Why is it reasonable to believe that the world will continue to exist after I die? I am not asking for an absolute proof, just a reasonably convincing argument.
It is reasonable to believe for two plausible reasons, namely:
The world has survived the death of billions of other people, so why should your death be any different?
There is no current theory in physics that could explain how a massive body such as the Earth could be destroyed as a consequence of the cessation of certain processes in your head.
Of course, those reasons are only plausible if you believe the Earth is real, and not a figment of your imagination.
Others here argue that you should infer based on the permanence of the universe based on the universe persisting after the death of others, and therefore it seems unlikely that it will cease to persist after your death, and this line of reasoning is very similar to overcoming solipsism.
I'll simply add to it by adding the nuance that every night you lose awareness of the universe when you sleep, and therefore in your own life, when you become unconscious, the universe persists also. Therefore stronger than death, the persistence of the universe through sleep is another angle to undermine the claim that your awareness of the universe is a necessary condition for its existence.
It all hinges on whether you are in any objective way substantially different from others. Although it’s hard to compare two minds in any rigorous way, it’s easy enough to compare bodies.
Slice into your abdomen and your neighbor’s. Do you discover significantly different anatomy or physiology? Draw samples of blood from you and a thousand randomly selected strangers, then do some analytical chemistry and check whether the sample from your own arm stands alone from all the others. Perform fMRIs on yourself and a dozen others while you all perform the same set of cognitive tasks. Do the measurements of your brain function stand out as qualitatively sui generis?
If not, then go ahead and kill one of them to see whether you continue living beyond their death. Unless you see some grounds for disputing comparability, I’d say that what you’re left with is a pretty good basis for assessing whether things are likely to keep on churning after you’ve taken your own turn at croaking.
Reason is the capacity of applying logic consciously by drawing conclusions from new or existing information, with the aim of seeking the truth.
If the existing information regarding the independant existence of the world, relative to yourself, is not enough, then you certainly do not have the capacity to apply logic.
By accepting you have logic, you accept (as reasonable) the inevitability of the independence of the world too.