People, by which I mean philosophers, often say that there is a difference between logical possibility and metaphysical possibility. Maybe there is, but I want to poke at one commonly given example of so-called non-logical metaphysical possibility a bit.

This example runs as follows: a thing can’t be both completely red and completely green, but this is not a matter of logic, because CR(x) and CG(x) are different predicates, and so in terms of ‘sheer consistency’ or whatever there’s no contradiction in holding (CR(x) & CG(x)), but nonetheless ‘if you know what they mean’ you’ll see that this is impossible. (This is sometimes referred to as ‘the color-exclusion problem’.)

Not sure I’m buying the setup today. Here’s another argument for comparison: a thing can’t be both a unicorn and a bicorn, but this isn’t a matter of logic, because U(x) and B(x) are different predicates, and so in terms of ‘sheer consistency’ or whatever there’s no contradiction in holding (U(x) & B(x)), but nonetheless ‘if you know what they mean’ you’ll see that this is impossible.

We would object to that argument presumably because we can explicate one-hornedness and two-hornedness in more exact terms, and once we do we see that it’s in fact sheerly inconsistent to hold that the same entity has exactly one horn and exactly two horns – this is a contradiction and hence ‘logically impossible’. What was happening in the original argument is that we were ignoring what the predicates meant – underinterpreting the signs, if you like.

This morning I am somewhat of the opinion that exactly the same thing is going on in the color-exclusion problem.

Can something be red and green at the same time? Of course; the Italian flag will do as an example, with white thrown in for good measure. Can it be completely red and completely green at the same time? No – but what are we saying when we say this?

It strikes me that to say that x is completely red is to say that x is red and that there is not a color other than red such that x has that color, or something like that. In which case the assertion that x is completely red and that x is completely green, or for that matter even completely red and also green, contradict one another – but in entirely the ordinary way. It’s inconsistent to say that a thing has no color but red, and also that it has the color green, in just the way that it’s inconsistent to say that a thing has exactly one horn and exactly two horns, or that an object has both exactly zero vertices and exactly four.

So on this way of thinking there’s no special ‘metaphysical necessity’ in the so-called ‘color exclusion problem.’ To say that something is completely such-and-such a color just is to say that it doesn’t have any other colors alongside the color it completely is. If it’s red *all over* there’s no space left into which to tuck another color; but we said that already when we said “all over.”

As a counter-argument: imagine a four-predicate universe, where the four predicates are round, square, entirely-green, entirely-red. We can’t have (round & not round) by logic, but we can have (round & entirely green) or (square and entirely red). Why can’t we have (round & square) or (entirely-green & entirely-red)? We can’t, but it’s not a logical contradiction, so this isn’t a matter of logic, but something else.

If you insist on representing it like this, there’s a sense in which you’re right, but it’s peculiar to insist on representing it like this. For example, here is an argument that all inferences (except perhaps “a, therefore a”) are invalid. The premises and the conclusion are different propositions. Therefore, the premises should be symbolized with different letters – p, q, r, and so on – and the conclusion with c. But inferring from one or an arbitrarily large set of propositions to another proposition is invalid. So all propositional inferences are invalid.

You might object to this that the inference from “George W. Bush was a U. S. President and Barack H. Obama is a U. S. President” to “Barack H. Obama is a U. S. President” is not an inference from some arbitary p to some arbitrary q, but rather from a compound proposition (p & q) to p alone, which inference would be valid. And you would be right; but you would only be right because you understand the words you are speaking and represent them in accordance with that understanding. *Qua* uninterpreted signs, there is no reason to think that representing this as inferring q from p&q is any better than representing this as inferring q from p. (That’s just what ‘uninterpreted’ means.)

Similarly if we understand round and square as descriptors of shapes in the plane, we can understand them as, say, ‘uniformly symmetrical 0-vertex figure’ and ‘uniformly symmetrical 4-vertex figure,’ and likewise ‘entirely red’ and ‘entirely green’ as ‘red and no other color’ and ‘green and no other color’, and then we’re just dealing with good old fashioned contradiction here. A thing can’t have green and no other color and also have red, and it can’t have exactly four vertices and exactly zero. That’s just the usual stuff.

I feel that I must be missing something obvious here, since so many gifted thinkers accept this distinction, but just now I am not sure I understand it, even though I’ve given presentations on it in the classroom – “and very good ones they were, as I thought” – from time to time.

What is it?