[FOM] The influence of Leibniz on Russell

Joao Marcos botocudo at gmail.com
Fri May 11 15:18:20 EDT 2007

> I know of only three examples of work in logic which is
> explicitly based on or inspired by these  ideas of Leibniz:
> 1. Frege's citing the lingua characteristica as influencing  his
>    work on the Begriffschrift
> 2. the "calculemus" project, which aims to  integrate theorem
>    proving and computer  algebra software
> 3. Martin Davis's  book  "The Universal Computer".
> Does anyone know of any other examples?

A  number of references on the subject can be found here:

It  seems that one of the main offsprings of the "lingua
characteristica" might
have been the distinction between *language as a universal medium* and
*language as calculus*.  According to the first view (universal medium),  there
is no way of observing our language from outside and describing it, as  we
describe other objects theorized by that very same language; according to  the
second view (calculus), we can perfectly do that, and even raise, just  as
well, meta-theoretical questions about our object language.

This  distinction has been proposed by

 VAN HEIJENOORT, J. Logic as language  and logic as calculus.
 Revue Internationale de Philosophie, 17:324--330,  1967.

inspired by Leibniz, in order to explain the apparent disregard  about semantic
notions to be found in the works of Frege and Russell.   According to Van
Heijenoort, that would explain why Frege and Russell never  heeded the
difference between the notions of *provability* and *validity* (a  difference
which would only be made clear later on, after Lowenheim and  Skolem).

Van Heijenoort's distinction was later updated by the  Hintikka's, at:

 Investigating  Wittgenstein. Basil Blackwell, 1986.

On that subject, the main thing  they do in their book (right at the beginning)
is to affiliate both  Wittgensteins and the later Quine to the Frege-Russell
school of "language  as a universal medium".

Now, I am not acquainted with the following more  recent book, but it certainly
adds more elements to the same discussion:

 HINTIKKA, J. Lingua Universalis vs. Calculus Ratiocinator.
 An  ultimate presupposition of twentieth-century philosophy. Kluwer, 1997.

Joao Marcos

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