Everything is possible
Just when I thought all viruses are specific, I caught an 'unspecific virus' last weekend -- at least that's what the doctors at the hospital identified it as. So I've been knocked out for about a week, but now I'm back with an exciting new theory of modality.
The theory is simple. It says that everything is possible. Pace Kripke, there are possible worlds where Queen Elizabeth is a poached egg and where Hesperus isn't Phosphorus. And pace almost everybody else, there are possible worlds where squares are round, bachelors married and where Hesperus isn't even self-identical.
Sure, we normally call such things impossible. But it is well known that we often ignore possibilities in everyday talk: it is absolutely impossible (stomp the foot, bang the table) for me to read all those books until tomorrow. And yet, speaking unrestrictedly, it is clearly possible. I could easily do it if the laws of nature were suitably different. When we say that married bachelors are impossible -- absolutely impossible (stomp the foot, bang the table) --, we also ignore some possible worlds: those with married bachelors.
Qua bachelors, the possible married bachelors are also unmarried. They are both married and unmarried. And herein lies the crucial point of the exciting new theory: that we must not infer impossibilities from contradictions or inconceivabilities. After all, Kripke demonstrated with his meter bar that such reasoning is fallacious: given that the meter is defined with reference to the meter bar, it is contradictory and inconceivable that the meter bar be anything but 1 meter long -- and still it could be longer. Inconceivability and inconsistency are no guide to impossibility.
It is ironic and sad that Kripke himself didn't see the impact of his own discovery; that later in Naming and Necessity, he moves from the inconceivability and a priori falsehood of Hesperus being non-self-identical or Queen Elizabeth having different parents to infer that these things are impossible. The right thing to say would have been that all these considerations tell us nothing at all about modal space.
Then why believe that everything is possible, rather than only some things? For reasons of theoretical simplicity and strength.
First, it is better not to draw a line than to draw an arbitrary line. We could say that everything that goes against classical logic is impossible, or everything that goes against the laws of nature, or everything that begins with the letter "F". But what's the point?
Second, this way of not drawing the line gives us all the power of impossible worlds without impossible worlds: false mathematical beliefs can be handled just as easily in possible-worlds terms as counterfactuals with logically impossible (but still possible) antecedents.
Third, this account opens the way for a simple reductive theory of modality. Take linguistic ersatzism, on which possible worlds are something like maximally consistent sets of sentences: Lewis complained that modality is required to define "maximally consistent". This problem is gone if worlds don't need to be consistent in the first place. Every set of sentences can be a world. We don't need to distinguish possible from impossible worlds if all worlds are possible. And of course we don't need to worry about a posteriori necessities: there are none.
Finally, the exciting new theory is good because it supports ontological diversity: all unrestricted supervenience claims come out false. Not only are there zombie worlds, physically like ours but without any consciousness, there are also worlds physically like ours but chemically, biologically, politically and mathematically different. Nothing turns out to be metaphysically reducible to anything else!
Acknowledgement: I owe the idea of 'strong possibilities' exploited here to Christian Nimtz.
And no, of course I don't believe a word of that. But I do find the position more attractive than the far more common view that there are strong necessities: that some things, though clearly conceivable, just happen to be impossible. And I would like to know what defenders of strong necessities would say against my account. They can hardly appeal to constitutive links between the modal and the conceptual/rational/epistemic.