Re: Godel did not destroy the Hilbert Frege Russell programme

On Mar 11, 10:44 pm, "elsiemelsi" <cyprin...@xxxxxxxxxxxxxxx> wrote:
you say
In the Introduction to the second edition of Principia, Russell



repudiated Reducibility as 'clearly not the sort of axiom with which
we
can rest content'...Russells own system with out reducibility was
rendered
incapable of achieving its own purpose"

This is correct and is actually implied by what I say above.

i say
you are really in double think arent you
you say you agree with the quote which says AR was abandoned rejected
in
PM and PM was with out AR

But it doesn't say that.

i say

we have agreed the oxford english dictionary say
repudiate = reject

but you say
the quote does not say abandoned rejected without
so what are these capitals in the quote

In the Introduction to the second edition of Principia, Russell REPUDIATED
Reducibility as 'clearly not the sort of axiom with which
we can rest content'...Russells own system WITH OUT reducibility was
rendered
incapable of achieving its own purpose"

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Let's go back up a few posts. A little while ago I wrote this:

"In the 1st edition, Russell and Whitehead presented a formal system
with twenty primitive propositions. One of them was the axiom of
reducibility for unary predicates, another was the axiom of
reducibility for binary predicates. In the 2nd edition, they presented
*the same system*. The main text was essentially unaltered. Some
errors in the references to propositions in proofs were corrected and
an appendix was added explaining how to modify the development of
first-order logic if the two propositional connectives were replaced
with Sheffer's stroke. In the introduction to the 2nd edition, Russell
discussed the changes he would like to make if he had the energy to
re-
write the book. He expressed dissatisfaction with the axiom of
reducibility. He gave a reference to work investigating the ramified
theory of types without extensionality. He also discussed what
happened if you added the axiom of extensionality, which he said was
recommended by Wittgenstein in the Tractatus Logico-Philosophicus. He
found that the resulting system was too weak to develop much of
ordinary mathematics. Subsequent work has shown that EFA can be
interpreted in this system (if we add the axiom of infinity) but not
much more. He concluded that he did not have a satisfactory
alternative to the axiom of reducibility. In any event, the system
presented in the main text was the same as before and included the
axiom of reducibility."

Now, first of all, do you think your quote from the Cambridge History
of Philosophy is inconsistent with this?
.

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