[FOM] Question of the Day: What is a Logic?

[Neil Tennant]

On Fri, 6 Oct 2006, Arnon Avron wrote:

> Concerning a paraconsistent logic as a possible base for 
> the foundations of mathematics, my answer is: No way. *Mathematics
> should be consistent*.

Arnon,

How can you justify to your reader the following inference, which is
implicit in the foregoing?:

	Mathematics should be consistent; 
  ergo, one should not use a paraconsistent logic for mathematics.

I don't get it. Suppose mathematics is consistent. And suppose one uses a
paraconsistent logic for mathematics. Then one can still prove all
mathematical theorems.  Where's the problem?

Neil Tennant