My name is Sinan Dogramaci and I teach philosophy at the University of Texas at
Austin and today I want to talk to you about the Puzzle of Grue. The Puzzle of
Grue really burst the bubble for philosophers like Carnap and Hempel who
had dreams of confirmation theory or inductive logic as a formal theory in
the way deductive logic was developed. With deductive logic
we've succeeded in identifying many patterns that make for good deductive
arguments where these patterns concerned just the forms or the logical syntax of
the premises and conclusions in the arguments.
Anything beyond form — in particular, the subject matter under discussion —
makes no difference to the quality of an argument as a deductive argument. The
premises that "All X's are Y" and "This is an X" deductively entail the
conclusion that "This is a Y" no matter what particular X's and Y's we're talking
about —
flamingos, bongos, bellybuttons, whatever.
Unfortunately, the philosopher Nelson Goodman gave us a puzzle that pretty
convincingly shows that whether an argument is a good
inductive argument cannot similarly just be a matter of form. Goodman showed that
we can cook up two arguments that share the very same form, but one is
intuitively an excellent argument in support of its conclusion while the
other is no good at all.
For the first argument, the good one,
we have this: Premise: All of the numerous emeralds observed in the past have been
green. Conclusion: all emeralds — those observed and those yet to be observed —
are green.
In order to see what the second argument is, the bad one with the same form, we
need to first introduce a new term. The term is "grue", and to define it,
we say that
a thing is grue if either it has been observed by now and it is green or it has
not been observed yet and it is blue.
So this new term we've introduced has what we call a "disjunctive definition" - an
either/or definition. The second argument we want to consider, then, is this. Premise:
all the numerous emeralds observed in the past have been grue. Conclusion: all
emeralds — those observed and those yet to be observed — are grue.
This is not a good argument. Its premise is perfectly correct — all observed
emeralds have been green and thus by definition they are also grue — but that
premise does not lend any support to the conclusion. The conclusion is not
probable at all! For the conclusion implies that the next new emerald to be
observed will be grue, and that means it will be blue, which is not likely at all.
The real puzzle here is that we have two arguments,
apparently with the exact same form. The only difference is the substitution of
the two simple predicates green and grue.
So the moral seems to be that form alone does not settle what makes a conclusion
probable.
Now, there's an objection that might come to mind here and which we should address
Is "grue", as I said a moment ago,
really as simple a term as "green"?
Perhaps its complexity makes the second argument actually have a different form.
After all, "grue" is a defined term, and we said its definition is disjunctive, so
maybe the term "grue" is not as simple as the perfectly simple term "green", right?
Well, that's one way to see things, but as Goodman was quick to point out there is
another perspective.
It might equally well be thought that "grue" is the simple one and "green"
is the more complex term. How could that be?
Well, to see how, consider one more new term: bleen.
Let's say an object is bleen if it is observed by now and blue or else, if
unobserved, green
Well, given that understanding of bleen, we now have a way of giving "green" its
own definition: an object is green
if it's grue and has been observed or if it's as yet unobserved and bleen.
That's really a pretty good definition of green.
Let's think it over. Emeralds, which we know are all green, meet the definition.
All the observed emeralds which are green are also grue and observed. And the
unobserved ones, which we also expect to be green, are bleen, since unobserved
bleen emeralds are green.
What does this mean? It makes it hard to maintain that "green" is really the
simpler term and "grue" the more complex one.
Maybe, in the end, "grue" is more complex, but it's difficult to say why that's
objectively so — and as long as we can't distinguish "green" and "grue" in their
complexity or otherwise in their logical form, then we can't distinguish, just by
appealing to form, arguments that do and don't make their conclusions probable.
So for this reason, among others, the development of inductive logic
— confirmation theory —
looks like it's not going to be easy.