Many Possible Worlds

Some notes on Possibilia and Contingent truths.

It seems to me that there are two main lines of dealing with hypotheticals and contingently-false propositions - rhetorically or ontologically.

On the "metaphysical" side you have the idea of possibilia - the proposed facts that correspond to counterfactuals, hypotheticals and suppositional propositions are real, just not "here in this world".  Of the possibilia solutions you have Lewis' multiverse or Leibniz's "ideas in the mind of God" - where the truth of an hypothetical depends on whether or not there is -in fact- this other kind of thing and whether or not it can be arranged as proposed.

On the other side you have a rhetorical or irrealist view of the matter where hypotheticals and the contingently false propositions are dealt with as pure words and where the assert-ability of such a proposition depends on the rules of the language in which they are asserted rather than on whether or not any such thing is "actually possible".  

One difference between these two approaches is best seen in examples, take this one:

(a) There might be nothing but shrimp.

An ontological approach might take this to be demonstrably false.  (As follows: If everything were shrimp, there would be no propositions, and so the proposition "everything is shrimp" is not true and therefore false in every possible world.)  Similarly with Leibniz's god-ideas, God can not conceive a world in which necessary existents do not exist, and some of those are not shrimp.

A rhetorical approach might take this proposition to be true.  It might be that there were nothing but shrimp.  Why not?  We understand what the sentence says, and while we know that -in fact- there are non-shrimp-things, it might have been the case that there weren't.  Such an approach would be unimpressed by the idea that there would be no proposition to express the shrimp-world's possibility nor that shrimp in the shrimp world would have to be simple or made up of shrimp.  

Both sides have weaknesses it seems to me.  The rhetorical approach's weakness is that we can change the rules of the discourse to make -anything possible-.  Dogs might be chickens or the number three as long as we allow ourselves to talk that way.  And it seems to me that this is obviously false - no matter how we talk, it seems to me, dogs can not be the number 3.  

The ontological approach, at the same time, has us postulating the existence of alternate universes, platonic heavens or god-thought-realms which seems to me miss the point of many counterfactuals, viz:

(b) I might have been born in Africa.

It seems to me that the "I" in (b) refers to ME, Robert Lindauer, in fact born in Burbank, California, and that if some other person in some other world was born in africa it is irrelevant to whether or not that proposition is true, even if that person is my doppleganger.  We have a way of expressing that fact:

(c) There is an alternate world where another person named Robert Lindauer was born in africa and he's very like you in many other respects.

And (c) seems expressible but straightforwardly false, or at least clearly irrelevant to (b) which is about Me whereas (c) is about someone else.

A platonic or quasi-platonic solution like Leibniz's which postulates the existence of a realm of possibilia seems to equally miss the point.  Even if there were an "ideal robbie that was born in ideal africa" that Robbie is clearly not me, and again, we have a way of expressing that kind of thing which is still not equivalent to proposing that I might have been born in africa, viz:

(d) God imagined Robbie being born in africa.

or 

(e) there is a platonic form corresponding to robbie having been born in africa.

Now we might imagine God imagining anything we like and so as far as differentiating between true and false I think (d) will not do.  Nor will a modified "God thought that there might have been a world in which Robbie was born in africa" which comes to the even worse problem which is what we are trying to define is -the-what- that God would have been entertaining about the proposition in question.   That is, the counterfactual nature of my birthplace being what we are trying to define, we can not therefore identify it as a thought in God's mind without first having defined what kind of thought it was for which we were looking.

The last one (e) is a more serious contender.   The Platonic form or "Proposition" that "I might have been born in Africa" is at least partially the same as that expressed by the expression ("Robbie might have been born in Africa, and I am Robbie.") even though they might have different meanings or intended interpretations.   The -fact- that makes it true would have been the same (viz, me being born in africa) and the arbitrariness of making -all- things possible similarly goes away.  I could have been born in Africa is true, ONLY IF, there exists a proposition P such that P is false but P is not self contradictory or self-defeating and P implies that I could have been born in africa.

Solution To Puzzle

Can God make a Weight so Heavy He can not lift it?  This puzzle is meant to demonstrate that the idea of God's omnipotence is incoherent.  In Leibniz's system, the puzzle is troubling, surely God could imagine such a weight, why could He not make it?  In Lewis' system the problem is doubly-troubling.  In worlds in which there is a God, some of them God is not omnipotent, and in the worlds in which God is Omnipotent we are given no help.   A rhetorical approach scoffs at the question and so for them it is irrelevant.  But for the Platonist, surely the question of what God is being asked to do is relevant, for if what He is being asked to do is simply impossible or nonsensical or even, for that matter, contradictory with the Dictates of God Himself, the question of whether or not He can do it is absurd, equivalent to asking whether 2 plus 2 could be 17.

In conclusion:

The possible worlds approach doesn't cover relevant cases correctly, in particular the ontological structure required to support the possible worlds mechanism makes simple cases of seeming possibilities trivially false.  It is, therefore, simply an inadequate analysis of our use of counterfactuals.   It may be an analysis of some concept, but it is NOT our concept of a counterfactual conditional.  Purely syntactical or rhetorical versions are equally poor but for the opposition reason, they are too liberal with their attribution of possibility.  Endowing even the most obscenely and obviously impossible statements to seem possible.  The Platonic version - the existence of coherent sets of propositions about the way the world might have been configured but is not, is perfectly clear and correctly captures our notion of counterfactual conditional.