# Overreliance on Connotation                      First, let’s assume that all that we know is truth, or more precisely that our certainty in currently held knowledge is invariable and that said certainty for a given concept is arbitrarily high. For simplicity’s sake we will divide the set of all that is known into two smaller sets, $A$ will refer to the set of concepts that are (based on some arbitrary threshold) good and $B$ will refer to the set of all concepts that are bad.

We now introduce an unknown concept, represented here as the element $c$. Person 1 claims that $c$ is akin to another element, $d$, which is unknown to Person 2. Person 1 then asserts that $d\in B$, and therefore $c\in B$. Independently of any other elements, Person 2 determines that $c\in A$ (based on their own analysis and criteria). What then happens at the meeting of Persons 1 and 2?

Based on our initial assumptions, Person 1’s argument for the placement of $c$ in $B$ is likely more compelling that the independent analysis of Person 2. If we are arbitrarily certain in $d\in B$ then so too must we be certain in $c\in B$. To that end, Person 2 should rethink their analysis1. If we’re to agree that sets $A$ and $B$ are objective (as stated by their certainty being arbitrarily high). then Person 1 was correct to classify $c$ based on already classified elements such as $d$.

However, if we were to say the confidence in what is known is not arbitrarily high and is often unknown, then the situation may be reversed. Assuming Person 1 still asserts $d\in B$ therefore $c\in B$ and Person 2’s analysis is acceptable, then what would be brought into question would be Person 1’s assertion. If we believe Person 2 that $c\in A$ and we believe that $c$ is akin to $d$ then we must necessarily question the assertion that $d\in B$2.

1. Assuming we do not consider the placement by Person 2 of $c\in A$ to be yet considered a certainty as the sets were declared at the beginning of this work. ↩︎

2. This is funny, to me. ↩︎