[FOM] The income of Peter or Paul

[somrh@yahoo.com]

--- On Sat, 2/28/09, Thomas Forster <T.Forster at dpmms.cam.ac.uk> wrote:
> 
> Fisher says  ``Whereas such a phrase as `the probability of
> A or B'
> has a simple meaning where A and B are mutually exclusive
> possibilities
> `the likelihood of A or B' is more parallel with `the
> income of Peter
> or Paul' you cannot know which it is until you know
> which is meant.''
> 
> Has anyone had anything sensible to say about the obvious
> parallel
> with the constructive account of disjunction?

Perhaps you have something in mind like the use of the additive rule in some of the Gettier counterexamples (such as Case II in his original paper: http://www.ditext.com/gettier/gettier.html)

If we take Case II, we might say that (h): "Either Jones owns a Ford, or Brown is in Barcelona." means something different when we consider its justification (based on "Jones owns a Ford") as compared to when we consider it as being true (based on "Brown is in Barcelona"). It's as if we go from PvQ when P is a definite proposition and Q is arbitrary to PvQ when Q is a definite proposition and P is arbitrary.

Is the rule ever used in mathematics? I can't recall a place where I ever desired to use it. I've always thought there was something "fishy" about it. In any event...

Another place to look might be within literature on "explosion" and paraconsistent logics (which also might be an interesting topic for the group if it hasn't already been discussed.) Explosion seems to be a consequence of disjunctive additive rule along with the disjunctive syllogism (or some equivalent set of rules). Why ought an inconsistent set or propositions permit any wff to be proven? 

Benjamin