I have read about inconsistent maths , a math in which contradictions are allowed. It uses , i think , paraconsistent logics..
My question is : Is learning inconsistent maths require knowledge of the maths we know ? Also , Does it have the same branches ordinary maths have ( topology , analysis , geometry , arthiemitic and so on ) ?
Why such maths is Not taught in universities for mathematicians?
I know it's related to logic ... but it's maths at last!
These articles may help with your question, if you haven't seen them already:
http://plato.stanford.edu/entries/logic-paraconsistent http://plato.stanford.edu/entries/mathematics-inconsistent
The gist of the first one is that paraconsistent logics have a variety of motivations. Broadly speaking, paraconsistency is associated with the idea that we're able to embrace, or at least contemplate, contradictions (such as in empirical evidence, human conversation, or scientific theories) without thereby losing all ability to reason logically and to be selective in our inferences.
Mathematics is not the most congenial environment for paraconsistency, since proof by contradiction is a standard technique premised on the idea that if an assumption leads to a contradiction, one must back away from the assumption. But the first article does describe some mathematical applications (see Sections 2.3 and 2.4), and it links to the second one, where that is the focus.
It's hard to see how one could study inconsistent maths without first having a decent grounding in standard maths.
