I've never understood the appeal of this so-called
paradox; unlike other real paradoxes it doesn't appear to say anything
logically interesting about concepts. It's obviously false and that's that. (At the moment I'm talking about the colour aspect of it, as discussed above, not the
induction aspect.)
The Martians are saying something highly nontrivial about a physical property, which the Earthlings aren't. They're saying on such-and-such a date (it's not important -- say it's the Great Occultation of Canopus, some cosmic event we can both see and which is significant to both planets) -- on some future date, emeralds will change colour.
We say they won't change colour. They say they will change colour. But nothing ever changes colour on a specified date. There is absolutely zero physical evidence, or theoretical support, or inductive probability, for the Martians' strong claim that emeralds will change colour. And that's the end of the story. It's simple.
Saying they'll change from green to blue on 2100-01-01 is like saying all mongooses spontaneously turned magenta for one day only on the 17th of August, 278 BCE. No, we haven't got photographic evidence that proves it didn't happen, but we know perfectly well it didn't happen, and it doesn't count as any kind of interesting question or paradox.
Questions from the audience. You. The back. Blue sports coat. I'm sorry? Ah, yes. Colour names. Yes, if I may repeat the question for the rest of the audience. Why do they use the same colour name when the emerald changes colour? And do languages that have the same word for "green" and "blue" have anything to do with it? That's a good question, and it brings up one or two issues which, while not actually bearing on the pseudo-paradox, might confuse some people if they're not clear on the difference between a colour and the name of a colour.
Let's take three well-known languages, English, Russian, and Japanese, and three well-known gemstones, the emerald, the sapphire, and the aquamarine. I assume you all know a sapphire is a fairly deep blue, and an aquamarine is a delicate watery blue -- or rather, what we call in English, "blue".
In English we have two basic colour words to cover these. An emerald is called green and an aquamarine and a sapphire are both blue. In Japanese a single colour-name covers all three colours (note: one name, three different colours). An emerald, an aquamarine, and a sapphire are all aoi. In Russian there is no word meaning "blue": they have separate basic colour terms for light blue and dark blue. So an emerald is zelyonyy, an aquamarine is goluboy, and a sapphire is siniy.
Eye tests and psychological tests and comparison of cultures proves that Russian, Japanese, and English people (a) have the same visual acuity and perceptions, and (b) hold the same theories about the physical nature of objects. None of us believe that rubies spontaneously grow wings on Thursdays, or that sapphires suddenly changed from being amethyst-coloured to being sapphire-coloured in 4004 BCE.
But we are asked to believe that Martians do believe some such nonsense. That on 2100-01-01 Martians claim emeralds will change colour from colour X to colour Y.
A Japanese interpreter of this Martian nonsense would say the Martian claim is about a change of colour from one shade of aoi to a different one. An English interpreter agrees, but says in English one shade of green to one shade of blue. A Russian interpreter agrees, and says in Russian one shade of green to one shade of... either siniy or goluboy, it's not quite clear from our garbled translation of the Martian. A Martian interpreter agrees, and says the emeralds will change colour from one shade of grue to another.
The English, Russian, Martian, and Japanese interpreters all agree that the claimed physical property of Martian physics involves a shift in spectrograph readings from a peak of n1 nm to a peak of n2 nm. We are all agreed in the peculiar change that will take place, according to Martian metaphysics, on the special date.
The only area of disagreement is the trivial, unparadoxical one of which basic colour term different languages would use to name the two different colours we all agree are different. And why shouldn't the Martians have different languages? In North-Martian they say the stones will change from park grue to dale grue. In South Martian they say they'll change from groi to groluboi. But all Martians claim some bizarre physical change will happen at the Great Occultation.
In English we say aquamarines are blue and we say sapphires are blue. We do not claim aquamarines and sapphires are the same colour. We do not claim that aquamarines could change to being sapphire-coloured.
Problem of induction be blowed. We all know properties don't change like this. We assign fixed attributes (like "green", "aoi", "siniy") on the basis of observed consistencies. We do NOT name attributes according to their behaviour in the forty-third century. Our naming embodies our observations; it embodies the consistent continuity we have observed over the times the names have been in use. It does not contain inductive claims across time; but we do as a matter of empirical fact know that such physical attributes do not change across time. As do the Japanese. As do the Martians.
n6's discussion below adds a number of interesting points. However, I don't think the fact that a question leads to a lot of
discussion necessarily makes it a good question. We all know
arguments tend to gravitate to things we don't want to argue about. We can define peculiar
predicates abundantly, but few of them will be
interesting, even to the
logician, even if they have logically strange
properties.
Define something as grylva if either it's green or it was licked by the Queen of Roumania. All green things are unproblematically identifiable as grylva. Very few other things are. We can wander round the old royal palace in Bucharest staring intently at escritoires, gilded mirrors, and cake-mixture stirring spoons, wishing the walls could talk. All the available evidence for grylvaness is just the evidence for greenness, though we suspect they're not the same thing.
We could examine this more closely, but I don't think that's a very illuminating or paradoxical predicate, even though it had the honour of being invented by me.
Likewise, I don't think Goodman's idea adds any further problem to induction. Yes, evidence for being green is evidence for being grue, but I don't think we need to care.