PWIP 42

Thoughts on Logic

Every proposition contains terms. The terms are defined using propositions. Perhaps one could consider the collection of all the terms with definitions the epistemic dictionary. There are actual dictionaries for languages and other subjects. Individuals contain in themselves certain symbols that they can give a kind of definition for. The terms are organized according to their epistemic closeness. This generates a knowledge network or web. Chains of propositions appear to form superstructures, like narratives and sciences.

Negation causes many problems in the search for truth through logic. All linguistic propositions can be negated through some kind of rejection response (though meaningful rejections come from informed justifications). Dissent can occur when terms conflict with each other. An object’s opposite may mix with it to produce a new object, or its negation leads them both to the null set or falsehood.

Epistemology is a subset of ontology. Everything that is discovered or is discoverable is innate to ontology. Ontology seems to be in control of all things since it is existence and existing is being what one is. Epistemology contains some parts of ontology. What does it mean for there to be ontological objects outside of epistemology? Some objects are perhaps unknowable. The dictionary could be the subset of epistemology that deals with knowable objects.

On the difference between “and” and “or” in logic and natural language

Can I clarify these concepts in my own mind? The term “and” means a term A is generated while a term B is generated. The term “or” means a term A can be generated, a term B can be generated. In logic (informal logic--since I’m no logician) “and” and “or” are binary functions that can span multiple terms. The term “and” as used in natural language is used for the truth function of the binary function that is true when all terms under its purview are true. The term “or” as used in natural language is used for the truth function of the binary function that is true when at least a few, but not all, of the terms under the function’s purview are true. In logic, changing the interpretation of the truth functions concerning the term “or” can result in the inclusive “or” or the exclusive “or”. The inclusive "or" appears to include the "and" function, whereas the exclusive "or" does not.

“And” seems to imply a time period. If the case is one can choose A and B, does the “and” change when one somehow takes A and B at different times; maybe A and B are taken at the same time, or A is taken then B is taken? The natural language (English language at least) doesn’t distinguish between the time beyond some condition on the “and,” such as simultaneity or ordering. A kind of “and” seems to exist between all terms. Relationships seem to be cases of “and.” It could be the logical “and” is implicit whenever multiplicity is involved.