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From: Virgil on 11 Feb 2010 15:21
In article <hl16k7$pp5$1(a)charm.magnus.acs.ohio-state.edu>,
Jim Burns <burns.87(a)osu.edu> wrote:

> Frederick Williams wrote:
> > MoeBlee wrote:
> >> On Feb 10, 2:22 pm, Frederick Williams
> >> <frederick.willia...(a)tesco.net> wrote:
> >>
> >>> Yes, FOL _may_ be unsound but who thinks it
> >> in the least likely? What do you find doubtful in
> >> the ordinary proof that first order logic is sound?
> >
> > Nothing. But I also know that I am fallible.
>
> But, what if you're wrong about being fallible?
>
> Jim Burns

Then he is right about being fallible!
From: HawkLogic on 11 Feb 2010 15:42
On Feb 11, 11:39 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> HawkLogic <hawklo...(a)gmail.com> writes:
> > How can soundness and "unexplored consequences" be compatible in any
> > axiomatic system?
>
> This important question has been extensively studied by Erik
> Freitnautzer, a renowned expert in recreational logic. In his 1967 paper
> /Unexplored Ordinals/ we find the following result:
>
>  For sufficiently large (non-constructive but countable) ordinals, the
>  structure of their (non-canonical) tree representation is isomorphic to
>  the (canonical) fiber-bundle on the lattice of Turing degrees of
>  incompatible consistent completions of the set of consequences of the
>  ordinal (when interpreted as a formal theory).
>
> (A tree representation in this context corresponds to the metrizable
> Hilbert space of unexplored consequences of an ordinal. Here we're
> implicitly relying on Kreisel's conceptual analysis and Gödel's
> interpretation of dialectical materialism.)
>
> --
> Aatu Koskensilta (aatu.koskensi...(a)uta.fi)
>
> "Wovon man nicht sprechan kann, darüber muss man schweigen"
>  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus


This reminds me of an interchange of ideas from another forum I once
attended:

Martin G.: "Nobody in their right mind reads Godel."

Doug H.: "Only insane people choose to be logical?
That must be false."

Ray S.: "It is, and I can prove it!"

Need more be said?
From: Tom on 15 Feb 2010 11:35
HL wrote:

> Is there?

It's there.

T.
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