FOM: On claiming that CH has a truth value
Roger Bishop Jones
rbjones at rbjones.com
Fri Oct 20 01:41:38 EDT 2000
In case no-one has noticed, I mention that "the point" of my contributions
to recent fom discussions concerning CH has been the very elementary
and ancient point that if you don't get clear what you are talking about
then you are doomed to perpetually talking at cross purposes.
In relation to CH this suggests that a discussion about the truth value
of CH should begin with explicit agreement about the semantics of the
language in which the CH under discussion is expressed.
In my last message I argued that there are clear and reasonable
assignments of semantics to first order set theory under which
CH has no definite truth value.
The situation prior to any agreement on semantics is even worse
In that circumstance the claim that CH has a truth value has no truth value.
Its up to us, we can chose whether CH has a truth value,
and what it is, by appropriate assignment of semantics to set theory.
Which is not to say that we should chose its value in this way.
It is more likely that the semantics of set theory will be chosen (if at
on other grounds and probable that we will then have a very hard job
deciding whether or not CH is true.
RBJones at RBJones.com
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