Friday, April 14, 2006

Goedel, Hofsteader and Leibniz
G.H.L within G.E.B?

I was reading a selection from Leibniz' 'Dialogue on the Connection Between Things and Words' (1677) today and was getting 'deja vu' from Douglas Hofsteader's Goedel, Escher Bach (GEB).

I went out looking and here is why: On Goedel's Philosophy of Mathematics, specifically his part on the existence of mathematical objects. So of course, if Goedel refers to Leibniz (which apparently he does), and Hofsteader refers to Godel, on something much the same subject as Leibniz.. it comes around logically that one will sound very much like the other -- even though it comes about it thirdhand(?).

Anyway -- what I am babbling on about is this:

I only mean that characters must show, when they are used in demonstrations, some kind of connection, grouping and order which are also found in the objects, and that this is required, if not in the single words -- though it were better so -- then at least in their union and connection.

This order and correspondence at least must be present in all languages, though in different ways. And that leaves me with hope ...For even though characters are as such arbitrary, there is still in their application and connection something valid which is not arbitrary; namely, a relationship which exists between them and things, and consequently, definite relations among all the different characters used to express the same things.

And this relationship, this connection is the foundation of truth. For this explains why no matter which characters we use, the result remains the same (as in algebra), or at least, the rsults which we find are equivalent and correspond to one another in definite ways. Some kind of characters is surely always required in thinking.

quot3ed from Leibniz' Dialogue on the Connections Between Things and Words - 1677



If you've read G.E.B -- you will find a ring of familiarity in the talk about 'arbitrary symbols' and the things they represent. I'll have to go back through that book myself and see if (probably), how and where he himself references Leibniz... it has been several years and G.E.B is one LONG and heavy-reading book.

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