Existence

I have been a bit curious about the notion of the use of “possible worlds” as a way of communicating whether a proposition is either empirically or rationally true. When a proposition is said to be necessarily true (e.g. Circles are round) it is said that there is no possible world in which circles exist and are not round; circularity and roundness are inherently tied together by their nature. However, it seems upon further reflection that the use of the quantifier “all possible worlds” could only suggest all possible worlds in which ideas or abstract objects like circles and the concept of roundness are like our actual world; or, in a related sense, where there exist beings whose deductive logical “systems” are like ours. If this is true is it possible that our invoking the use of the phrase “all possible worlds” should really indicate “all possible worlds like our own”? While it may be nonsensical to state that there are square circles in some possible world, does it follow that this cannot be true in all possible worlds. Is it logically possible that that which we cannot conceive could be nonetheless true in some other possible world?

Comments

It seem that some issues are getting blurred here. You suggest that when we say there are no possible worlds with round squares, we're implicitly talking only about worlds where the concepts of 'round' and 'square' are as they are in our world, or -- perhaps you see this as the same thing -- only in worlds with beings who think the way we do. But that makes it sound as though it's a matter of how people talk or think. The real point is this: we use the words 'round' and 'square' to pick out certain concepts. People who don't speak English might use different words. Some creatures may not have these concepts at all. And there could be square things or round things -- things that fit the concept we're getting at -- even if there were no thinkers at all. But to revert to world-talk, there aren't any worlds where any round things are also square things --even though there might be worlds where beings use the words 'round' and 'square' to pick out concepts different from ours that don't exclude one another.

In fact worlds aren't really the issue here. Philosophers differ sharply in how they think about possible worlds. Some have a robustly realist understanding of them, and others see world-talk as a convenient fiction. But they all agree: given what we mean by 'round' and by 'square' -- given, if you prefer, the concepts we pick out with these words -- it's not possible for anything to be both round and square. Put another way: the world might have been different in an infinity of respects. It might have had golden mountains; it might have had creatures made of silicon; it might have had very different physical laws. But it couldn't have had round squares.

Of course someone could use the words 'round' and 'square' differently, and depending on what they meant, the things they use the sound "round" to describe might overlap with the thing falling under their use of the sound "square." But given what we mean, round squares are impossible. And since they are impossible, there aren't any possible worlds with round squares -- whether or not those worlds include beings with different concepts than ours, or beings who have any concepts at all.

Now you might ask how we know this truth about roundness and squareness. It's a perfectly good question whose answer is still controversial. And it may be that some of our opinions about such matter are flat-out wrong; we may think some things are possible that really aren't. For the advocate of possible worlds, this means that, contrary to our opinion, there are no worlds where such things are true. Likewise we may think some thing are impossible that really are possible. But if they are possible, it's not because some nearby set of concepts fit together in certain ways, nor because some other beings might talk or think differently than we do. It's because, for example, X and Y -- what we mean by 'X' and 'Y' -- don't actually exclude one another. Like so many things, it's not really about us.

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