT. 1923
BRACERS 57257. ALS. Polish Acad. Sci(s)
Proofread by A.G. Bone

<letterhead>
31 Sydney Street
London. S.W. 3.
21.10.23

Dear Sir

Thank you very much for your letter of Sp. 21. I shall be very glad to receive the publication you mention, but unfortunately I do not know Polish, so I shall not be able to understand your book. I will see, however, whether a translator is to be found.

The MS. you sent me interested me greatly. I have no doubt that, if one simply cuts out the axiom of reducibility, without other change, it is not possible to do much more than you have done. It is clear the axiom must be cut out. But I now incline to the view (which I understand is also advocated by some in Poland) that all functions of propositions are truth-functions, and all functions of functions are extensional. On this basis, the theory of inductive numbers can be built up as before, with a little trouble. Well-ordered series and Dedekindian series still require the sort of limitations that occur in your MS, but not finite series.

I did not quite understand the contradiction you deduced from the axiom of reducibility, though I am not surprised that a contradiction should be deducible.

The enclosed may interest you. I learn that they do not desire, in the early numbers, to print articles using much of the symbolism of mathematical logic; otherwise, you might be willing to cooperate, and possibly some of your friends might.

Yours very truly
Bertrand Russell.