What is Goodman trying to do? The New Riddle of Induction

It is really easy to misunderstand Goodman’s article on the new riddle of induction. So, let me try to say a little something about (a) what he is attempting to show, and (b) what he is not attempting to show. 

First, Goodman is trying to show that there a very common idea is false. What is this common idea? That there is a logic of induction. That is, that just as there is a logic of deduction, there is a logic of induction.

What does that mean?

If it is raining, then it is wet

It is raining

Hence, it is wet

If cats are demons, then their father is Bob

Cats are demons

Hence, their father is Bob

Notice that both arguments above have the exact same form. We can express that form as follows:

If p, then q

p

Hence, q

Any argument, no matter the content—no matter what the ps and qs get replaced with—that has the above form is valid. That is, any argument in the above form is such that if the premises are true, then the conclusion must be true as well. Deductive arguments are truth-preserving. If the argument is valid (has a valid form –e.g. the form above is valid), and the premises are true, then truth is preserved in the conclusion. With deductively valid arguments you cannot go from truth in the premises to falsity in the conclusion. The cat argument above shows this nicely. Note that while both premises are actually false (as far as we know J), IF they were true, then the conclusion would be true. Deductive reasoning follows a precise logic that can be studied and applied quite nicely. 

What about inductive logic? 

Well, it sure seems like induction or inductive arguments have a similar logic to them. 

100,000 days ago the sun came up

999,999 days ago the sun came up

999,998 days ago the sun came up

.

.

.

Yesterday, the sun came up

Today, the sun came up

Hence, tomorrow the sun will come up

Another Example

Electron 1 is negatively charged

Electron 2 is negatively charged

.

.

.

Electron 10000000000 is negatively charged

Hence, the next electron to be observed will be negatively charged

Or 

Hence, all electrons are negatively charged. 

Both of the above inductive argument sure looks like they too follow a pattern. If enough evidence is gathered (data) about electron charge or the motion of the earth or whatever, then we are justified in concluding something about the next electron or all electrons or the next day or whatever. 

But, this is precisely what Goodman is challenging in the paper. While deduction has a sound and complete logic, induction does not and never will. We cannot formalize the rules of inductive reasoning because there are no rules to formalize. 

Let me say that a bit differently. Goodman’s argument shows, assuming it works for the moment, that no matter how much evidence you gather for some conclusion of an inductive argument, you can always, without any trickery or anything like that, construct an argument with the exact same form and the exact same evidence that leads to a conclusion that contradicts the conclusion of the first one.  

In other words, say we have a really strong inductive argument for the conclusion that the next electron to be observed is negatively charged (we have an incredible amount of evidence for that). If Goodman is right, then it is quite easy to construct an inductive using all of the same evidence for the conclusion that the next electron to be observed is positively charged. 

Let’s look at the details really quickly:

We have excellent evidence that the next emerald to be discovered is green. What is that evidence? Well, it looks like this

Emerald Argument 1

Emerald1 is green

Emerald2 is green

.

.

.

Emerald10000000 is green

Hence, the next emerald to be discovered will be green

Goodman now constructs a new predicate (science does this all the time—quarks, bosons, genes, etc were recently introduced into the scientific vocabulary to refer to various objects). 

Grue definition: x is grue if, and only if, x is green and is observed before now or x is blue and is not observed before now

Now notice what happens to the above Emerald Argument. If Emerald1 is green, then it is grue (because Emerald1 is green and was observed before now—it’s part of our evidence remember). Same for Emerald1, and all the way through to Emerald10000000. So we can construct the following argument without changing the evidence we have at all:

Emerald Argument 2

Emerald1 is grue

Emerald2 is grue

.

.

.

Emerald10000000 is grue

Hence, the next emerald to be discovered will be grue

In other words, if the first argument is a good one—it sure as heck looks inductively strong—then the second argument is just as good. But the first argument concludes, naturally enough, with ‘the next emerald to be discovered will be green’ and the second argument concludes with ‘the next emerald to be discovered will be grue’ which implies that the next emerald to be discovered will be blue.

So, on the basis of the exact same evidence, by using induction, we are justified to conclude that the next emerald to be discovered will be both green and it will be blue (or put more strongly, the next emerald to be discovered will be both green and non-green). Yikes! What is happening?

Ok, Goodman is not saying that the next emerald might suddenly change colors and magically become blue. His point, remember, is that on the basis of the exact same evidence, using the exact same form of reasoning, it is perfectly valid to conclude that the next emerald is green and it is perfectly valid to conclude that the next emerald is blue (non-green). 

We use the predicate ‘…is green.’ But we could have used the predicate ‘…grue.’ What’s stopping us? If not, why not?  According to Goodman, the only difference between the predicates is that one is familiar and the other is not. But that is neither scientifically nor logically relevant at all (if it were then both science and logic are dead, since they both introduce new ideas, concepts, predicates all the time). 

What should we say in response?