FOM: social construction?

[Martin Davis]

At 06:30 PM 3/19/98 -0500, wtait at ix.netcom.com wrote:

>Martin Davis wrote (19/3)
>>I'm suggesting that when
>>we say that 7 or sqrt(2) or sqrt(-1) or the real number system "exist" what
>>we (as mathematicians) mean (or at least ought to mean) is that we know how
>>to determine some of their properties as definite and have good reason to
>>think of those we can not decide as definite problems to work on. 

>I am with you in spirit, Martin; but I don't think this is what you mean 
>to say. You seem to be making the assertion of existence in mathematics 
>amount to an assertion about us, what we do or could do---which would 
>suit Hersh, if I understand him, but would not suit you, if I understand 
>you (in previous communications).
>
>Bill Tait
>
Thank you Bill. Careless wording on my part. Let me try to do better:

I'm suggesting that when
we say that 7 or sqrt(2) or sqrt(-1) or the real number system "exist" what
we (as mathematicians) mean (or at least ought to mean) is that they are
objective in the sense that they have properties which we can determine (or
try to determine) but which we have no power to alter.

Better?
Martin