Re: Peirce List Discussion • Charles Pyle

Let’s consider Peirce’s logical graphs at the alpha level, the abstract forms of which can be interpreted for propositional logic.  I say “can be interpreted” advisedly because the system of logical graphs itself forms an uninterpreted syntax, the formulas of which have no fixed meaning until interpreted.  As it happens, the forms themselves do not determine their interpretations uniquely.  There is at minimum a degree of freedom that allows them to be interpreted in two different ways, corresponding to what Peirce called his entitative graphs and his existential graphs.

Bringing this to bear on the empty sheet of assertion we have the following facts:

The blank SA is a symbol and wants interpretation to give it a meaning.  Under the entitative reading (En) it means “false”.  Under the existential reading (Ex) it means “true”.  What in turn these “interpretants” mean requires a further, denotative interpretation relative to the universe of discourse at hand, “true” denoting the whole universe and “false” denoting the empty set.