Re: Ontolog Forum • Ferenc Kovacs
Re: Anja-Karina Pahl • Contradiction and Analogy as the Basis for Inventive Thinking
One of the insights coming out of Peirce’s logical work is the fact that negative operations are more powerful than positive operations in the sense that negative operations can generate all possible operations while positive operations by themselves do not suffice. This is epitomized by his discovery of the amphecks as sole sufficient operators for propositional logic.
The propositional logic algorithm I wrote for my Theme One Program turns this principle to good effect in two ways:
- The graph-theoretic syntax is based on a graph-theoretic operator, a type of controlled negation called the minimal negation operator, that generalizes Peirce’s graph-theoretic operator for negation.
- It turns out that recognizing contradictions quickly makes for a high degree of efficiency in finding the “models” or satisfying interpretations of a propositional formula.
Relations of contradiction are also critical in statistical inference, but I’ll need to save that for another day.
to a binary value in 
that is, a characteristic function or indicator function 
and 
the fiber of 
under 
is the set of elements denoted or indicated by the predicate. That is the semantics, anyway. As far as syntax goes, there are many formal languages whose syntactic expressions serve as names for those functions and nominally speaking one may call those names predicates.
where 
is the object domain (think universe of discourse) and 
and 
are domains of signs (think channels or languages) being used to talk and think about 
is most often applied in one of two ways.
In cases where 
we are often concerned with transformations taking place within a single set of signals and we may write 
to signify our focus on sign relational triples of the form 
where 
is a sign that follows 
in a logical or temporal sequence, in short, where 
Inquiry Into Inquiry 