8 Jan
2003
8 Jan
'03
3:05 p.m.
"Sarad AV" writes:
there will be no inconsistency in a formal axiomatic systems
Huh?
-but can any one point me to a contradicting set of axioms in an axiomatic system?
In general you have to consider the whole system, including derivation rules, not just the axioms, although you can certain start with a set of axioms like: { x=1, x=2} or, come to think of it, { 1=2 } Most famously, Frege's system was shown to be inconsistent by Russel. More recently, the first edition of Quine's Mathematical Logic (1940) was shown to be inconsistent by Rosser. For Frege, see "From Frege to Gvdel: A Source Book in Mathematical Logic, 1879-1931" by Jean van Heijenoort