- What is necessarily or possibly true
- Modal logic with four operators: true, false, possible, necessary
- A property is necessary if it is true in all worlds, a property is possible if it is true in at least one world.
- False sentences may have different intensions (false but possible, false and impossible)
- Kripke's semantics can interpret all sentences that can be reduced to "it is possible that" and "it is necessary that"
- The truth value of a sentence is always relative to a particular world
- A necessary truth is one that is true in all possible worlds (e.g., 2+2=4)
- A possible truth is one that is true in some world (e.g., 'I am a millionaire')
- A proposition does not have a truth value, but a set of truth values, one for each possible world
- Tarski's theory is purely extensional (for each model the truth of a predicate is determined by the list of objects for which it is true), whereas Kripke's modal logic is intensional.
- Proper names and names of natural kinds are "rigid designators", i.e. in every possible world they designate the same object
- They are linked to their referents through a causal chain. If a scientist discovered that water in not H20, water would still be called water and would still be what it is today