Re: Peter Smith says Godel is rubbish
- From: Jan Burse <janburse@xxxxxxxxxxx>
- Date: Sun, 25 Nov 2007 15:21:09 +0100
elsiemelsi schrieb:
but as i askedActually the difference between equivalence between
1)
what does godel do when wants his formular to mean
16. 0 N x ≡ x
(n+1) N x ≡ R(3) * n N x
ie ≡ means ≡
and not
16. N(0 x)= x
N (n+1, x)= R(3) * N (n, x)
sentences (i.e. the biconditional sign) and equivalence
between terms (i.e. the equality sign) is anyway
superficial. Namely because the biconditional is
an equivalence:
A B | A <-> B A = B A NOT XOR B
--------------------------------------
0 0 | 1 1 1
0 1 | 0 0 0
1 0 | 0 0 0
1 1 | 1 1 1
So equality restricted to the boolean domain (i.e.
truth values) amounts to the biconditional. So Gödel
is more than right in using the same symbol. Because
its essentially the same. Asking for two sentences
whether they are follow from each other if and only if
is they same as asking whether they have the same
truth value.
There might be some suttle differences involved when
not classical logic is used, or when it should be
emphasized that we are interested in a proof theoretic
notion, then we could use -||-. But I assume this
is not the case in the present gödel text.
Bye
.
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