Hidden Premises
Ethymene: argument that contains a hidden premise, that contains unstated premises that are obviously true. Hidden premises: What is reasonable to choose as a hidden premise
- Not the conclusion of the argument.
- Choose some formulas where you still need to use all (or almoset all) the existing premises to prove the argument is valid.
- Must be something that would be valid in every interpretation for this argument.
- Often is a universally quantified formula.
What is a Theory?
Definition: A set of axioms (facts) about specific constants, functions and predicate symbols.
Axioms become premises of the argument we are trying to prove.
Model of the theory: an interpretation in which all the axioms of the theory are true.
Theory: Predicate Logic with Equality
Syntax
Use symbol = for the equality predicate. Its argument must be terms. (This predicate describes equality of values.) a = b is an atomic wff. It can be used anywhere an atomic wff can be used in predicate logic formula.