Ever heard of the color grue? According to some, you see it whenever you stare at an emerald. Think about it as you walk across the beautiful bleen grass.
Henry Nelson Goodman enjoyed the best things in life - good friends, hard work, and making people question their reality. He worked with the concept of induction. Induction is the idea that we can prove, via our experience, that what holds true in some cases will hold true in all cases. This idea won't always hold up in terms of rigorous proof, but it serves us very well throughout our life. It's the reason we learn as children that we shouldn't touch the burner on the stove. It's the reason why, when we jump up on a trampoline, we fully expect to come back down. There are many cases in which it's safe to generalize.
There are also many cases in which induction trips us up. Our experience wasn't as universal as we assumed it was. There were complicating factors of which we were unaware. We grouped together cases that didn't belong in the same category and excluded cases that did. There's a reason why scientists are encouraged to question everything as thoroughly as possible.
Which is how we come to the little matter of Goodman's Paradox and its new color. Emeralds are currently green. Let us say there is the possibility that at some point in time, maybe the year 3000, or just a year from today, all the emeralds, everywhere, will suddenly turn blue. That is a property of emeralds.
What's grue? Grue is defined, for our purposes, as "the property of being green before November 22, 2014, and blue afterwards." So now we can say that all emeralds are grue. Not only is it a challenge to prove this idea untrue, but every green emerald we see between now and a few days before Thanksgiving in 2014, provides more evidence for the "grue theory."
The paradox comes in when you use inductive reasoning for the grue idea. Do we all know that emeralds are green? We do. We've seen them. We've heard them described. Yes, we haven't seen every single one, but we've seen enough that we can generalize. But the theory of emeralds being grue is just as valid, given the definition of grue and the evidence we've gathered, as the theory of emeralds being green. Inductive generalization, drawing conclusions about all members of a group from a few members of that group, shows us that emeralds are grue.
Then again, inductive prediction leads us to believe that grue doesn't exist. We don't have any record or memory of gemstones switching color, and so we assume, through inductive prediction, that they never will. So induction leads us to believe that no emeralds are grue. (If you want to get really complicated, the gems we've seen are but a small group of the total gems in the universe, so even our experience of gem stones not changing color can be a matter of inductive generalization.)
So what do you think? Are emeralds grue? Are they green? Do you care what they are as long as someone delivers a large untraceable shipment of them to your door in a steel suitcase and you'll fence them and split the profits with an internet writer? Does Monday work for you?
Top Image: Rob Lavinsky, iRocks.com