BR TO RALPH G. HAWTREY, 22 June 1908
BRACERS 55817. ALS(X). Churchill College, Cambridge.
Proofread by K. Blackwell

<letterhead>1
Bagley Wood,
Oxford.
June 22. 1908

Dear Hawtrey

The letter I asked you to return2 was fallacious, not in the way of being “guileful”, but because, so far as I can now see, a Ppa is required which I had formerly considered and thought unnecessary. This Pp explicitly introduces the assumption that overlapping ranges are identical. It is:

“When $\phi a$, $\psi a$, and $\phi x$ are true, then $\psi x \; \vee \sim \psi  x$ is true”, i.e. $\psi x$ is significant.

I am not inclined to be dogmatic about types, but I think one must have some other principle than the reflexive one for generating them. Reflexive fallacies afford a regulative control of one’s types, but cannot generate them, because you fall into reflexive fallacies if you attempt such a generation. For this reason, and also on account of a sort of symbolic instinct, which I rely upon more than I can explicitly justify, I am inclined to stick to the idea of ‘structure’ as the essential thing. It is plain that your theory could be adopted without altering more than half a dozen of the props,b because the whole point of types is to restrict, and mine is a theory which restricts more. Accepting your view, that a variable may have a range which is not a type, whatever my theory allows yours allows, but not vice versa; therefore mine is safer. When I have finished the writing out of my half of the book,3 I shall come back to types. You may rely upon me to lay bare any “guilefulness” there may be in the Pp’s. I consider the proof of them to be inductive; it seems to me you would call the law of gravitation “guileful” unless there was an à priori argument to prove its truth.

I will send you $\ast 30$ff, where the proper mathematical development begins. I should like you to have cognizance of the uses of the symbolism, and then to return to fundamentals.

Yrs ever
Bertrand Russell.

Typeset by A. Duncan 2019/02/08;  proofread against a photocopy of a photocopy, K. Blackwell 2019/02/08.

• 1

  [document] The letter was edited from a photocopy.

• 2

  letter I asked you to return Unidentified?

• 3

  bookPrincipia Mathematica.

Textual Notes

• a

  Pp Primitive proposition.

• b

  props Propositions.