[FOM] Does consistency imply existence? (Was: CH and mathematics)

Benjamin somrh at yahoo.com
Sun Jan 20 08:01:28 EST 2008

I had further thoughts on this issue and decided to
make it its own topic because it might be worth
discussing in its own right, irrespective of CH. 

--- Bill Taylor <W.Taylor at math.canterbury.ac.nz>
> a: IMHO, this must destroy Thomas' view that
> "consistency is existence",
>    at least for the mathematical realist.   Do
> others agree?

One way to conceive of a form is to conceive of it as
an "abstract possibility" that can be materialized or
instantiated in the "realm of becoming". So we might
think of this particular hydrogen atom or that
particular hydrogen atom but we could very well think
of universal "hydrogen atom" itself. 

Further, we can (and do!) speculate on uninstantiated
elements, at least elements which are not known to
exist anywhere in the universe but which chemists and
physicists may try to create in laboratory. We can
speculate on the qualities it has due to its formal
features and so we can think of the form has having an
"existence" in an "abstract possibility" sense even if
it doesn't "exist" in an instantiated sense.

We can also further consider the word "possibility"
which has many senses. We talk of "physical
possibility" and "logical possibility" and perhaps we
can talk of other sense. 

We say that something is logically possible iff it
doesn't entail a contradiction (i.e. it is

In this sense the consistency definition not only does
not "destroy" Platonic realism but may even be
equivalent to Platonic realism (so long as we construe
"form" as "abstract possibility" and we construe
"possibility" as "logically possible" as defined

How this would be fleshed out in terms of CH I'm not
entirely sure.


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