These two letters are taken from the Frege-Russell correspondence in Frege, Philosophical and Mathematical Correspondence, ed. Gabriel, Hermes, Kambartek and Veraart, Chicago 1980).
They are interesting in part for the quaint form of address (dear colleague) and also for Russell's postal address (Ivy Lodge, Tilford). Tilford is a secluded village in Surrey, still very picturesque (with a village green and cricket club). Russell moved there in 1904 in order to work out a theory of denoting that could be used in Principia Mathematica, but which would avoid the Paradox (now known as Russell's paradox) that he had discovered while working on the Principles of Mathematics. Despite a visit there, I could not locate Ivy Lodge, and it was not in any postal records at the time I looked (2002).
The letters show Russell toying with ideas about 'denoting' that are very different from what emerged in his celebrated paper 'On Denoting'. His thought here, of which Frege clearly does not approve, is that the objects which bear proper names themselves enter into the thoughts and propositions we express by their use. (In 'On Denoting', of course, they do not). This idea later became known as Direct Reference, and thoughts whose existence depend on the existence of the objects they are 'about' have sometimes been called Russellian thoughts.
I did not attempt to translate the German word (Bedeuting) that is sometimes rendered 'reference', sometimes 'denotation', sometimes just 'meaning'. On the assumption that Russell was writing in German, I did the same in his letter.
Frege to Russell
... Mont Blanc with its snowfields is not itself a component part of the thought that Mont Blanc is more than 4,000 metres high ... The sense of the word 'Moon' is a component part of the thought that the moon is smaller than the earth. The moon itself (i.e. the Bedeutung of the word 'Moon' is not part of the sense of the word 'Moon'; for then it would also be a component part of a thought. We can nevertheless say: 'The Moon is idential with the heavenly body closest to the earth'. What is identical, however, is not a component part but the Bedeutung of the expression 'the Moon' and 'the heavenly body closest to the earth'. We can say that 3+4 is identical with 8-1; i.e. that the Bedeutung of '3+4' coincides with the Bedeutung of '8-1'. But this Bedeutung, namely the number 7, is not a component part of the sense of '3+4'. The identity is not an identity of sense, nor of part of the sense, but of Bedeutung ...
Russell to Frege
... Concerning sense and Bedeutung, I see nothing but difficulties which I cannot overcome ... I believe that in spite of all its snowfields Mont Blanc itself is a component part of what is actually asserted in 'Mont Blanc is more than 4,000 metres high'. We do not assert the thought, for this is a private psychological matter: we assert the object of the thought, and this is, to my mind, a certain complex (an objective proposition, one might say) in which Mont Blanc is itself a component part. If we do not admit this, then we get the conclusion that we know nothing at all about Mont Blanc. This is why for me the Bedeutung of a proposition is not the true, but a certain complex which (in the given case) is true. In the case of a simple proper name like 'Socrates', I cannot distinguish between sense and Bedeutung; I see only the idea, which is psychological, and the object. Or better: I do not admit the sense at all, but only the idea and the denotation. I see the difference between sense and Bedeutung only in the case of complexes whose Bedeutung is an object, e.g. the values of ordinary mathematical functions like ξ + 1, ξ2
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