24,302 reputation
22067
bio website logicmatters.net
location Cambridge, United Kingdom
age
visits member for 2 years
seen 1 hour ago

Recently retired from Cambridge Philosophy Faculty, interested in logic and philosophy of maths.

I waste time on twitter @PeterSmith (http://twitter.com/PeterSmith/)

For more about me, see http://www.logicmatters.net/about/


23h
comment The ambiguity of set theory language
I know it is frowned upon to make too many "great stuff!" comments -- but this, as Asaf has already said, is great stuff.
1d
reviewed Close Why is mathematics not reducible to logic?
Jul
5
awarded  Yearling
Jul
5
comment Is the completeness theorem for first-order logic relative to one's choice of set theory?
Thanks user18921 -- yes, that wasn't well put and I've corrected along the lines you suggest.
Jul
5
revised Is the completeness theorem for first-order logic relative to one's choice of set theory?
added 8 characters in body
Jul
2
awarded  Curious
Jun
30
answered Simplification of a Disjunctive Normal Form Logic Equation
Jun
24
comment Criticism on truth of Gödel sentence in standard interpretation
Example, take the theory PA + $\neg$Con, where Con is the standard consistency sentence for PA. This theory is unsound on the standard interpretation. Milne's observation is that while, still on the standard interpretation, its canonical (standardly generated) Gödel sentence is true, it also has non-canonical Gödel sentences in the general sense of fixed points for $\neg$Prov which aren't true. So saying "Gödel sentences are always true on the standard interpretation" is wrong if you are using (as some writers do) "Gödel sentence" in the wider sense that covers non-canonical cases.
Jun
24
comment Criticism on truth of Gödel sentence in standard interpretation
Well, there is an issue too about which predicate we use to represent provability -- if Prov(x) represents provability so does Prov(x) $\land \varphi$, for any old theorem $\varphi$. In unsound theories the junk can be false, and using that provability predicate leads to more complications.
Jun
24
answered How much time per day to mathematicians usually spend working?
Jun
24
revised Criticism on truth of Gödel sentence in standard interpretation
added 135 characters in body
Jun
24
answered Criticism on truth of Gödel sentence in standard interpretation
Jun
24
revised Defining a partial function in a formal theory
added 10 characters in body
Jun
24
answered Defining a partial function in a formal theory
Jun
23
revised Truth of Godel's sentence in standard interpretation
added 279 characters in body
Jun
23
comment Reduction ad absurdum in Chiswell&Hodges
Your derivation works. But in fact C&H (if you look very carefully) allow you to discharge "assumptions" that actually appear nowhere, so the bottom three lines of your proof already suffice!
Jun
23
answered Truth of Godel's sentence in standard interpretation
Jun
22
revised Reduction ad absurdum in Chiswell&Hodges
added 30 characters in body
Jun
22
revised Reduction ad absurdum in Chiswell&Hodges
added 1 character in body; edited title
Jun
22
revised Why is removing the negation worse than adding it?
added 30 characters in body