Subject: Re: [lojban] Not talking about imaginary worlds

From: Björn Gohla <[email-masked]>
Date: Mon, 2 Jul 2001 23:25:18 +0200

On Monday 02 July 2001 11:40, Edward Cherlin wrote:
> We will have to do what the mathematicians do--Work out how to express
> ourselves clumsily in the current language, and then invent a better one
> when we have a better idea of what we are doing.

not being proficient enough in mathematics yet i do not fully grasp the depth 
of the arguments brought forward here. however in spite of risking to restate 
some of what was written, the following:

i imagine a hierachy of "universes", each of these is determined by the 
propositions that are certain within them, and they contain a potentially 
infinite number of propositions that are undecided. by determining an 
undecided proposition a new universe is created which inherits all 
certainties from its ancestor adding to them the proposition whose 
affirmation created the new universe. all other uncertainties persist.  

applied to discourse that means a speaker starts out with a universe 
containing all propositions that are true form his perspective, whether all 
those propositions are considered seperately for the sake of universe 
creation or as one does not matter much. as long as the speaker does not 
question what he holds to be true, corresponding to traversing the hierarchy 
rootwards, we are not concerned with what lies "below" the universe 
representing the speakers knowledge. the concept becomes feaseble once one 
considers propositions that are not decided in the current universe, they 
could be either true or false, bearing the potential for two new universes. 
thus if the speaker wants to argue based on the tentative truth or falsity of 
the proposition in question, he "enters" one of the universes and from then 
on anything said will presume the proposition determined. he may of course 
equally well leave the universe again and enter the opposite or create ones 
within others, "recursively speculating" so to say.

in the terms of this concept the usual "if p is true then q is true" phrases 
could be described as taking the undecided proposition p, entering the 
universe where p is true, and then affirming q. this is equivalent to saying 
"suppose p is true. q is true". the latter seems to be employed when the 
consequence demands a longer description so the condition is syntactically 
detached.

the root of the hierarchy could be imagined as being determined by a 
proposition of the sort "i think therefore i am".

- -- 
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pub 1024D/834F4976 2001-01-07 Björn Gohla (Wissenschaftler, Weltbürger) 
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