I just realized that for the proposition "If p is necessarily true then p is true", i.e. "box p implies p", to be a tautology, we need the condition that every world is accessible to itself. That is, for every model M=(W,R) we need the reflexivity of the accessibility relation.
Here's my question:
It makes sense to assert that if a proposition is necessarily true then it is true. So every world must be accessible to itself. Because if not, then what makes sense above may not make sense anymore.
Does this mean that every world is accessible to itself? Of course there are models where reflexivity of the accessibility relation is absent. But in a philosophical point of view, I think it's safe and fair to assert that a necessary truth is a truth. And argue that every world is accessible to itself as a consequence of the above assertion. Perhaps I haven't fully understood the meaning of a world being accessible to another world. Any help is appreciated. Thanks!
Edit: I changed "p is necessarily true implies p is possibly true" to "p is necessarily true implies p is true". But I'm happy with both statements being tautologies.