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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Tue, 24 Sep 2002 12:04:32 +0200

At 22:26 -0700 21/09/2002, Brent Meeker wrote:

*>I don't see how this follows. If you have a set of axioms, and
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*>rules of inference, then (per Godel) there are undecidable
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*>propositions. One of these may be added as an axiom and the
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*>system will still be consistent. This will allow you to prove
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*>more things about the mathematical structures. But you could
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*>also add the negation of the proposition as an axiom and then
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*>you prove different things. So until the axiom set is
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*>augmented, the mathematical structures they imply don't exist.
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Why? The *tree* of possible extensions of theories can exist

(in platonia let us say).

The tree of possible models of theories can also exists in Platonia.

Actually both those trees are posets (or even categories).

And those theories/models posets are related by categorical (in the

category sense, not in the logical sense) so-called adjunction, relating

theories and models of theories in a mathematically rich sense.

What is true for Everett's worlds is a fortiori true for

mathematical models or models' sequences. The splitting and relative

1-indeterminacy cannot be used against their ontological 3-atemporal

existence, it seems to me.

Bruno

Received on Tue Sep 24 2002 - 03:08:03 PDT

Date: Tue, 24 Sep 2002 12:04:32 +0200

At 22:26 -0700 21/09/2002, Brent Meeker wrote:

Why? The *tree* of possible extensions of theories can exist

(in platonia let us say).

The tree of possible models of theories can also exists in Platonia.

Actually both those trees are posets (or even categories).

And those theories/models posets are related by categorical (in the

category sense, not in the logical sense) so-called adjunction, relating

theories and models of theories in a mathematically rich sense.

What is true for Everett's worlds is a fortiori true for

mathematical models or models' sequences. The splitting and relative

1-indeterminacy cannot be used against their ontological 3-atemporal

existence, it seems to me.

Bruno

Received on Tue Sep 24 2002 - 03:08:03 PDT

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