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Topic: A finite set of all naturals
Replies: 32   Last Post: Aug 15, 2013 4:07 PM

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 Ben Bacarisse Posts: 1,972 Registered: 7/4/07
Re: A finite set of all naturals
Posted: Aug 12, 2013 7:04 AM
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fom <fomJUNK@nyms.net> writes:
<snip>
> Here is the proof he provides when pressed to produce:
>
> https://groups.google.com/d/msg/comp.ai.philosophy/AVnJgA5ZIk0/fk1sQQNSYVgJ

I could not resist taking just a little peek... That post claims to be
"written in the language of arithmetic L(PA)" but it contains this
definition early on:

Def-03a: even1(x) <-> Ey[x=y+y]
Def-03b: even2(x) <-> Ey[x=2*y]
Def-03c: even(x) <-> (even1(x) \/ even2(x))

Does this mean that Ax[even1(x)=even2(x)] is not a theorem of the system
being used, or does it mean that the author is inclined to use overly
complex definitions? Either way, I didn't find it an encouraging start.

Maybe I don't understand the notation, because just a few lines further
on I see:

Def-05c: aGC(x) <->
(even(x) /\ (SS0<x)) -> Ap1p2[prime(p1) /\ prime(p2) /\
(p1+p2<x \/ x<p1+p2)]

but isn't Ap1p2[prime(p1) /\ prime(p2) /\ (p1+p2<x \/ x<p1+p2)] simply
false?

<snip>
--
Ben.

Date Subject Author
8/12/13 Ben Bacarisse
8/12/13 Peter Percival
8/12/13 fom
8/12/13 Ben Bacarisse
8/12/13 namducnguyen
8/12/13 namducnguyen
8/12/13 antani
8/12/13 namducnguyen
8/13/13 Marshall
8/13/13 quasi
8/13/13 namducnguyen
8/13/13 quasi
8/13/13 namducnguyen
8/13/13 namducnguyen
8/13/13 quasi
8/13/13 namducnguyen
8/14/13 quasi
8/14/13 namducnguyen
8/14/13 quasi
8/14/13 namducnguyen
8/15/13 namducnguyen
8/15/13 Virgil
8/15/13 namducnguyen
8/15/13 antani
8/13/13 antani
8/13/13 Peter Percival
8/13/13 Ben Bacarisse
8/13/13 namducnguyen
8/14/13 Peter Percival
8/14/13 Shmuel (Seymour J.) Metz

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