prop 1: "p ( p)"
Proposition 1, where the symbols "" and "" are intended as logical disjunction and negation respectively and "p" is an arbitrary proposition, is plausibly true in all possible worlds.
It doesn't appear to have any ontological implications.

prop 3: "Either the population of New York is greater than 1 million, or it isn't."
Proposition 3 would probably be thought meaningless if New York did not exist, and so it might not be true.
But it cannot be false, it is an instance of the tautology expressed by proposition 1.
We may therefore prefer not to say it is contingent, and we may be willling to consider it necessary.


prop 2: "2 + 2 = 4"
It is difficult to conceive any possibility that
proposition 2 is false except that the sentence we use to express the proposition means something other than we normally mean by "2+2=4".
Assuming the semantics of the language is fixed, the proposition may be thought necessary.
There is embodied in the semantics an ontological presupposition which merits discussion.

prop 4: "The population of New York is greater than 1 million."
Proposition 4 is true in some possible worlds and false in others.
It need not necessarily be true and hence it is not logically necessary and we say it is contingent.

