I often hear talk of possible worlds and am told that this is a way of thinking about necessity and contingency. I do not know what necessity and contingency are, let me be honest. And thinking about possible worlds does not help me. But comparing talk of necessary and contingent truths to talk of hoity and toity truths has helped me.

I recently read Toity Worlds by Prof. Boule Sheet. It's a very important work, I think.

Sheet argues that all truths can be sorted into two categories: hoity truths and toity truths. And what he says about them seems to mirror almost perfectly those other two categories that some like to sort truths into - the necessary and the contingent. But the beauty of hoity truths and toity truths is that they give us a simulation, so to speak, of the necessary and the contingent. I will run that simulation now in the hope that it will tell us something about the confused nature of what some people have been saying about contingency and necessity.

For instance, when asked to define what hoity means, Sheet tells us that a hoity truth is not a toity truth. And he tells us as well that a toity truth is not a hoity truth. Well, that is also true of the necessary and the contingent. For if a truth is necessary, then it is not contingent. And if a truth is contingent, then it is not necessary.

So, if a truth is hoity, it is not toity. And if a truth is toity, it is not hoity. Clear?

Sheet also then introduces us to toity worlds to try and give us a handle on matters. Thinking of matters in terms of toity worlds is just supposed to help us grasp the concept, though I have to admit that it is hard to see how this could work for those of us - such as myself - who are starting out unclear on the matter, for surely unless we already understand what toity means, the notion of a toity world is going to be one we are not going to understand, as it is just 'world' with the word 'toity' appended to it, a word we do not yet understand aside from it being 'not hoity'. The whole exercise looks a little suspicious from the get go and likely to appeal to those empty kettles who have nothing to say but like to find a way to say it anyway.

But anyway, let's go with it. I mean, Professor Boule Sheet is very respected, at least in my mind, so we should at least make some effort to understand what he may be going on about.

So, when it comes to toity truths, a toity truth is a proposition that is true in at least one toity world. That is, Sheet assures us, just another way of saying that a proposition is toity. (Not really helpful, for it is like saying that another way of saying that something is bread, is to say that it is made of bread).

But a hoity truth is, well, a proposition that is true in all toity worlds. Now that's a little odd, isn't it? If a proposition is true in all toity worlds, why is that proposition not just, well, toity? What was the point in introducing us to toity worlds if hoity truths are inhabiting them? It's confusing. Is to me.

Ah, but Sheet says that the actual world is also a toity world. For any truth that is actually true, says Sheet, also a toity truth. So any true proposition - whether hoity or toity - is true in a toity world of some sort. It's just that the ones he calls hoity are true in all of the toity worlds, which includes the actual world.

But that has really removed none of the confusion, at least not in my case. We want to know what being toity involves. We were introduced to the notion of a toity world precisely in order to do that. And then we are told that toity truths are true in some of these toity worlds. But then we are told that hoity truths are true in all of them. Well how, then, are hoity truths not just a species of toity truth? It seems that if a toity truth is true in enough toity worlds, then it somehow becomes a hoity truth. How does that work, given hoity truths are supposed to be the very opposite of toity truths?

Ah, well Sheet says that this is just the definition of a hoity truth: a hoity truth is a truth that is true in all toity worlds. Well, that's naughty. We were told that hoity truths are, by definition, 'not' toity truths. That is, that they are the opposite of them. But then we are told that the definition of a hoity truth is that it is a truth in all toity worlds. But that makes being hoity not the opposite of toity, but a kind of toity truth. Again, that's to say white is the opposite of black, but that black is actually a lot of white.

Here's what Sheet should say to avoid being guilty of substituting one definition of hoity for a different one. He should say that though hoity truths will be true in all toity worlds, it does not follow that a truth that is true in all toity worlds is thereby hoity. Being hoity entails being true in all toity worlds, but being true in all toity worlds does not entail being hoity. If Sheet said that, then though we'd still be no wiser about what hoityness is, we'd at least not be being conned into accepting a definition very different to the one we started with.

All of that, it seems to me, could be said just as truly of necessary and possible truths, where necessary truths are the hoity ones and possible truths are the toity ones. Necessary truths are the opposite of contingent truths. But one must not then define necessary truths as a species of contingent truth, which is what one would be doing if one made the very notion of a necessary truth identical to the notion of a truth that is true in all possible worlds. We can accept, perhaps, that a necessary truth will indeed by true in all possible worlds (though we will want an explanation of course). But we should not accept that as the very definition of a necessary truth. For then one is getting necessity out of contingency and not preserving the fact it is supposed to be the exact opposite of contingency. Seems to me, then, that those who think the very definition of a necessary truth is that it is a truth that is true in all possible worlds have made a serious blunder: that is not the definition of the term, it is, at best, a feature of necessary truths. And nothing stops a truth from being true in all possible worlds and also being contingent. To think otherwise is to have thought you can make some white paint black by mixing it with all the other white paint there is.