[FOM] Falsify Platonism?

joeshipman@aol.com joeshipman at aol.com
Thu Apr 22 23:38:45 EDT 2010

But how could one ever demonstrate that CH does not possess a truth 
value? Even if you could demonstrate that the truth value of CH was 
essentially unknowable, to pass from that to "it has no truth value" is 
an unjustified step unless you are already sneaking in the 
anti-Platonistic axiom that all truth is knowable. It seems obvious to 
me that one could no more disprove Platonism than one could disprove 
theism. If you assert that God exists but make no statements about what 
he does, your assertion cannot be refuted, since his existence or 
nonexistence in your sense has no consequences.

Now one may take the position that we have not defined our terms 
clearly enough, and "the universe of sets" is simply not well-defined 
enough  for CH to have a truth value (since to settle the truth value 
of CH you only need to go up to a pretty low rank, this is implausible, 
but a statement like GCH which talks about sets of arbitrary rank can 
be plausibly considered as too vague to have a meaning). But this is 
still not refuting Platonism, any more than my statement "all bloogs 
are skwozzled" refutes Platonism by virtue of its terms not having been 
sufficiently defined for it to have a truth value.

-- JS

-----Original Message-----
From: Brian Hart <hart.bri at gmail.com>

One way to falsify set-theoretical Platonism might be by demonstrating
that CH does not posess a truth value since it is a presumption of
Platonism in general that all mathematical statements possess such a

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