Here’s a quick reflection I came up with today thanks to the conversation I’m having with Robert Oerter on his blog. Can one say anything true about a world in which nothing exists? By ‘nothing’ I don’t mean empty space, but rather I mean ‘not-anything’.
Some suggest that we can say the following: “not-anything exists”. We can express this as:
Where E stands for ‘exists’.
However, it would follow from this that we should also be able to say things like ‘a pink-striped blue tiger does not exist‘ is true at that world. A logically possible world is, it is supposed, a maximally consistent set of propositions. Therefore, since there is some maximally consistent set of propositions describing the world in which not-anything exists (namely all the propositions of the form (∀x)~Ex), there is such a logically possible world.
The problems with this are numerous I think. First, logically possible worlds are not maximally consistent sets of propositions. Patrick Grim has proved that there is no such thing as ‘the set of all true propositions’, and this would mean that, if logically possible worlds were maximally consistent sets of propositions, the actual world would not be a logically possible world. [I note that Ben Wallis, to whose blog I linked in my discussion with Robert Oerter, actually doesn’t seem to accept that Patrick Grim has demonstrated that the set of all true propositions doesn’t exist, but I think he has]. However, that’s absurd and confused. Therefore we have to find a different way to speak about logically possible worlds.
More importantly, however, I think a logically possible world has to be a model. When I communicate what I think the world could possibly be like to you, I am trying to share with you some model of the way the world could be which I have in mind, and which I want you to have in mind. However, there is no model of a world in which nothing exists, since there isn’t anything which can strictly be said about that world.
Somebody may object by saying – well, surely we can say something about such a world; after all, we can say that plenty of ‘simple predicates’ (all of them in fact) do not obtain. By a simple predicate here I mean something positive (eg. ‘exists‘ is a simple predicate, whereas ‘does not exist‘ is not a simple predicate since it is reducible to the first predicate and a negation connective). I don’t think people generally talk about ‘simple predicates’ in this way, but I don’t mind being a little idiosyncratic on my own blog. If some combination of propositions does not include at least one simple predicate applied to some predicate-bearer S (anything which can act legitimately grammatically as a predicate-bearer), then there is no model of the world which it suggests.
Moreover, there is no propositional content to saying that ‘nothing exists’, since it does not propose any model of the world (there is no cognitively meaningful ‘content’ expressed by the proposition or set of propositions). However, logically possible worlds just are models, so there is no logically possible world in which nothing exists, because there is no model of the world corresponding to ‘nothing exists’.
Moreover, and more damning, we have to think about logically possible worlds as predicate bearers, or collections of predicate bearers. However, in a logically possible world where nothing (not-anything) exists, there are no predicate bearers, and that world is consequently not a predicate-bearer. This means that even negating a statement like “a pink-striped blue tiger exists” wouldn’t be ‘true’ (or ‘false’) because it would literally be unpredicable.
Ok, let’s try to summarize these points:
- There are no simple predicates which are true of a logically possible world in which nothing exists, and therefore it doesn’t provide any model at all of the way the world could be which is intelligible.
- Logically possible worlds are consistent models which we have in mind, at least potentially, and which we can share with others, but a ‘logically possible world in which nothing exists’ is not a model (consistent or otherwise), and therefore we cannot even potentially have it in mind.
- There is no propositional content, which is to say cognitively meaningful content, involved in the claim that not-anything exists. This is just to reiterate that there is no model of the world corresponding to, or communicated by, the combination of words ‘nothing exists’.
- Logically possible worlds are predicate bearers, or collections of predicate bearers, but a logically possible world in which nothing exists is not a predicate bearer or a collection of predicate bearers.
- From the previous point: no proposition would be true in/at a logically possible world in which nothing existed because nothing would be predicable of that world (and here I use ‘nothing’ to be ‘not anything’ – in other words ‘nothing’ is not a predicate but a term of universal negation).
I think that should establish pretty clearly why there is no logically possible world in which nothing exists.