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

-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?

s.

-- Joao Pedro Leao ::: [EMAIL PROTECTED] Harvard-Smithsonian Center for Astrophysics 1815 Massachussetts Av. , Cambridge MA 02140 Work Phone: (617)-496-7990 extension 124 VoIP Phone: (617)=384-6679 Cell-Phone: (617)-817-1800 ---------------------------------------------- "All generalizations are abusive (specially this one!)" -------------------------------------------------------