[FOM] Classical logic and the mathematical practice

[Moshe David]

Dear FOM memebrs,

I'm a young researcher in complex analysis  and I have a bothersome 
question...
If you could answer my question I would be grateful !!!

Q : Why the majority of the (working) mathematicians are still using 
classical logic ? to sharpen my question :
we use the excluded middle without any worry and say that the real field is 
the disjoint union of  \Bbb Q and \Bbb Q^c
though we know that there will be a chance that the rationality of some real 
numbers (e.g. the Euler constant) is undecidable assuming ZFC.
Is the using of classical logic is not actually Realism/Platonism ? , is 
there any ontological or epistemological justification to use classical 
logic when we know
that intuitionist logic is more safer and remote from Realism  ?

Best regards,

Moshe David
Math. Dept. BIU