FOM: 'constructivism' as 'minimalistic platonism'
Fred Richman
richman at fau.edu
Fri Jun 2 10:14:17 EDT 2000
Stephen G Simpson wrote:
> From the realist point of view, there is nothing wrong with tertium
> non datur. If P states something unambiguous about something real,
> then necessarily P is either so or not so, i.e., we can confidently
> assert "P or not P", even if we don't know which of the two is the
> case.
This is an issue that has puzzled me for some time. I take it that the
last sentence in the quote is some sort of argument that deduces the
(confident) law of excluded middle from the realist point of view.
I've heard this stated a number of times before, but it is normally
just stated, as here. Is there some more convincing argument, with the
details filled in?
My suspicion is that the law of excluded middle is simply being
assumed as part of the realist point of view, in which case, of
course, no derivation is necessary. But why is the law of excluded
middle necessarily part of a realist point of view? If I believe in
the objective existence of the natural number series, am I committed
to the proposition "either there exists an odd perfect number, or all
perfect numbers are even"?
--Fred
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