Necessary existents

In a recent post Bill Vallicella mentions a paper Necessary Existents by Timothy Williamson, which I have taken a look  at.   Williamson discusses the following argument.
(1) Necessarily, if I do not exist then the proposition that I do not exist is true.
(2) Necessarily, if the proposition that I do not exist is true then the proposition that I do not exist exists. 
(3) Necessarily, if the proposition that I do not exist exists then I exist.
(4) Necessarily, if I do not exist then I exist. 
(5) Necessarily, I exist.
Williamson's penultimate paragraph runs thus:
There are few knockdown arguments in philosophy, and the foregoing argument for necessary existence is not one of them. Someone determined to reject its conclusion at all costs can surely reject one of its premises, perhaps by abjuring the very idea of a proposition. The argument is directed to those with more open minds, who are willing to rethink the status of its superficially implausible conclusion in the light of the argument itself and of the proposed metaphysics. The cost of rejecting a premise may be higher than the cost of accepting the conclusion.
But surely we can knock the argument down with a simple counter-example.  Let the possible worlds be rows of six balls randomly chosen from a bag containing three white balls and three black balls.  Let 'I' denote a run of three adjacent black balls.  Then there are possible worlds like WBWBWB in which I doesn't exist and hence I cannot be a necessary being. In fact, I exists in just four of the twenty possible worlds.

What is wrong with this?


  1. This is a late reply, but better late than never?

    I think Williamson might respond by saying 'I' (as three adjacent black balls) still exists, it just doesn't exist concretely. What it exists as is a possible I: something that -could have been- I, if the worlds had aligned that way. In four of the twenty possible worlds, I exists concretely. In the other sixteen, I exists as a possibility.

    Similarly, in this world, unicorns don't exist concretely, but something exists such that it could have been a unicorn. That something just isn't concrete.
    Dinosaurs no longer exist concretely, but all dinosaurs still exist as beings which were dinosaurs.

    Then of course there is a big question as to what on earth it means for something to not exist concretely, but only exist as a 'could have been x'...

  2. Hello Anonymous, and thank you for the comment.

    Having now read Williamson's paper several more times I've begun to see just how radical he is. His idea seems to be that we can distribute the modal sentential operator 'possibly' into a sentence such as 'possibly, there is a unicorn' to arrive at 'there is a possible unicorn'. The 'possibly' turns into a predicate. Admittedly, we do use locutions like this, eg, 'andy murray is a possible Wimbledon champion', but not in Williamson's sense. Andy Murray is concrete but the possible unicorn isn't. And we do talk of 'possible worlds'. These are clearly (to me) abstractions. But does a possible world contain possible people? (distribution of 'possible' again). I think not.

    I'd be interested to hear if Williamson has taken this idea any further. If it were worked up formally much as Zalta's stuff on abstract objects (which W mentions and I find congenial) and it really does simplify modal logic, then I'd have to reconsider.

    But I have trouble with modality. BV describes me as 'modally blind'. My own view is that what I take to be the mainstream conception is mistaken. It is metaphysical. W wants to make it even more metaphysical. I see modality as logical and grounded in our ability to make valid inferences. The mainstream grounds validity on modality. We trivially accept statements like 'I might have been brown eyed.' Suppose the genetics of human eye colour were such that blue-eyed parents cannot produce a brown-eyed child, and we have a well worked out theory as to why this is so. Then, defining 'I' as 'son of A and J', and knowing that both A and J are blue-eyed, we infer that I *must* not be brown-eyed. In the absence of such a genetic theory 'I might have been brown-eyed' comes to mean 'there is no proof that I'm not brown-eyed'. But I've not come across anything like this in the literature. Maybe it's obviously wrong!