[FOM] Question of the Day: What is a Logic?
neilt at mercutio.cohums.ohio-state.edu
Fri Oct 6 15:12:29 EDT 2006
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*.
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?
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