Even if there were logic, and if there were existence, and if those that exist, do actually exist, and those that don’t exist, don’t, we cannot really know if we exist ourselves.

I have no idea if I exist. Again, it is more meaningful to think that I do exist. It would actually be quite depressing if I didn’t: if I did not exist, what would my life matter? There wouldn’t even be "my life". My thoughts would be someone else’s thoughts, or maybe they would not even be thoughts, who knows.

Therefore it is rational, or at least healthier, to think that I do exist.