Logical Operators

Given the pattern for intersection above, one might naturally ask how this relates to the "Law of Intersection [L7]" already introduced where the logical symbol for conjunction was introduced:

• α : β ⊇ γ ≡ γ = α ∩ β ≡ γ = β ∩ α 

The answer is that the law of intersection tells how a simple act of predication can be understood as an instance of inclusive intersect from the perspective of the occasion which is providing the intrinsic aspect through the Thing Channel.  In the Law above, this is the gamma occasion.  A rendering of this law in English would be "Alpha means gamma counter-predicates beta", or in other words, gamma is-present-in beta.  As such, there is a consequence, as the law goes on that "Gamma equals Alpha intersecting Beta" and because intersection is commutative, we also have "Gamma equals Beta intersecting alpha".

So, every occasion of predication is itself (the gray occasions of Inclusion, or SEH\\ in the conjunction and disjunction trickle diagrams above), an act of inclusive intersection, but when there are two (or more) of these predications converging on a common occasion, the expression becomes of an overlapping intersect (imagine the typical overlapping circles of a Venn Diagram).