FOM: Determinacy of statements -- reply to Richman

Fred Richman richman at
Sun Jun 25 09:08:36 EDT 2000

JoeShipman at wrote:
> Richman:

> >I don't see this. Why is TPC either true or false in that intended
> > model? If I am questioning the law of excluded middle, then I am not
> > apt to go along with this claim.
> The law of the excluded middle may be problematic when applied syntactically
> to sentences independent of any models.  But FOR A GIVEN MODEL, a properly
> formed sentence is either true or false by the definition of the satisfaction
> relation.

How could any constructivist go along with your second statement? Of
course a constructivist could *define* the law of excluded middle to
be true (in the model) by excluding any sentence that fails to satisfy
it (in the model), but then he would exclude sentences like TPC. Your
claim here seems to rest on the grounds that if the model is "the
integers as a completed whole", then the law of excluded middle holds
for TPC in that model. That is exactly what I do not see.

> Constructivists are free to deny that the intended model exists (either
> because they can't see that any models exist or don't think that the
> "intended" one has actually been unambiguously identified), but if they
> accept the existence of a model they should accept the satisfaction relation
> on it as well.

I'm sure they accept the satisfaction relation, they just don't accept
the claim that a properly formed sentence is either true in the model
or false in the model. As I understand it, the satisfaction relation
converts a string of symbols that is syntactically a sentence into a
statement about the model. The question is whether that statement
about the model satisfies the law of excluded middle. There are no
general grounds for a constructivist to think that it would.


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