On the Nature of Evidence, and the Use of Possible World Semantics. Part 1 (draft):

N.B. In many, if not most, of the posts to this blog I will regard the universe as both temporally and spatially discrete (though not necessarily finite). In general the arguments presented are simple to extend to the continuous case, but are easier to explain and easier to follow in the discrete case.

What do we mean by "Evidence"

Evidence is the stuff that gives us reason to believe things. It is an accepted observation or statement of fact that lends support to some other statement or its negation. Evidence does not exist in a vacuum, it is always for or against some other statement.

On Possible Worlds and a Refinement Thereof

A possible world is a conceived state of affairs that we have no reason to believe is self-contradictory or otherwise impossible. In other words, it is a world which does not obtain merely because the universe happens to be otherwise. This terminology is useful but imperfect, since the set of "possible worlds" may include worlds that are not in fact possible! An example illustrates the point: imagine a world, otherwise like the real world, in which I was christened Mitt instead of Tim. I would call myself Mitt, my ID cards would say "Put, Mitt", and the url of this blog would be MittPut.blogspot.com, etcetera. In every other macroscopic way the world would be similar: the US would still have gone to war with Iraq in 2003, IBM would still be a leading computer manufacturer. Clearly we want to include this world in the set of "possible worlds"; we have no reason to believe it is not possible, it is historical accident that we live in the world we do and not in the world of Mitt Put. But we don't actually know if Mitt's world is possible. Perhaps chaotic systems really are quite common and any world up to that point similar to ours in which I am named Mitt would be drastically different. Perhaps in every world in which there is a Mitt Put the US goes to war with Iran in 2003, or with Iraq in 2005