Will mathematics be easier to teach if its logic allow contradiction?

I wish Appalachian cultural traditions could help every American student succeed in learning math.

One of our idioms, "Stupidity is the highest wisdom." is an example of "X and not X".

When we teach mathematics, we rely on an underlying cognition system of classical logic, this logic is like a tree -- begin with axioms that don't contradict with each other.

Is this the root cause of inequality in logic and mathematics education?

Dominant ideology is invented by rich white intellectuals. They are built on classical propositional logic. Non-classical logic systems , that legitimizes contradictory axioms, dialogical proofs and reaches contradicting conclusions, are naturally suppressed by the ideology dominance. Thus, classical logic does not support opposition to white supremacy and class oppression, because it rejects "X and not X", while minorities and poor are deprived of abilities to achieve X.

I am not educated on this topic, but I feel it's nothing new in society's practice. Dialogues, for example, contain two separate trees of propositions that might come from different roots. In language education, different regions could have different words and pronunciations.

If we have an alternative logic system that tolerates "X and not X", we might be able to find out new ways to teach math.

Can we build a fundamentally diverse set of mathematics on this alternative logic system? Will underclass and minority students find this new mathematics more learnable and acceptable?

Submitted December 20, 2021 at 11:31PM by innofuel https://ift.tt/3J7D8JK