This infamous "definition" is circunscribed to
a theory, as in "we say that a physical theory
has an EPR if,..."

Mathematical reality is not the output of
(mathematical) theories but usually its input.
But I think mathematical reality does not
necessary equate to mathematical truth,
nor does the later equate to proof, as
everyone knows by now...

The mathematical reality that Hardy refers to
is the reality of mathematical objects (numbers,
geometric figures, functions, equations, algebras...)
of which we happen to have knowledge, or
rational acquaintance, if you prefer, but not
through our senses! It is undeniable that what
we can agree about concerning these objects
is a lot more certain than what we can agree
about our sensorial (physical) experiences.
We can surely called them Elements of
Mathematical Reality for purposes of
comparison (and aknowledge, for
example, that Quantum Mechanics
contains both EPRs and EMRs and
that not all of the later map to the former...)

Than my paraphrase would be  something along the
following lines: "If, without in any way,
disturbing the physical support of our
mental capabilities,  we can ascertain
with certainty (not necessarily prove)
the attributes of a mathematical object,
than there is an EMR corresponding to
it." This is tentative, of course...


-Joao Leao

scerir wrote:

"If, without in any way disturbing a system,
we can predict with certainty the value of
a physical quantity, there exists an element
of reality corresponding to this physical
quantity", wrote once EPR.

(Of course the strong term here is *predict*,
because prediction is based on something,
a theory, a logic, a model, ... which
may be wrong!)

Is there a similar definition, in math?



Joao Pedro Leao  :::  [EMAIL PROTECTED]
Harvard-Smithsonian Center for Astrophysics
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