&gt; I am struggling to find a succinct way to explain why this is but the following example might be work.<p>That example mostly explains why fuzzy membership quantities aren&#x27;t the same thing as probabilities.<p>&gt; You end up running into contradictions all over the place and having a non-binary system of logic makes it nearly impossible to develop any formal system of reasoning.<p>Such systems (e.g., fuzzy logic) have been developed, so its clearly not impossible to develop them, and they tend to <i>include</i> classical binary logic as a special case.