Notes

Meaning = Stipulated or descriptive (reportive)

Definitions = of truth and connectives (stipulated) what we mean by ^ is a truth function such that x, y, z. Alternatively we find such a function and label it ^

By truth, if A accurately describes the world then it is true (stipulated definition of truth as correspondence theory). If A does not accurately describe world then we say ~A or A is false (stipulated definition of false).

Axioms = From definition of negation, LNC follows since whenever ~A is true, then A is false by definition of ~.
LEM follows, Whenever A is false, ~A is true by definition of ~.
a=a by definition of = it is the same object because the same constant name picks out the same object.

Therefore since LEM (at least true or false) and LNC (can not be both true and false) are both true, each atomic of the form A has at least one truth value.


To-dos:
- Talk about models
- Prove that if every atomic formula has unique value then more complex formulas have a unique value. Probably by induction.
- By truth table test, we can establish further axioms (valid formulas, tautologies, whatever) by truth table test.
- All the possible valuations in a truth table test is exhausted by those lines on a truth table test why? Each line corresponds to a model. Why does each line correspond to a model? How do we know we have enough lines to correspond to all possible models?