XPost: comp.theory, sci.math
From: acm@muc.de
[ Followup-To: set ]
In comp.theory polcott wrote:
> On 2/15/2026 1:27 PM, Alan Mackenzie wrote:
>> In comp.theory Tristan Wibberley
>> wrote:
>>> On 15/02/2026 01:41, Richard Damon wrote:
>>>> On 2/14/26 3:59 PM, polcott wrote:
>> [ .... ]
>>>>> So it looks like you are saying that no one can count
>>>>> until after they first count to infinity?
>>>> No, he is pointing out that if you claim to encode ALL the knowledge
>>>> that is expressible in language, you can't stop until you finish, and
>>>> since there are an infinite number of those in Peano Arithmetic, you
>>>> can't stop at any finite number.
>>> You're talking about decompressing the encoding of knowledge. Stating
>>> the axioms (and full detail of inference rules) symbolically is
>>> sufficient to /encode/ the knowledge if you have lambda calculus or
>>> illative combinatory logic.
>> Olcott's system, by his own admission, is insufficiently powerful to
>> express a true proposition it can't prove. Thus Peano arithmetic is
>> outside of its scope. You can't count in Olcott's system.
> Unintentionally counter-factual.
> You merely lack a sufficient grasp of Proof Theoretic Semantics.
I don't need this. You lack a sufficient grasp of mathematical logic.
By Gödel's incompleteness theorem, any system powerful enough to count in
is powerful enough to express a true proposition it can't prove.
Your system, so far as I can't discern, lacks this power. So you can't
count in it.
> PTS is the exact same ideas that have been saying for many
> years. The only difference is that now you can look up and
> see all of the details of exactly how I was right all along.
But everybody else can see how you've always been wrong. Maybe you're
wrong about what proof theoretic semantics says, too.
> --
> Copyright 2026 Olcott
--
Alan Mackenzie (Nuremberg, Germany).
--- SoupGate-Win32 v1.05
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