Does Fitch's paradox prove an inherent contradiction in the open-world
assumption?

Nilone wrote:
disproved it somewhat with his theorem.

Gödel theorem proves that in any system of sufficient reasoning power,
there are truths about the system which can not be derived from within
the system. There is no contradiction, unless your truths somehow
include "all truths are provable", which is close to what Fitch has said.

Actually, it could be that Fitch simply proved that a knowable truth is
knowable, when he intended to prove something else.
--
Daniel Pitts' Tech Blog: <http://virtualinfinity.net/wordpress/>

On 16 dec, 12:07, Nilone <rea... (AT) gmail (DOT) com> wrote:
Only if you assume that the database contains everything that is
known. It rarely does. :-)

Besides, do you really believe that everything that is true can be
known? ;-)

-- Jan Hidders

Jan Hidders wrote:
Heh... not to mention vice-versa, the chronic slant of so many!

On Wed, 16 Dec 2009 13:09:42 -0800 (PST), Jan Hidders
<hidders (AT) gmail (DOT) com> wrote:

A segue to the continuum hypothesis?

Sincerely,

Gene Wirchenko

On Dec 16, 11:09*pm, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote:
"All truths are known" is only problematic if you assume that truth
exists independent of cognition. From a phenomenalistic point of
view, both entities and predicates exist purely in the mind, which
means that all truths are known, but doesn't exclude the possibility
of creating new truths based on sense data. I'm currently leaning in
this direction (in the sense that Mach espoused), especially after
coming across relational quantum mechanics.

But I'm getting off-topic here. It seems to me now that Fitch's
paradox just illustrates the distinction between OWA and CWA formally.

Nilone wrote:
To be more clear/blunt, in the context of the RM, D&D have it that it is
a value of the relation that has no attributes. This may seem obscure
in general language, but in the db machine context it is much
simpler/clearer than the above.

On Dec 17, 5:06*am, paul c <toledobythe... (AT) oohay (DOT) ac> wrote:
A relation with no attributes is a simple proposition, so you're
saying the chosen assumption is a value in the db, right? I prefer
this, although TTM states they subscribe to CWA.

Is it necessarily a db-wide choice, or could it be useful to
distinguish the choice per relation?

On 17 dec, 03:56, Nilone <rea... (AT) gmail (DOT) com> wrote:
Which in my world view it is. It's positively weird to say that
Fermat's last theorem was not true until a proof was found. If you
want to do so, be my guest, but I'd argue you would be using another
definition of truth than I am.

-- Jan Hidders

On Dec 17, 4:51*pm, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote:
Good point. I'm not sure that's what I want to say, either. I'll
give it some more thought.