On Thursday, April 25, 2013 3:58:56 PM UTC-4, FredJeffries wrote: > On Apr 25, 8:25 am, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote: > > > Newberry <newberr...@gmail.com> writes: > > > > Torkel Franzen argues that all the axioms of ZFC are manifestly true > > > > the logic apparatus is truth preserving therefore all is good and the > > > > system is consistent. > > > > > > Really?? > > > > > > Where did he make this claim? > > > > > > In "The Popular Impact of Gödel's Incompleteness Theorem" > > > > http://www.ams.org/notices/200604/fea-franzen.pdf > > > > he says: > > > > "we can easily, indeed trivially, prove PA consistent using > > reasoning of a kind that mathematicians otherwise > > use without qualms in proving theorems of > > arithmetic. Basically, this easy consistency proof observes > > that all theorems of PA are derived by valid > > logical reasoning from basic principles true of the > > natural numbers, so no contradiction is derivable in PA"
So it seems that perhaps he didn't make the claim regarding ZFC but only regarding the weaker system of PA; which is hardly surprising since PA is generally considered to be nonproblematic in a way that ZFC is not. Of course strict finitists such as Edward Nelson might be unconvinced, but such skeptics are in a small minority.