tag:blogger.com,1999:blog-23478689.post5254239353896134912..comments2014-08-30T19:38:59.046+00:00Comments on Logic Matters: Gödel Without Tears -- 4Peter Smithhttp://www.blogger.com/profile/03957579588136008664noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-23478689.post-57981497927469356082009-11-02T16:41:49.273+00:002009-11-02T16:41:49.273+00:00Many, many thanks a.c. :-) Corrected.Many, many thanks a.c. :-) Corrected.Peter Smithhttp://www.blogger.com/profile/03957579588136008664noreply@blogger.comtag:blogger.com,1999:blog-23478689.post-1387855243962809122009-11-02T15:59:29.130+00:002009-11-02T15:59:29.130+00:00Sentence near the top of p 2:
Q, then, is a very ...Sentence near the top of p 2:<br /><br />Q, then, is a very weak arithmetic. Still, it will turn out to be ‘modest amount of arithmetic’ needed to get Theorem 2 to ﬂy, and also containing Q gives us a ‘suﬃciently strong arithmetic’ in the sense of Theorem 6.<br /><br />Should the "it will turn out to be" be "it will turn out that the"?<br /><br />Also should be a comma after "and also containing Q".<br /><br />- - - - -<br /><br />Minor detail at the end of section 12 on p 6:<br /><br />"The answer will emerge over shortly enough" reads oddly to me.<br /><br />- - - - -<br /><br />Last sentence before 13.1: missing space between "and" and PI_1.<br /><br />- - - - -<br /><br />2nd sentence of 1st para of 13.1:<br /><br />"We can now express such claims in formal arithmetics like Q and PA wﬀs of the shape ..."<br /><br />Should be "... using wffs of the shape ...".<br /><br />- - - - -<br /><br />Proof of Theorem 17 on p 8:<br /><br />Two (separate) "then"s in the 2nd sentence when only one ought to be needed.<br /><br />The proof concludes:<br /><br />Contraposing, if T is consistent, it proves any Π1 sentence it proves is true.<br /><br />Is that what was intended? Or should it be only that if T is consistent, any Π1 sentence it proves is true. (Taking out the "it proves" before "any".)a.c.noreply@blogger.com