Cortical Circuit Reasoning

Invalid Reasoning

With the introduction of a subjective notion of truth and trying to create some reasoning framework, we need to make some accommodations for inconsistencies and contradictions in our view of the world. According to Paraconsistent Logic, we need to drop a logical principle to prevent the principle of explosion from invalidating our framework. These are the two suggested:

Disjunction introduction	A⊢A∨B
Disjunctive syllogism	A∨B,¬A⊢B

Of these two, it seems that disjunction introduction is the most contrary to way the cortical circuits work. Yes, the brain can add unrelated information to an assertion it believes to be true, but not in a logical statement that gives rise to doubt of the originally held belief. Knowing $A$ is true and introducing $A\vee B$ raises the possibility that $A$ might not be true and it was $B$ all along. However, implying that $A\wedge B$ would be more likely, since $B$ is a component or coexistent with the phenomenon of $A$.

Disjunctive syllogism is the most similar to inhibition of circuits given some contrary evidence. That, or it can be a form of mutual inhibition, the proposition of $B$ winning over the proposition of $A$, because $A$ has the most evidence.

Locality-Sensitive Logic

Instead of having a unified framework in classical logic, in which logical axioms can be applied to any arbitrary set of propositions, we assign relations or topology to the elements in the set. We then adjust the axioms such that they can only be applied to propositions that are “near” to each other. In this way, a logical system becomes locally consistent, but not globally consistent.

This seems more like how people think anyway. Often times people have wildly inconsistent ideas in their heads, but they seem to function in the world regardless, by keeping those modes of thoughts compartmentalized. It’s likely this is how the brain works by design.

When the brain connects to unrelated concepts and builds a conjoined understanding, this creates the “aha!” moment. However, it also creates a topological link in the set of logical propositions, creating a larger set of possible logical expressions. This also creates more shortcuts in the reasoning space and improves the consistency of the overall framework.