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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: 1,566
Registered: 7/4/07
Re: A finite set of all naturals
Posted: Aug 12, 2013 10:23 AM
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Peter Percival <peterxpercival@hotmail.com> writes:

> Ben Bacarisse wrote:
>> 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>

>
> Yes, since not every natural number is a prime, and a conjunct claims
> otherwise, the whole is false. Perhaps
>
> Ap1p2[[prime(p1) /\ prime(p2)] -> (p1+p2<x \/ x<p1+p2)]
>
> was meant.


That was my guess too, but the reader shouldn't have to guess. For one
thing, other errors, they may not be so obvious.

Since the post is more than a year old, these sort of issues may have
been corrected, but it's a shame there is no TeX-formatted version (as
you suggested) for easy reading. The journal will definitely want one.

--
Ben.


Date Subject Author
8/12/13
Read Re: A finite set of all naturals
Ben Bacarisse
8/12/13
Read Re: A finite set of all naturals
Peter Percival
8/12/13
Read Re: A finite set of all naturals
fom
8/12/13
Read Re: A finite set of all naturals
Ben Bacarisse
8/12/13
Read Re: A finite set of all naturals
namducnguyen
8/12/13
Read Re: A finite set of all naturals
namducnguyen
8/12/13
Read Re: A finite set of all naturals
antani
8/12/13
Read Re: A finite set of all naturals
namducnguyen
8/13/13
Read Re: A finite set of all naturals
Marshall
8/13/13
Read Re: A finite set of all naturals
quasi
8/13/13
Read Re: A finite set of all naturals
namducnguyen
8/13/13
Read Re: A finite set of all naturals
quasi
8/13/13
Read Re: A finite set of all naturals
namducnguyen
8/13/13
Read Re: A finite set of all naturals
namducnguyen
8/13/13
Read Re: A finite set of all naturals
quasi
8/13/13
Read Re: A finite set of all naturals
namducnguyen
8/14/13
Read Re: A finite set of all naturals
quasi
8/14/13
Read Re: A finite set of all naturals
namducnguyen
8/14/13
Read Re: A finite set of all naturals
quasi
8/14/13
Read Re: A finite set of all naturals
namducnguyen
8/15/13
Read Re: A finite set of all naturals
namducnguyen
8/15/13
Read Re: A finite set of all naturals
Virgil
8/15/13
Read Re: A finite set of all naturals
namducnguyen
8/15/13
Read Re: A finite set of all naturals
antani
8/13/13
Read Re: A finite set of all naturals
antani
8/13/13
Read Re: A finite set of all naturals
Peter Percival
8/13/13
Read Re: A finite set of all naturals
Ben Bacarisse
8/13/13
Read Re: A finite set of all naturals
namducnguyen
8/14/13
Read Re: A finite set of all naturals
Peter Percival
8/14/13
Read Re: A finite set of all naturals
Shmuel (Seymour J.) Metz

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