[FOM] Wittgenstein?

[William Tait]

On Tuesday, April 22, 2003, at 03:11  PM, sean.stidd at juno.com wrote:


> It is a common myth that Wittgenstein invented the truth-tables, but 
> this is not so: one can find them in Frege. Wittgenstein himself 
> specifically disavows any claim to having invented them in the 
> Lectures on the Foundations of Mathematics, Cora Diamond, ed. (at work 
> now so don't have the page number handy).

Page 177, where he attributes the truth tables to Frege..

> That said I do not dispute at all the claim that W's contributions to 
> the philosophy of logic were (and IMO remain) very important. He just 
> didn't invent the truth tables. What was original to W was his use of 
> the truth tables to elucidate a combinatoric conception of the 
> propositional connectives.

LW's thesis in the Tractatus is that every proposition is a 
truth-function of independent  elementary propositions and that a 
logical or mathematical truth is a tautology. Even if we ignore the 
question of independence, this restricts mathematics to predicative 
mathematics, since, e.g., even second-order  impredicative arithmetical 
propositions cannot in general be understood as truth functions of 
atomic arithmetical propositions.

If we add the independence condition, then the only domains of 
discourse possible consists essentially of  sets of independent tosses 
of coins. What real domains of discourse can be understood in such 
terms?

It is in its mad way a beautiful book, and I can sympathize with people 
who try to make a coherent sense of it. But until someone can explain 
his notion of object and of elementary proposition as a certain kind of 
concatenation of objects, in a way that fits the rest of the text,  the 
basic doctrine of the book remains obscure.

In any case, let me provoke: I would say that the Tractatus had no role 
whatsoever in the subsequent development of logic or mathematics.

Bill Tait